https://zerobit-site-g094.onrender.com/research/ How to read a record, a backtest and a claim, from a systematic crypto desk. en https://zerobit-site-g094.onrender.com/research/what-is-drawdown-in-trading/ https://zerobit-site-g094.onrender.com/research/what-is-drawdown-in-trading/ Sat, 07 Nov 2026 00:00:00 +0000 Drawdown is the fall from a peak to the trough that follows. It tells you what a strategy would have asked you to sit through, which matters more than the return it would have paid. https://zerobit-site-g094.onrender.com/research/what-a-labeled-record-looks-like/ https://zerobit-site-g094.onrender.com/research/what-a-labeled-record-looks-like/ Sat, 07 Nov 2026 00:00:00 +0000 Three kinds of numbers exist in trading research, and almost every record you will ever see blends them. Here is what it looks like when they are kept apart, figure by figure. https://zerobit-site-g094.onrender.com/research/the-six-sleeve-portfolio/ https://zerobit-site-g094.onrender.com/research/the-six-sleeve-portfolio/ Sat, 07 Nov 2026 00:00:00 +0000 CopyOrders' method runs six independent sleeves on equal capital, each with its own regime filter, so that no single idea decides the record and standing aside is a position, not a failure. https://zerobit-site-g094.onrender.com/research/how-to-read-a-backtest/ https://zerobit-site-g094.onrender.com/research/how-to-read-a-backtest/ Sat, 07 Nov 2026 00:00:00 +0000 A backtest shows how a set of rules would have behaved in the past. Seven checks separate one you can learn from, from one that was built to be shown to you. https://zerobit-site-g094.onrender.com/research/how-to-check-a-trading-creators-claims/ https://zerobit-site-g094.onrender.com/research/how-to-check-a-trading-creators-claims/ Sat, 07 Nov 2026 00:00:00 +0000 Most trading content is a screenshot and a story. Five questions turn either into something you can evaluate, and the creators worth following answer all five without being asked. https://zerobit-site-g094.onrender.com/research/does-copy-trading-work/ https://zerobit-site-g094.onrender.com/research/does-copy-trading-work/ Sat, 07 Nov 2026 00:00:00 +0000 Copy trading works mechanically and fails financially more often than it should, for three reasons that have nothing to do with the signals. Here is how to judge whether it is for you. https://zerobit-site-g094.onrender.com/research/backtest-vs-live-trading/ https://zerobit-site-g094.onrender.com/research/backtest-vs-live-trading/ Sat, 07 Nov 2026 00:00:00 +0000 A live record almost always underperforms the backtest it came from. The gap is not a scandal; it is five specific things, and a record that keeps the labels apart lets you measure it. https://zerobit-site-g094.onrender.com/research/which-quant-models-earn-their-keep/ https://zerobit-site-g094.onrender.com/research/which-quant-models-earn-their-keep/ Fri, 06 Nov 2026 00:00:00 +0000 Markov chains top this working list. GARCH and principal components sit just below. Autoencoders and Nelson-Siegel rank lower because they are easy to misuse. https://zerobit-site-g094.onrender.com/research/how-two-closed-candles-set-session-bias/ https://zerobit-site-g094.onrender.com/research/how-two-closed-candles-set-session-bias/ Fri, 06 Nov 2026 00:00:00 +0000 Harry Sharp's session bias, as told to the firm, uses two finished candles, a clean path, and a spring. The win rate he quotes belongs to his tracker, not an audit. https://zerobit-site-g094.onrender.com/research/how-to-find-a-daily-trading-bias/ https://zerobit-site-g094.onrender.com/research/how-to-find-a-daily-trading-bias/ Fri, 06 Nov 2026 00:00:00 +0000 A daily trading bias is the direction you allow for one session, read from the last daily candle and the last closed four-hour candle before you look for a zone. https://zerobit-site-g094.onrender.com/research/why-a-quoted-market-return-is-only-a-model/ https://zerobit-site-g094.onrender.com/research/why-a-quoted-market-return-is-only-a-model/ Tue, 03 Nov 2026 00:00:00 +0000 A cited 10 percent stock return, or 8 percent, is history projected forward. It is not a fact about the next 20 years, and it may skip inflation. https://zerobit-site-g094.onrender.com/research/what-a-trader-panel-required-before-funding/ https://zerobit-site-g094.onrender.com/research/what-a-trader-panel-required-before-funding/ Tue, 03 Nov 2026 00:00:00 +0000 Fabio and Andrea, on an the firm pitch day, kept personal money back until a sample could be checked. The offers that survived were smaller prop accounts. https://zerobit-site-g094.onrender.com/research/how-prop-firms-choose-traders/ https://zerobit-site-g094.onrender.com/research/how-prop-firms-choose-traders/ Tue, 03 Nov 2026 00:00:00 +0000 A prop firm funds a trader after the sample, the risk, and the payoff can be checked. A described method with none of those three is not treated as an edge. https://zerobit-site-g094.onrender.com/research/why-expected-value-is-not-enough-to-trade/ https://zerobit-site-g094.onrender.com/research/why-expected-value-is-not-enough-to-trade/ Sun, 01 Nov 2026 00:00:00 +0000 An edge is a positive expected value, and it fails if one losing streak ends the account. Quants stumble when a backtest replaces live updating. https://zerobit-site-g094.onrender.com/research/scalping-versus-options-trading/ https://zerobit-site-g094.onrender.com/research/scalping-versus-options-trading/ Fri, 30 Oct 2026 00:00:00 +0000 Scalping and options trading can run on the same morning and still be different businesses: one hunts a short mechanical edge, the other reads options order flow. https://zerobit-site-g094.onrender.com/research/how-many-trades-before-a-win-rate-settles/ https://zerobit-site-g094.onrender.com/research/how-many-trades-before-a-win-rate-settles/ Fri, 30 Oct 2026 00:00:00 +0000 Gianluca Bruni says that ten trades can disguise a sixty percent win rate. He wants about a hundred before the rate means much. The session's dollars are not that test. https://zerobit-site-g094.onrender.com/research/a-capped-fund-beside-free-quant-education/ https://zerobit-site-g094.onrender.com/research/a-capped-fund-beside-free-quant-education/ Fri, 30 Oct 2026 00:00:00 +0000 This plan is a fund under general solicitation, capped at 100 investors, plus free lessons and career material. Partner interviews were only starting. https://zerobit-site-g094.onrender.com/research/how-random-variables-map-outcomes-to-numbers/ https://zerobit-site-g094.onrender.com/research/how-random-variables-map-outcomes-to-numbers/ Wed, 28 Oct 2026 00:00:00 +0000 A random variable turns each outcome into a number. Discrete laws use a mass function. Continuous laws use a density, and probability is an area. https://zerobit-site-g094.onrender.com/research/what-is-an-ict-scalping-strategy/ https://zerobit-site-g094.onrender.com/research/what-is-an-ict-scalping-strategy/ Tue, 27 Oct 2026 00:00:00 +0000 An ICT scalp, in this account, is one of two Nasdaq models: a liquidity sweep that fails, or a second leg into a fair value gap after structure shifts. https://zerobit-site-g094.onrender.com/research/how-two-ict-nasdaq-scalps-set-risk/ https://zerobit-site-g094.onrender.com/research/how-two-ict-nasdaq-scalps-set-risk/ Tue, 27 Oct 2026 00:00:00 +0000 Candace Lao says that her Nasdaq payouts come from two ICT models, with a stated forty percent win rate that needs at least two to one. Those figures are hers and the host's, not an audit. https://zerobit-site-g094.onrender.com/research/how-hedge-funds-stack-orthogonal-bets/ https://zerobit-site-g094.onrender.com/research/how-hedge-funds-stack-orthogonal-bets/ Tue, 27 Oct 2026 00:00:00 +0000 Funds split teams so each return is meant to be uncorrelated with the market and with the other teams. One hedged mix showed a Sharpe near 1.9. https://zerobit-site-g094.onrender.com/research/what-ai-changes-about-mathematical-research/ https://zerobit-site-g094.onrender.com/research/what-ai-changes-about-mathematical-research/ Sun, 25 Oct 2026 00:00:00 +0000 A model that restates your theorem threatens credit, not curiosity. What remains is choosing a risk and iterating faster than a plan that never ships. https://zerobit-site-g094.onrender.com/research/how-to-study-quant-topics-with-a-language-model/ https://zerobit-site-g094.onrender.com/research/how-to-study-quant-topics-with-a-language-model/ Fri, 23 Oct 2026 00:00:00 +0000 Use a language model to map prerequisites, draft notes, and grade gaps. Do not advance with a partial score, and do not treat the model as a source that cannot be wrong. https://zerobit-site-g094.onrender.com/research/how-a-failed-reclaim-plans-the-open/ https://zerobit-site-g094.onrender.com/research/how-a-failed-reclaim-plans-the-open/ Fri, 23 Oct 2026 00:00:00 +0000 Chris Creamer says the open is planned as bullish, bearish, or rotational before the bell. A failed reclaim, not a wick, is what confirms the hold. The session's results are his tape, not an audit. https://zerobit-site-g094.onrender.com/research/failed-breakout-at-the-market-open/ https://zerobit-site-g094.onrender.com/research/failed-breakout-at-the-market-open/ Fri, 23 Oct 2026 00:00:00 +0000 A failed breakout at the open is a move that cannot hold the level it just took. The trade, when there is one, is the flip after that failure, not the first push. https://zerobit-site-g094.onrender.com/research/what-a-probability-model-is-for/ https://zerobit-site-g094.onrender.com/research/what-a-probability-model-is-for/ Wed, 21 Oct 2026 00:00:00 +0000 A probability model lists outcomes and weights so you can compute an expectation. It does not name the next flip, and it misses any outcome you left out. https://zerobit-site-g094.onrender.com/research/order-flow-effort-versus-result/ https://zerobit-site-g094.onrender.com/research/order-flow-effort-versus-result/ Tue, 20 Oct 2026 00:00:00 +0000 Effort versus result in order flow asks whether the trading that showed up actually moved price. A lot of effort and little result is a failed auction, not a reason to join it. https://zerobit-site-g094.onrender.com/research/how-fama-macbeth-tests-a-return-factor/ https://zerobit-site-g094.onrender.com/research/how-fama-macbeth-tests-a-return-factor/ Tue, 20 Oct 2026 00:00:00 +0000 Fama-MacBeth regresses next month's returns across stocks, then averages those monthly slopes. In one beta test the slopes were insignificant. https://zerobit-site-g094.onrender.com/research/how-effort-and-result-filter-gold/ https://zerobit-site-g094.onrender.com/research/how-effort-and-result-filter-gold/ Tue, 20 Oct 2026 00:00:00 +0000 Darius Kehlmann says that context, location, and confirmation share one weight on gold. A volume profile is effort and a TPO is time. The payout figures are the host's introduction, not an audit. https://zerobit-site-g094.onrender.com/research/what-a-same-day-funding-contest-tests/ https://zerobit-site-g094.onrender.com/research/what-a-same-day-funding-contest-tests/ Sat, 17 Oct 2026 00:00:00 +0000 The firm flew five traders to California to compete for five hundred thousand dollars. The host named Brandon after a timed pitch and a half hour. No published gain and loss backs that call. https://zerobit-site-g094.onrender.com/research/what-a-prop-firm-funding-contest-tests/ https://zerobit-site-g094.onrender.com/research/what-a-prop-firm-funding-contest-tests/ Sat, 17 Oct 2026 00:00:00 +0000 A funding contest in this session tests whether a trader can explain one setup and then mark a target and a stop on a one-minute chart, under a clock. https://zerobit-site-g094.onrender.com/research/why-the-first-million-takes-the-longest/ https://zerobit-site-g094.onrender.com/research/why-the-first-million-takes-the-longest/ Fri, 16 Oct 2026 00:00:00 +0000 A teacher saving under $1,000 a month needs about 27 years to reach $1 million at a 7.5 percent real assumption. Later years compound a larger base. https://zerobit-site-g094.onrender.com/research/why-prop-firm-challenges-resemble-casinos/ https://zerobit-site-g094.onrender.com/research/why-prop-firm-challenges-resemble-casinos/ Tue, 13 Oct 2026 00:00:00 +0000 A simulated challenge can collect a fee and never risk firm capital. One 50/50 sketch took $8.9 million in fees and netted about $2.72 million. https://zerobit-site-g094.onrender.com/research/how-a-low-win-rate-scalp-is-built/ https://zerobit-site-g094.onrender.com/research/how-a-low-win-rate-scalp-is-built/ Tue, 13 Oct 2026 00:00:00 +0000 Pietro Velasro says his World Cup results came from a method that wins about thirty-two to thirty-five percent of the time. The rate, the places, and the payoff rules are his account, not an audit. https://zerobit-site-g094.onrender.com/research/can-a-low-win-rate-strategy-work/ https://zerobit-site-g094.onrender.com/research/can-a-low-win-rate-strategy-work/ Tue, 13 Oct 2026 00:00:00 +0000 A low win rate can still be a workable strategy when the winners are larger than the losers and the losing streak fits inside the risk limit you actually have. https://zerobit-site-g094.onrender.com/research/value-area-trading-strategy/ https://zerobit-site-g094.onrender.com/research/value-area-trading-strategy/ Fri, 09 Oct 2026 00:00:00 +0000 Value area trading sells from one area of accepted price toward the next. This session refuses the open, refuses a chase, and only sells when value itself has shifted. https://zerobit-site-g094.onrender.com/research/probability-problems-from-means-to-ito/ https://zerobit-site-g094.onrender.com/research/probability-problems-from-means-to-ito/ Fri, 09 Oct 2026 00:00:00 +0000 On five log returns the mean, median, and mode can all equal 0.01. The same ladder ends at geometric Brownian motion and a rough-volatility question. https://zerobit-site-g094.onrender.com/research/which-math-courses-quants-use-daily/ https://zerobit-site-g094.onrender.com/research/which-math-courses-quants-use-daily/ Tue, 06 Oct 2026 00:00:00 +0000 Algebra, multivariable calculus, and linear algebra show up in daily quant work. Real analysis, abstract algebra, and school geometry almost never do. https://zerobit-site-g094.onrender.com/research/three-strategies-for-a-prop-challenge/ https://zerobit-site-g094.onrender.com/research/three-strategies-for-a-prop-challenge/ Tue, 06 Oct 2026 00:00:00 +0000 Three systematic ideas for one challenge: a break out of a noise band, a VWAP pullback armed by the opening range, and a single overnight trade aimed at three to one. https://zerobit-site-g094.onrender.com/research/why-classroom-statistics-break-on-prices/ https://zerobit-site-g094.onrender.com/research/why-classroom-statistics-break-on-prices/ Fri, 02 Oct 2026 00:00:00 +0000 Textbook estimates converge only if the distribution stays fixed. Live returns mix regimes, so the mean is noisy and the real choice is model risk. https://zerobit-site-g094.onrender.com/research/position-sizing-in-trading/ https://zerobit-site-g094.onrender.com/research/position-sizing-in-trading/ Fri, 02 Oct 2026 00:00:00 +0000 Once a tested edge exists, size is a fraction of the edge, not a feeling about the last candle. This account treats the risk model as the thing that carried the result. https://zerobit-site-g094.onrender.com/research/worked-examples-from-arithmetic-to-research/ https://zerobit-site-g094.onrender.com/research/worked-examples-from-arithmetic-to-research/ Tue, 29 Sep 2026 00:00:00 +0000 The same person can compute 37 plus 48 and also state an unsolved fluid equation. What changes is the object: a number, then a proof, then a question nobody has closed. https://zerobit-site-g094.onrender.com/research/what-a-prop-firm-live-session-shows/ https://zerobit-site-g094.onrender.com/research/what-a-prop-firm-live-session-shows/ Tue, 29 Sep 2026 00:00:00 +0000 A filmed prop session shows how four styles behave under one rule set and a clock. It is a contest, not a method you can copy from the result alone. https://zerobit-site-g094.onrender.com/research/what-a-dull-prop-session-did-to-plans/ https://zerobit-site-g094.onrender.com/research/what-a-dull-prop-session-did-to-plans/ Tue, 29 Sep 2026 00:00:00 +0000 The firm put four traders in one Dubai session under prop rules. Their dollar figures contradict each other. The only steady claim is that the beginner finished green and called it gambling. https://zerobit-site-g094.onrender.com/research/how-to-rebuild-after-a-project-is-destroyed/ https://zerobit-site-g094.onrender.com/research/how-to-rebuild-after-a-project-is-destroyed/ Fri, 25 Sep 2026 00:00:00 +0000 A collaborator with admin access can erase years of work in one act. Revoke that access, reseed what you still know, and keep the project small on purpose. https://zerobit-site-g094.onrender.com/research/how-to-grade-a-trading-edge/ https://zerobit-site-g094.onrender.com/research/how-to-grade-a-trading-edge/ Fri, 25 Sep 2026 00:00:00 +0000 An edge gets a grade only after it stays the same long enough to measure. The grade here is asymmetry: how much the winners pay against how much the losers cost. https://zerobit-site-g094.onrender.com/research/why-scalpers-exit-at-1-5-risk/ https://zerobit-site-g094.onrender.com/research/why-scalpers-exit-at-1-5-risk/ Wed, 23 Sep 2026 00:00:00 +0000 This scalp takes orders from one side of a range and delivers them to the other, then stops near 1.5 times the risk. Most of the lookalike candles in a day are skipped. https://zerobit-site-g094.onrender.com/research/how-market-neutral-portfolios-isolate-bets/ https://zerobit-site-g094.onrender.com/research/how-market-neutral-portfolios-isolate-bets/ Tue, 22 Sep 2026 00:00:00 +0000 A market-neutral hedge removes the shared market factor so one long-short bet can win or lose on its own. Beta drifts, so the hedge is reset. https://zerobit-site-g094.onrender.com/research/what-an-early-quant-offer-actually-paid/ https://zerobit-site-g094.onrender.com/research/what-an-early-quant-offer-actually-paid/ Fri, 18 Sep 2026 00:00:00 +0000 One junior quant offer paid a $156,000 salary plus a $24,000 target bonus, near $180,000 before tuition and signing money. The internship had been $50 an hour. https://zerobit-site-g094.onrender.com/research/hurst-exponent-in-trading/ https://zerobit-site-g094.onrender.com/research/hurst-exponent-in-trading/ Fri, 18 Sep 2026 00:00:00 +0000 Traders use a Hurst-style reading to tell a trending tape from a choppy one, then look for a small pullback and a break of the last few bars in the trend's direction. https://zerobit-site-g094.onrender.com/research/how-a-hurst-proxy-gates-a-break/ https://zerobit-site-g094.onrender.com/research/how-a-hurst-proxy-gates-a-break/ Fri, 18 Sep 2026 00:00:00 +0000 The firm reconstructs a funded trader's fifteen-minute rules: a Hurst proxy above fifty, slight anti-persistence, then a close through the prior five-bar high. The monthly figure is the host's, not an audit. https://zerobit-site-g094.onrender.com/research/what-deep-hedging-changes-about-delta/ https://zerobit-site-g094.onrender.com/research/what-deep-hedging-changes-about-delta/ Tue, 15 Sep 2026 00:00:00 +0000 Fair-price delta hedging targets zero average gain. Deep hedging learns a discrete rehedge from risk-adjusted results, and model risk stays. https://zerobit-site-g094.onrender.com/research/seasonality-trading-strategy/ https://zerobit-site-g094.onrender.com/research/seasonality-trading-strategy/ Tue, 15 Sep 2026 00:00:00 +0000 A seasonal trade is a calendar window that rose in most past years, entered at the open of the window and exited at the close, then checked on years the rules never saw. https://zerobit-site-g094.onrender.com/research/mnq-scalping-strategy/ https://zerobit-site-g094.onrender.com/research/mnq-scalping-strategy/ Fri, 11 Sep 2026 00:00:00 +0000 On micro Nasdaq, the long and the short in this record are different systems. The long needs a wick through a volatility band. The short is one candle and a clock. https://zerobit-site-g094.onrender.com/research/how-a-bid-ask-spread-captures-the-middle/ https://zerobit-site-g094.onrender.com/research/how-a-bid-ask-spread-captures-the-middle/ Fri, 11 Sep 2026 00:00:00 +0000 A market maker quotes a bid and an ask around a forecast. If the result lands between them, both bettors lose and the quote captures the spread. https://zerobit-site-g094.onrender.com/research/how-to-structure-a-quant-resume/ https://zerobit-site-g094.onrender.com/research/how-to-structure-a-quant-resume/ Tue, 08 Sep 2026 00:00:00 +0000 A quant resume rarely creates the interview. Once you are in the room, it should list only the projects, tools, and results you want the interviewer to ask about. https://zerobit-site-g094.onrender.com/research/when-a-sweep-still-needs-a-retest/ https://zerobit-site-g094.onrender.com/research/when-a-sweep-still-needs-a-retest/ Fri, 04 Sep 2026 00:00:00 +0000 Tim says that a sweep without a reclaim is not the trade. The short starts once price falls back through the order block, and the minimum payoff he repeats is two to one. His hit rate is his claim, not an audit. https://zerobit-site-g094.onrender.com/research/liquidity-sweep-and-retest/ https://zerobit-site-g094.onrender.com/research/liquidity-sweep-and-retest/ Fri, 04 Sep 2026 00:00:00 +0000 A liquidity sweep runs price through a level where stops sit, then fails. The retest is the second touch of that level, traded only if the larger structure agrees. https://zerobit-site-g094.onrender.com/research/how-a-college-student-reached-a-quant-desk/ https://zerobit-site-g094.onrender.com/research/how-a-college-student-reached-a-quant-desk/ Fri, 04 Sep 2026 00:00:00 +0000 A non-target student reached a quant desk by publishing work and asking people to pass a resume, not by blasting applications. The offer arrived before the degree did. https://zerobit-site-g094.onrender.com/research/what-rough-volatility-means-for-option-pricing/ https://zerobit-site-g094.onrender.com/research/what-rough-volatility-means-for-option-pricing/ Tue, 01 Sep 2026 00:00:00 +0000 Rough volatility means log-volatility moves scale more slowly than Brownian motion. Pricing models that skip that roughness misstate exotic paths. https://zerobit-site-g094.onrender.com/research/order-flow-scalping-above-vwap/ https://zerobit-site-g094.onrender.com/research/order-flow-scalping-above-vwap/ Tue, 01 Sep 2026 00:00:00 +0000 This order-flow scalp only stays with a long while price holds above VWAP. If the idea is already wrong, the stop is cut before the market fills it. https://zerobit-site-g094.onrender.com/research/why-day-trading-courses-leave-no-skill/ https://zerobit-site-g094.onrender.com/research/why-day-trading-courses-leave-no-skill/ Fri, 28 Aug 2026 00:00:00 +0000 A course that blames you when the pattern fails does not leave a testable skill. Durable skill is probability, position size, and work someone can hire you for. https://zerobit-site-g094.onrender.com/research/when-small-ranges-break-and-large-ones-fade/ https://zerobit-site-g094.onrender.com/research/when-small-ranges-break-and-large-ones-fade/ Fri, 28 Aug 2026 00:00:00 +0000 Patrick Nil says that about seventy percent of days are ranges, and that a small zone is a breakout while a large one is a fade. The World Cup record and win rates are his and the host's, not an audit. https://zerobit-site-g094.onrender.com/research/how-many-touches-before-a-breakout/ https://zerobit-site-g094.onrender.com/research/how-many-touches-before-a-breakout/ Fri, 28 Aug 2026 00:00:00 +0000 One breakout model waits for three touches of a level inside a range that formed after an impulse, and skips the trade when the range is still being built. https://zerobit-site-g094.onrender.com/research/selling-options-premium/ https://zerobit-site-g094.onrender.com/research/selling-options-premium/ Tue, 25 Aug 2026 00:00:00 +0000 Selling a put collects premium that looks like a high win rate. This account says a 20 or 30 delta short put still blows up, and the edge is the risk frame, not the win rate. https://zerobit-site-g094.onrender.com/research/how-path-signatures-price-exotic-options/ https://zerobit-site-g094.onrender.com/research/how-path-signatures-price-exotic-options/ Tue, 25 Aug 2026 00:00:00 +0000 Listed options pin down the ending distribution, not the path taken. A signature compresses that path so an exotic payoff becomes a short weighted sum. https://zerobit-site-g094.onrender.com/research/why-win-rate-without-expectancy-misleads/ https://zerobit-site-g094.onrender.com/research/why-win-rate-without-expectancy-misleads/ Fri, 21 Aug 2026 00:00:00 +0000 A high hit rate says nothing until you know the average win, the average loss, and the capital behind them. Sales calls do not fill in those missing numbers. https://zerobit-site-g094.onrender.com/research/when-a-trading-edge-is-gone/ https://zerobit-site-g094.onrender.com/research/when-a-trading-edge-is-gone/ Fri, 21 Aug 2026 00:00:00 +0000 An edge is gone when the data, not a feeling, says the market no longer matches the model. The fix in this account is to stop that model, not to add a new rule on the spot. https://zerobit-site-g094.onrender.com/research/nasdaq-order-flow-scalping/ https://zerobit-site-g094.onrender.com/research/nasdaq-order-flow-scalping/ Wed, 19 Aug 2026 00:00:00 +0000 This Nasdaq scalp reads effort in the order flow: aggressive buying or selling that price does not accept, then a stop trailed as that effort continues. https://zerobit-site-g094.onrender.com/research/how-nasdaq-effort-stacks-one-to-one/ https://zerobit-site-g094.onrender.com/research/how-nasdaq-effort-stacks-one-to-one/ Wed, 19 Aug 2026 00:00:00 +0000 Fabio Valentini says that Nasdaq effort reads who is dominating, and that several one-to-one scalps fit a drift better than one large target. The win-rate remarks are his, not an audit. https://zerobit-site-g094.onrender.com/research/what-a-statistical-edge-actually-is/ https://zerobit-site-g094.onrender.com/research/what-a-statistical-edge-actually-is/ Tue, 18 Aug 2026 00:00:00 +0000 An edge is a price better than the expected outcome, not a candle story. In markets that expectation moves, so a fixed chart rule is not a lasting edge. https://zerobit-site-g094.onrender.com/research/why-cherry-picked-backtests-fail/ https://zerobit-site-g094.onrender.com/research/why-cherry-picked-backtests-fail/ Fri, 14 Aug 2026 00:00:00 +0000 A backtest that starts from a chart you already like mostly confirms a bias. A useful test changes the rules and checks whether the result still holds. https://zerobit-site-g094.onrender.com/research/vwap-trading-strategy/ https://zerobit-site-g094.onrender.com/research/vwap-trading-strategy/ Fri, 14 Aug 2026 00:00:00 +0000 A VWAP strategy uses the volume-weighted average as the fair price for the session. This version stacks three of them and keeps the stop to about ten ticks. https://zerobit-site-g094.onrender.com/research/how-three-session-vwaps-time-a-scalp/ https://zerobit-site-g094.onrender.com/research/how-three-session-vwaps-time-a-scalp/ Fri, 14 Aug 2026 00:00:00 +0000 Robert Rother says he fades or joins the first touch of a session VWAP, with the book as confirmation. The one-minute fill he shows is two hundred seventy-five dollars on the account on screen. His history is the host's introduction. https://zerobit-site-g094.onrender.com/research/why-the-entry-is-the-last-slice/ https://zerobit-site-g094.onrender.com/research/why-the-entry-is-the-last-slice/ Tue, 11 Aug 2026 00:00:00 +0000 Chris Creamer says the click is the last five to ten percent. Location is discount outside value, and confirmation is effort that fails. The July return and the win rate are his account, not an audit. https://zerobit-site-g094.onrender.com/research/why-a-trading-bot-still-has-a-human-bias/ https://zerobit-site-g094.onrender.com/research/why-a-trading-bot-still-has-a-human-bias/ Tue, 11 Aug 2026 00:00:00 +0000 A trading bot stores a human choice of model and settings. How fast those settings change decides the year, and judgment stays inside the update. https://zerobit-site-g094.onrender.com/research/what-is-forced-participation-in-trading/ https://zerobit-site-g094.onrender.com/research/what-is-forced-participation-in-trading/ Tue, 11 Aug 2026 00:00:00 +0000 Forced participation is the moment trapped traders have to exit, and that exit is the move. The entry is the last step, after environment and location. https://zerobit-site-g094.onrender.com/research/why-coin-flip-math-fails-on-returns/ https://zerobit-site-g094.onrender.com/research/why-coin-flip-math-fails-on-returns/ Fri, 07 Aug 2026 00:00:00 +0000 A two-for-one coin has an edge only while the odds stay fixed. Regimes move, and one 2025 sample mean sat 1.7 million years out on a normal curve. https://zerobit-site-g094.onrender.com/research/why-a-weak-payoff-can-pass-challenges/ https://zerobit-site-g094.onrender.com/research/why-a-weak-payoff-can-pass-challenges/ Fri, 07 Aug 2026 00:00:00 +0000 Matteo Conti says a VWAP pullback wins often and pays poorly, which his simulations pass challenges and do not suit a private account. The pass rates are his test, not an audit. https://zerobit-site-g094.onrender.com/research/vwap-pullback-strategy/ https://zerobit-site-g094.onrender.com/research/vwap-pullback-strategy/ Fri, 07 Aug 2026 00:00:00 +0000 On a trend day, a VWAP pullback is a return to the session average in the direction of the drift, taken only while that drift is still intact. https://zerobit-site-g094.onrender.com/research/how-one-gold-account-scalps-the-reopen/ https://zerobit-site-g094.onrender.com/research/how-one-gold-account-scalps-the-reopen/ Tue, 04 Aug 2026 00:00:00 +0000 The firm reads one funded gold account that waited for the six p.m. Eastern reopen and scalped inside about two minutes. The host's log math is abnormal, his own word, and it is not an audit or a plan to copy. https://zerobit-site-g094.onrender.com/research/how-a-levered-long-short-book-breaks/ https://zerobit-site-g094.onrender.com/research/how-a-levered-long-short-book-breaks/ Tue, 04 Aug 2026 00:00:00 +0000 A short borrows shares and can be forced shut. Funding longs with that borrow is leverage, and the lecture cites a 42 percent weekly tail on a ruined book. https://zerobit-site-g094.onrender.com/research/gold-scalping-strategy/ https://zerobit-site-g094.onrender.com/research/gold-scalping-strategy/ Tue, 04 Aug 2026 00:00:00 +0000 One gold scalp waits for the futures reopen near 6 p.m. New York and is usually done within about two minutes. The window is the strategy, not a signal that works all day. https://zerobit-site-g094.onrender.com/research/why-the-quoted-price-of-risk-is-off/ https://zerobit-site-g094.onrender.com/research/why-the-quoted-price-of-risk-is-off/ Sun, 02 Aug 2026 00:00:00 +0000 Quoted risk is the crowd's breadth, not a true probability. Deeper work can disagree, as when Ackman read mall debt in the financial crisis. https://zerobit-site-g094.onrender.com/research/how-the-black-scholes-equation-is-built/ https://zerobit-site-g094.onrender.com/research/how-the-black-scholes-equation-is-built/ Sat, 01 Aug 2026 00:00:00 +0000 Hedge the option with delta shares and the random terms cancel. The hedged book must earn the riskless rate, which produces the pricing equation. https://zerobit-site-g094.onrender.com/research/why-stock-diversification-fails-in-a-crash/ https://zerobit-site-g094.onrender.com/research/why-stock-diversification-fails-in-a-crash/ Fri, 31 Jul 2026 00:00:00 +0000 Caterpillar and Nvidia looked unrelated in early 2025, then fell with the index. A long put is the lecture's way to break that shared crash and free cash to buy. https://zerobit-site-g094.onrender.com/research/how-to-trade-after-the-news/ https://zerobit-site-g094.onrender.com/research/how-to-trade-after-the-news/ Fri, 31 Jul 2026 00:00:00 +0000 Trading the news, in this account, starts after the number is out. The first half hour sets the size of the battle. The middle of a noisy week is left alone. https://zerobit-site-g094.onrender.com/research/advanced-projects-for-quant-judgment/ https://zerobit-site-g094.onrender.com/research/advanced-projects-for-quant-judgment/ Thu, 30 Jul 2026 00:00:00 +0000 Build a trading system you can override, a library for rough volatility and signatures, and a lab that times Python tools against a known option price. https://zerobit-site-g094.onrender.com/research/when-volatility-drag-helps-or-hurts/ https://zerobit-site-g094.onrender.com/research/when-volatility-drag-helps-or-hurts/ Wed, 29 Jul 2026 00:00:00 +0000 Half the variance usually taxes compounded growth. A rare high-payoff position can raise geometric growth instead, if you can repeat it without a ruinous loss. https://zerobit-site-g094.onrender.com/research/nr4-breakout-strategy/ https://zerobit-site-g094.onrender.com/research/nr4-breakout-strategy/ Tue, 28 Jul 2026 00:00:00 +0000 An NR4 is the narrowest range of the last four bars. The breakout trades the expansion out of that quiet bar, with the stop on the other side of the range. https://zerobit-site-g094.onrender.com/research/how-an-adapted-nr4-waits-on-volatility/ https://zerobit-site-g094.onrender.com/research/how-an-adapted-nr4-waits-on-volatility/ Tue, 28 Jul 2026 00:00:00 +0000 The firm reconstructs an unnamed funded trader whose breakout waits for four shrinking hourly ranges, then one break. The payout band and the payoff ratio are the host's reading of one account, not a forecast. https://zerobit-site-g094.onrender.com/research/arithmetic-versus-geometric-brownian-motion/ https://zerobit-site-g094.onrender.com/research/arithmetic-versus-geometric-brownian-motion/ Tue, 28 Jul 2026 00:00:00 +0000 Arithmetic Brownian motion adds shocks and can go negative. Geometric motion scales with price, stays positive, and drops half the variance from its drift. https://zerobit-site-g094.onrender.com/research/why-generic-financial-advice-breaks-down/ https://zerobit-site-g094.onrender.com/research/why-generic-financial-advice-breaks-down/ Sun, 26 Jul 2026 00:00:00 +0000 Advice quality varies, and a plan you follow can beat a better plan you ignore. A language model mimics experience without the conditions behind it. https://zerobit-site-g094.onrender.com/research/what-is-a-liquidity-grab/ https://zerobit-site-g094.onrender.com/research/what-is-a-liquidity-grab/ Fri, 24 Jul 2026 00:00:00 +0000 A liquidity grab is a push through obvious stops that fails to continue. The trade, if any, waits for the reversal after the grab, and most setups are skipped. https://zerobit-site-g094.onrender.com/research/time-the-entry-after-the-liquidity-grab/ https://zerobit-site-g094.onrender.com/research/time-the-entry-after-the-liquidity-grab/ Fri, 24 Jul 2026 00:00:00 +0000 Tim Flossbach, enters only after a liquidation pocket is taken and a turn is visible. He wants at least two-to-one and skips most charts. https://zerobit-site-g094.onrender.com/research/how-an-ai-trading-assistant-keeps-a-thesis/ https://zerobit-site-g094.onrender.com/research/how-an-ai-trading-assistant-keeps-a-thesis/ Fri, 24 Jul 2026 00:00:00 +0000 An order-placing model needs a saved thesis and hard limits. The demo still dropped data, blocked orders, and moved a target to the last price. https://zerobit-site-g094.onrender.com/research/what-a-2025-drawdown-says-about-sizing/ https://zerobit-site-g094.onrender.com/research/what-a-2025-drawdown-says-about-sizing/ Thu, 23 Jul 2026 00:00:00 +0000 The lecture reports about 44 percent versus 16 percent for the index, a 30 percent hole from short volatility, and a month-long window to redeploy into the rebound. https://zerobit-site-g094.onrender.com/research/intermediate-quant-projects-worth-building/ https://zerobit-site-g094.onrender.com/research/intermediate-quant-projects-worth-building/ Wed, 22 Jul 2026 00:00:00 +0000 Build a market-making sim that can use the wrong model, a derivatives pricer you can solve three ways, and an order book with price-time priority. https://zerobit-site-g094.onrender.com/research/which-strategy-passes-a-prop-firm-challenge/ https://zerobit-site-g094.onrender.com/research/which-strategy-passes-a-prop-firm-challenge/ Tue, 21 Jul 2026 00:00:00 +0000 On one firm's challenge book, pass rates differed by style: reversal, breakout, trend, price action, and order flow. The ranking is that book, not a proof that one style is best. https://zerobit-site-g094.onrender.com/research/investing-from-a-toy-to-market-risk/ https://zerobit-site-g094.onrender.com/research/investing-from-a-toy-to-market-risk/ Tue, 21 Jul 2026 00:00:00 +0000 Investing is paying for a risky shot at a reward. A fair price is the crowd's guess, and stocks that look unrelated can still share one market. https://zerobit-site-g094.onrender.com/research/how-five-prop-styles-ranked-on-challenge-data/ https://zerobit-site-g094.onrender.com/research/how-five-prop-styles-ranked-on-challenge-data/ Tue, 21 Jul 2026 00:00:00 +0000 On the firm's book of about 10,000 traders, order flow led and reversal finished last. Stated pass rates ran from 5 percent to about 15 percent. https://zerobit-site-g094.onrender.com/research/why-priced-in-does-not-mean-correct/ https://zerobit-site-g094.onrender.com/research/why-priced-in-does-not-mean-correct/ Sun, 19 Jul 2026 00:00:00 +0000 A fast price reaction is not proof the price is right. Alpha is the leftover orthogonal to a risk model, and a home run still required you to be positioned. https://zerobit-site-g094.onrender.com/research/scalp-the-vwap-pullback-a-large-order-creates/ https://zerobit-site-g094.onrender.com/research/scalp-the-vwap-pullback-a-large-order-creates/ Fri, 17 Jul 2026 00:00:00 +0000 Robert Rother scalps ES pullbacks at day VWAP with an 11-tick target and a 10-tick stop. He states a win rate near 75 to 80 percent, his tally, not an audit. https://zerobit-site-g094.onrender.com/research/pullback-to-vwap/ https://zerobit-site-g094.onrender.com/research/pullback-to-vwap/ Fri, 17 Jul 2026 00:00:00 +0000 A large order often has to work back toward the session's volume-weighted average. The pullback trade is that return, not a guess at the high or the low of the day. https://zerobit-site-g094.onrender.com/research/beginner-projects-that-teach-quant-work/ https://zerobit-site-g094.onrender.com/research/beginner-projects-that-teach-quant-work/ Fri, 17 Jul 2026 00:00:00 +0000 Start with a performance dashboard, a grid-search visualizer, and a binomial option tree. Each project teaches a job skill that a generated repo will not. https://zerobit-site-g094.onrender.com/research/how-lower-correlation-raises-a-sharpe-ratio/ https://zerobit-site-g094.onrender.com/research/how-lower-correlation-raises-a-sharpe-ratio/ Thu, 16 Jul 2026 00:00:00 +0000 Lower correlation cuts portfolio variance and can raise the Sharpe ratio if expected return holds. A crisis can erase a zero that was only statistical. https://zerobit-site-g094.onrender.com/research/how-to-read-a-portfolio-alpha-and-beta/ https://zerobit-site-g094.onrender.com/research/how-to-read-a-portfolio-alpha-and-beta/ Wed, 15 Jul 2026 00:00:00 +0000 Beta is how your returns move with the market, and alpha is the leftover. A rolling regression shows both changing, and neither number is a forecast. https://zerobit-site-g094.onrender.com/research/what-four-funded-traders-use-to-clear-a-test/ https://zerobit-site-g094.onrender.com/research/what-four-funded-traders-use-to-clear-a-test/ Tue, 14 Jul 2026 00:00:00 +0000 Four the firm traders clear a test with one or two planned trades. One copied a Nasdaq long across ten accounts for about $6,000 in under a minute. https://zerobit-site-g094.onrender.com/research/how-to-pass-a-prop-firm-challenge/ https://zerobit-site-g094.onrender.com/research/how-to-pass-a-prop-firm-challenge/ Tue, 14 Jul 2026 00:00:00 +0000 Four funded traders describe four different ways through a challenge. What they share is a written risk limit, not a shared entry signal. https://zerobit-site-g094.onrender.com/research/how-portfolio-risk-and-return-actually-fit/ https://zerobit-site-g094.onrender.com/research/how-portfolio-risk-and-return-actually-fit/ Tue, 14 Jul 2026 00:00:00 +0000 Risk is not a coupon for higher return. Historical averages do not pick your future path, and diversification inside one market still leaves that market's risk. https://zerobit-site-g094.onrender.com/research/why-bitcoin-swings-like-a-new-monetary-asset/ https://zerobit-site-g094.onrender.com/research/why-bitcoin-swings-like-a-new-monetary-asset/ Sun, 12 Jul 2026 00:00:00 +0000 The lecture reads Bitcoin's swings as bottom-up price discovery of a scarce money, rhyming with gold after the 1970s peg broke, amplified by retail attention. https://zerobit-site-g094.onrender.com/research/why-a-normal-model-misses-market-crashes/ https://zerobit-site-g094.onrender.com/research/why-a-normal-model-misses-market-crashes/ Fri, 10 Jul 2026 00:00:00 +0000 A normal curve fit to S&P returns puts five-sigma days thousands of years apart. The lecture counts 19 such days in about 25 years, and uses regimes instead. https://zerobit-site-g094.onrender.com/research/inside-bar-breakout-strategy/ https://zerobit-site-g094.onrender.com/research/inside-bar-breakout-strategy/ Fri, 10 Jul 2026 00:00:00 +0000 An inside bar sits entirely inside the prior bar. This breakout does not buy the first poke out. It waits for a retest of the supply or demand the break just left behind. https://zerobit-site-g094.onrender.com/research/enter-when-broken-supply-turns-into-support/ https://zerobit-site-g094.onrender.com/research/enter-when-broken-supply-turns-into-support/ Fri, 10 Jul 2026 00:00:00 +0000 The firm's founder buys a breakout after broken supply holds as support. On gold he took about six points, then left the rest running near 40. https://zerobit-site-g094.onrender.com/research/what-compound-annual-growth-actually-measures/ https://zerobit-site-g094.onrender.com/research/what-compound-annual-growth-actually-measures/ Tue, 07 Jul 2026 00:00:00 +0000 CAGR is the constant rate that matches a jagged path's ending wealth. It compresses that history, and it does not forecast what the next year will do. https://zerobit-site-g094.onrender.com/research/price-a-prop-attempt-before-the-first-fee/ https://zerobit-site-g094.onrender.com/research/price-a-prop-attempt-before-the-first-fee/ Tue, 07 Jul 2026 00:00:00 +0000 A worked the firm simulator used 2-to-1 and a 40 percent win rate on a 100k test. At $350 risk, 5,000 runs showed a 65.1 percent pass rate. https://zerobit-site-g094.onrender.com/research/how-to-calculate-a-prop-firm-challenge/ https://zerobit-site-g094.onrender.com/research/how-to-calculate-a-prop-firm-challenge/ Tue, 07 Jul 2026 00:00:00 +0000 A prop challenge is arithmetic before it is a chart: target, daily loss, max loss, and how many losers in a row still fit. Run those numbers before you pay for an attempt. https://zerobit-site-g094.onrender.com/research/how-to-read-a-market-bubble-as-expectations/ https://zerobit-site-g094.onrender.com/research/how-to-read-a-market-bubble-as-expectations/ Sun, 05 Jul 2026 00:00:00 +0000 A bubble label is a forecast in disguise. The lecture treats prices as expectations that can break, and asks whether your portfolio survives the break. https://zerobit-site-g094.onrender.com/research/when-a-trading-strategy-must-stay-secret/ https://zerobit-site-g094.onrender.com/research/when-a-trading-strategy-must-stay-secret/ Fri, 03 Jul 2026 00:00:00 +0000 A strategy that only levers market beta need not be secret. Secrecy starts when you alone hold a dataset, a market-making edge, or an undocumented premium. https://zerobit-site-g094.onrender.com/research/name-the-days-context-before-any-entry/ https://zerobit-site-g094.onrender.com/research/name-the-days-context-before-any-entry/ Fri, 03 Jul 2026 00:00:00 +0000 Tom Vorwalt marks balance, the prior close, and liquidity before any setup. A 40 percent hit rate, he says, needs more than 2-to-one to earn its keep. https://zerobit-site-g094.onrender.com/research/market-context-before-a-trade/ https://zerobit-site-g094.onrender.com/research/market-context-before-a-trade/ Fri, 03 Jul 2026 00:00:00 +0000 Context is the higher-timeframe story that decides which side of a level you are allowed to trade. The entry is the last step, and some days the context says do nothing. https://zerobit-site-g094.onrender.com/research/why-prop-firm-accounts-fail/ https://zerobit-site-g094.onrender.com/research/why-prop-firm-accounts-fail/ Tue, 30 Jun 2026 00:00:00 +0000 Most failed prop accounts in this firm's review did not die from the entry. They died from one behavior: adding size, moving a stop, or trading after the daily limit was already gone. https://zerobit-site-g094.onrender.com/research/how-one-bad-day-ends-a-funded-account/ https://zerobit-site-g094.onrender.com/research/how-one-bad-day-ends-a-funded-account/ Tue, 30 Jun 2026 00:00:00 +0000 The firm's review of more than 5,000 failed accounts says over 90 percent died from one or two trades inside 24 hours. The figures are the firm's. https://zerobit-site-g094.onrender.com/research/four-ways-to-use-a-million-dollars/ https://zerobit-site-g094.onrender.com/research/four-ways-to-use-a-million-dollars/ Tue, 30 Jun 2026 00:00:00 +0000 The lecture's four sketches are Treasuries, public equities, a private venture, and spending the pile down. Only the first is treated as riskless. https://zerobit-site-g094.onrender.com/research/what-a-quant-job-is-actually-like/ https://zerobit-site-g094.onrender.com/research/what-a-quant-job-is-actually-like/ Sun, 28 Jun 2026 00:00:00 +0000 A quant seat is mostly data work that often leads nowhere, pays less than it looks, and takes years of math before the title politics even start. https://zerobit-site-g094.onrender.com/research/why-advertised-day-trading-results-fall-apart/ https://zerobit-site-g094.onrender.com/research/why-advertised-day-trading-results-fall-apart/ Fri, 26 Jun 2026 00:00:00 +0000 A one-off gain is not a growth rate you can compound. A win rate that looked strong in an old sample can flip once the market regime changes. https://zerobit-site-g094.onrender.com/research/how-to-trade-a-range-after-a-strong-move/ https://zerobit-site-g094.onrender.com/research/how-to-trade-a-range-after-a-strong-move/ Fri, 26 Jun 2026 00:00:00 +0000 After a strong impulse, price often builds a range. One model fades the edges of that range and stands aside while the impulse is still running. https://zerobit-site-g094.onrender.com/research/fade-the-box-that-forms-after-a-thrust/ https://zerobit-site-g094.onrender.com/research/fade-the-box-that-forms-after-a-thrust/ Fri, 26 Jun 2026 00:00:00 +0000 Patrick Niel, a repeat world-championship finalist, fades the range after an impulse and caps his own book near 1 percent. He cites a 50 to 60 percent win rate. https://zerobit-site-g094.onrender.com/research/why-stock-picking-can-lose-to-the-index/ https://zerobit-site-g094.onrender.com/research/why-stock-picking-can-lose-to-the-index/ Tue, 23 Jun 2026 00:00:00 +0000 A hot stock can post a higher average growth rate and still leave worse crash paths, because most of the gain is beta plus a volatility penalty. https://zerobit-site-g094.onrender.com/research/what-a-200k-prop-firm-account-changes/ https://zerobit-site-g094.onrender.com/research/what-a-200k-prop-firm-account-changes/ Tue, 23 Jun 2026 00:00:00 +0000 A larger funded balance changes the dollar value of one percent. It does not remove challenge fees, failed attempts, or the firm's loss limits. https://zerobit-site-g094.onrender.com/research/what-1-to-3-percent-pays-on-200k-funding/ https://zerobit-site-g094.onrender.com/research/what-1-to-3-percent-pays-on-200k-funding/ Tue, 23 Jun 2026 00:00:00 +0000 On a 200k funded balance, the firm's host puts 1 percent near $2,000 a month and 3 percent near $6,000. Fees and failed attempts still count. https://zerobit-site-g094.onrender.com/research/what-alpha-means-in-a-pricing-model/ https://zerobit-site-g094.onrender.com/research/what-alpha-means-in-a-pricing-model/ Sun, 21 Jun 2026 00:00:00 +0000 Alpha is the intercept after you account for a pricing model's factors. Beating the S&P 500 can be beta, and the intercept can vanish if you add factors. https://zerobit-site-g094.onrender.com/research/the-one-percent-risk-rule/ https://zerobit-site-g094.onrender.com/research/the-one-percent-risk-rule/ Fri, 19 Jun 2026 00:00:00 +0000 The one percent rule here is a daily loss limit: risk about one percent, then turn the computer off. One trade is allowed to run. A second idea does not get a fresh budget. https://zerobit-site-g094.onrender.com/research/diversification-and-hedging-are-different-tools/ https://zerobit-site-g094.onrender.com/research/diversification-and-hedging-are-different-tools/ Fri, 19 Jun 2026 00:00:00 +0000 Diversification cuts volatility when assets are not perfectly correlated. A hedge trades an uncertain future for a payoff the contract itself specifies. https://zerobit-site-g094.onrender.com/research/what-makes-a-trader-fundable/ https://zerobit-site-g094.onrender.com/research/what-makes-a-trader-fundable/ Tue, 16 Jun 2026 00:00:00 +0000 A fundable trader is one a firm can leave capital with overnight rules still intact. A strategy that makes money on a personal account can still fail that test. https://zerobit-site-g094.onrender.com/research/what-a-firm-checks-before-it-funds-you/ https://zerobit-site-g094.onrender.com/research/what-a-firm-checks-before-it-funds-you/ Tue, 16 Jun 2026 00:00:00 +0000 The firm says nine in ten traders fail most challenges because a profitable stretch is not yet a process the firm can fund. Survival is the test. https://zerobit-site-g094.onrender.com/research/implied-volatility-versus-what-the-market-later-does/ https://zerobit-site-g094.onrender.com/research/implied-volatility-versus-what-the-market-later-does/ Tue, 16 Jun 2026 00:00:00 +0000 Implied volatility is backed out of option prices. Realized volatility is estimated from returns, and a regression of the two is how the lecture shows the premium. https://zerobit-site-g094.onrender.com/research/why-a-crash-can-help-a-prepared-portfolio/ https://zerobit-site-g094.onrender.com/research/why-a-crash-can-help-a-prepared-portfolio/ Sun, 14 Jun 2026 00:00:00 +0000 A crash hurts people who must sell into it. A portfolio that holds convexity or spare cash in that state can buy assets others are forced to unload. https://zerobit-site-g094.onrender.com/research/why-a-portfolio-can-be-built-without-a-backtest/ https://zerobit-site-g094.onrender.com/research/why-a-portfolio-can-be-built-without-a-backtest/ Fri, 12 Jun 2026 00:00:00 +0000 A useful portfolio can be designed from how return streams relate, then checked with simple regressions, rather than from a curve that only fit the past. https://zerobit-site-g094.onrender.com/research/risk-reward-ratio-for-scalping/ https://zerobit-site-g094.onrender.com/research/risk-reward-ratio-for-scalping/ Fri, 12 Jun 2026 00:00:00 +0000 Risk reward is the distance to the exit divided by the distance to the stop. One scalp in this note uses about nine points of risk for about fourteen points of target. https://zerobit-site-g094.onrender.com/research/how-a-positive-payoff-scalp-is-managed/ https://zerobit-site-g094.onrender.com/research/how-a-positive-payoff-scalp-is-managed/ Fri, 12 Jun 2026 00:00:00 +0000 Matthias shows a Nasdaq scalp with a nine-point stop and about fourteen points of gain. He wants the payoff above one-to-one and stops after two losses. https://zerobit-site-g094.onrender.com/research/how-volatility-drag-lowers-geometric-growth/ https://zerobit-site-g094.onrender.com/research/how-volatility-drag-lowers-geometric-growth/ Tue, 09 Jun 2026 00:00:00 +0000 Geometric growth is about the average return minus half the variance. A positive average can still compound poorly when the path swings hard. https://zerobit-site-g094.onrender.com/research/why-sharpe-is-not-the-growth-objective/ https://zerobit-site-g094.onrender.com/research/why-sharpe-is-not-the-growth-objective/ Sun, 07 Jun 2026 00:00:00 +0000 The Sharpe ratio and compounded growth are different goals. A sleeve with negative growth can lift the mix. Leverage without that sleeve can deepen the hole. https://zerobit-site-g094.onrender.com/research/why-buying-the-index-still-needs-a-plan/ https://zerobit-site-g094.onrender.com/research/why-buying-the-index-still-needs-a-plan/ Fri, 05 Jun 2026 00:00:00 +0000 Buying the index for 30 years still fails if job, house, and stocks fall together. A hedge that pays in the drop is the lecture's alternative to selling with the crowd. https://zerobit-site-g094.onrender.com/research/score-the-economy-then-time-the-forex-zone/ https://zerobit-site-g094.onrender.com/research/score-the-economy-then-time-the-forex-zone/ Fri, 05 Jun 2026 00:00:00 +0000 Tobias scores growth, the central bank, and risk mood before a zone. His NZD/CAD example used at least a 29-pip stop and a fixed two-to-one target. https://zerobit-site-g094.onrender.com/research/forex-fundamental-analysis/ https://zerobit-site-g094.onrender.com/research/forex-fundamental-analysis/ Fri, 05 Jun 2026 00:00:00 +0000 A fundamentals-first forex process scores the economy, the central bank, and the risk mood before it looks for a zone on the chart to time the idea. https://zerobit-site-g094.onrender.com/research/which-trading-style-fits-prop-firm-rules/ https://zerobit-site-g094.onrender.com/research/which-trading-style-fits-prop-firm-rules/ Tue, 02 Jun 2026 00:00:00 +0000 A style fits a prop account when its normal losing streak stays inside the daily and overall loss limits. The style that earns the most on a personal account may not. https://zerobit-site-g094.onrender.com/research/which-style-can-survive-a-funded-loss-limit/ https://zerobit-site-g094.onrender.com/research/which-style-can-survive-a-funded-loss-limit/ Tue, 02 Jun 2026 00:00:00 +0000 The firm calls day trading the cleanest fit under a loss cap, swing trading workable with less size, and multi-week holds a poor fit. Costs still matter. https://zerobit-site-g094.onrender.com/research/how-a-hedge-sleeve-changes-a-stock-portfolio/ https://zerobit-site-g094.onrender.com/research/how-a-hedge-sleeve-changes-a-stock-portfolio/ Tue, 02 Jun 2026 00:00:00 +0000 A stock index here shows a 0.77 Sharpe ratio and a 25 percent drawdown. A dull sleeve, then leverage, is the attempt to cut that drag and keep the engine. https://zerobit-site-g094.onrender.com/research/why-a-researcher-left-the-quant-desk/ https://zerobit-site-g094.onrender.com/research/why-a-researcher-left-the-quant-desk/ Sun, 31 May 2026 00:00:00 +0000 Isolation, not the math, is why this researcher left a Bloomberg desk at 22, then a PhD and an unfinished degree. The skills stayed. The silence did the harm. https://zerobit-site-g094.onrender.com/research/how-total-expectation-splits-an-average/ https://zerobit-site-g094.onrender.com/research/how-total-expectation-splits-an-average/ Fri, 29 May 2026 00:00:00 +0000 An average equals each slice's average times that slice's probability. The identity holds when the slices drift. In markets, the lecture says, they drift quickly. https://zerobit-site-g094.onrender.com/research/gamma-exposure-trading/ https://zerobit-site-g094.onrender.com/research/gamma-exposure-trading/ Fri, 29 May 2026 00:00:00 +0000 Gamma exposure is how options positions can pin or release an index. This framework starts with where volume accumulated, then asks who is forced to hedge. https://zerobit-site-g094.onrender.com/research/frame-the-index-day-with-volume-and-gamma/ https://zerobit-site-g094.onrender.com/research/frame-the-index-day-with-volume-and-gamma/ Fri, 29 May 2026 00:00:00 +0000 Manuel frames an index session from accepted volume, then from gamma. He stops after two losers and caps a trade near 1 percent of the account. https://zerobit-site-g094.onrender.com/research/when-prop-size-beats-the-cash-you-put-at-risk/ https://zerobit-site-g094.onrender.com/research/when-prop-size-beats-the-cash-you-put-at-risk/ Tue, 26 May 2026 00:00:00 +0000 A $2,500 month on $10,000, in the firm's sketch, needs nearly 3 percent risk a trade. The same target on $100,000 of funding needs about 0.35 percent. https://zerobit-site-g094.onrender.com/research/prop-firm-versus-your-own-capital/ https://zerobit-site-g094.onrender.com/research/prop-firm-versus-your-own-capital/ Tue, 26 May 2026 00:00:00 +0000 The comparison that matters is gain relative to the cash you personally have at risk: a challenge fee on one side, the whole account on the other. https://zerobit-site-g094.onrender.com/research/how-a-cash-secured-put-is-paid/ https://zerobit-site-g094.onrender.com/research/how-a-cash-secured-put-is-paid/ Tue, 26 May 2026 00:00:00 +0000 You collect a premium for the duty to buy 100 shares at the strike. Puts look rich versus later moves, and a high win rate can still end the account. https://zerobit-site-g094.onrender.com/research/why-the-reward-follows-the-work/ https://zerobit-site-g094.onrender.com/research/why-the-reward-follows-the-work/ Sun, 24 May 2026 00:00:00 +0000 Wanting the prize instead of the work is the lecture's reason the prize stays out of reach. Wealth, here, follows hard problems done for a long time, not a finish line. https://zerobit-site-g094.onrender.com/research/why-uncorrelated-strategies-raise-the-sharpe/ https://zerobit-site-g094.onrender.com/research/why-uncorrelated-strategies-raise-the-sharpe/ Fri, 22 May 2026 00:00:00 +0000 A 0.8 Sharpe and a 0.9 Sharpe became 1.2 at a half-and-half mix in the lecture. The gain needs independence. Two equity books can lose it together in a selloff. https://zerobit-site-g094.onrender.com/research/three-checks-before-a-nasdaq-breakout-click/ https://zerobit-site-g094.onrender.com/research/three-checks-before-a-nasdaq-breakout-click/ Thu, 21 May 2026 00:00:00 +0000 Jonas Bearthrop joins Nasdaq breakouts only after structure, the heatmap, and absorption agree. A structure-only test showed about 45 to 50 percent at two-to-one. https://zerobit-site-g094.onrender.com/research/market-structure-order-flow-and-liquidity/ https://zerobit-site-g094.onrender.com/research/market-structure-order-flow-and-liquidity/ Thu, 21 May 2026 00:00:00 +0000 One breakout model will not separate three reads: the swing structure, the order flow at the level, and the liquidity that has to be taken before price can leave. https://zerobit-site-g094.onrender.com/research/why-one-winning-trade-is-not-an-edge/ https://zerobit-site-g094.onrender.com/research/why-one-winning-trade-is-not-an-edge/ Tue, 19 May 2026 00:00:00 +0000 One earnings gap has no other version. Edge here is a positive average trade whose inputs keep changing, so a chart line or a long backtest cannot settle it. https://zerobit-site-g094.onrender.com/research/why-a-passion-is-built-by-trying/ https://zerobit-site-g094.onrender.com/research/why-a-passion-is-built-by-trying/ Sun, 17 May 2026 00:00:00 +0000 The path runs from coding to math to markets, including work that was shut down. Passion here means choosing that work, including the part of the time you dislike. https://zerobit-site-g094.onrender.com/research/what-a-chatgpt-order-bot-actually-does/ https://zerobit-site-g094.onrender.com/research/what-a-chatgpt-order-bot-actually-does/ Fri, 15 May 2026 00:00:00 +0000 The bot sends broker news and a price to a model, which returns a thesis, a target, and order arguments. One pass produced a 250 target, then a routing error stopped it. https://zerobit-site-g094.onrender.com/research/how-to-choose-a-prop-trading-firm/ https://zerobit-site-g094.onrender.com/research/how-to-choose-a-prop-trading-firm/ Fri, 15 May 2026 00:00:00 +0000 Before you pay a prop firm, ask how a losing day is defined, what the challenge fee buys if you fail, and whether a trader who follows the rules actually gets paid. https://zerobit-site-g094.onrender.com/research/ask-about-drawdown-fees-and-payouts-first/ https://zerobit-site-g094.onrender.com/research/ask-about-drawdown-fees-and-payouts-first/ Fri, 15 May 2026 00:00:00 +0000 Intraday trailing can fail a day that is still up $5,000 if open gain is given back. The firm says its trail updates at the close and its first try is $1. https://zerobit-site-g094.onrender.com/research/how-a-wheel-screen-picks-strikes/ https://zerobit-site-g094.onrender.com/research/how-a-wheel-screen-picks-strikes/ Fri, 08 May 2026 00:00:00 +0000 The wheel sells calls against shares and puts against cash. Sell the call only when the strike clears your cost. A 30 delta is not the same sale after the price falls. https://zerobit-site-g094.onrender.com/research/what-prop-firm-access-costs-before-any-payout/ https://zerobit-site-g094.onrender.com/research/what-prop-firm-access-costs-before-any-payout/ Thu, 07 May 2026 00:00:00 +0000 The firm's promo says three tries can cost about $1,700 before trading gain. It wants end-of-day risk and paid winners. The 5 percent growth path is only a scenario. https://zerobit-site-g094.onrender.com/research/what-is-a-prop-trading-firm/ https://zerobit-site-g094.onrender.com/research/what-is-a-prop-trading-firm/ Thu, 07 May 2026 00:00:00 +0000 A prop trading firm rents you access to a larger balance after an evaluation. The fee, the intraday loss rule, and the payout terms decide whether that access is usable. https://zerobit-site-g094.onrender.com/research/what-a-trading-sentiment-feed-is-not/ https://zerobit-site-g094.onrender.com/research/what-a-trading-sentiment-feed-is-not/ Wed, 06 May 2026 00:00:00 +0000 The lecture posts a $113,000 Nvidia book and a short put closed for $440 next to a tweet-based score. That score is a reading of the stream, not a buy or sell by itself. https://zerobit-site-g094.onrender.com/research/how-a-european-option-payoff-works/ https://zerobit-site-g094.onrender.com/research/how-a-european-option-payoff-works/ Tue, 05 May 2026 00:00:00 +0000 A European call pays the gain above the strike at expiry, in 100-share lots, and only if that gain is positive. Premium shifts the picture, and delta is not a frequency. https://zerobit-site-g094.onrender.com/research/will-ai-shrink-quant-teams/ https://zerobit-site-g094.onrender.com/research/will-ai-shrink-quant-teams/ Sun, 03 May 2026 00:00:00 +0000 A small failure rate times a huge pile of automated tasks creates many edge cases. The lecture expects smaller quant teams, and more people fixing what the models break. https://zerobit-site-g094.onrender.com/research/using-black-scholes-for-relative-option-prices/ https://zerobit-site-g094.onrender.com/research/using-black-scholes-for-relative-option-prices/ Fri, 01 May 2026 00:00:00 +0000 Black-Scholes turns two premiums into comparable implied volatilities and deltas. Both describe the market now. A delta is not a hit rate you can count on later. https://zerobit-site-g094.onrender.com/research/why-a-reached-goal-feels-smaller/ https://zerobit-site-g094.onrender.com/research/why-a-reached-goal-feels-smaller/ Thu, 30 Apr 2026 00:00:00 +0000 Expectations and the band of ordinary days both move as you adapt. A long goal, once reached, already sits inside that band, so the trip carried the weight. https://zerobit-site-g094.onrender.com/research/how-a-covered-call-changes-a-short-call/ https://zerobit-site-g094.onrender.com/research/how-a-covered-call-changes-a-short-call/ Tue, 28 Apr 2026 00:00:00 +0000 A covered call is long shares plus a short call. You keep the premium if you hold the short, assignment caps the upside, and a drop through your cost is still a loss. https://zerobit-site-g094.onrender.com/research/how-to-read-a-listed-options-chain/ https://zerobit-site-g094.onrender.com/research/how-to-read-a-listed-options-chain/ Fri, 24 Apr 2026 00:00:00 +0000 A chain lists calls and puts for one expiry, marks in-the-money strikes, and shows bid, ask, volume, and model Greeks. Delta is a model reading, not a long-run hit rate. https://zerobit-site-g094.onrender.com/research/why-harsh-comments-outweigh-silence/ https://zerobit-site-g094.onrender.com/research/why-harsh-comments-outweigh-silence/ Fri, 17 Apr 2026 00:00:00 +0000 A bias toward bad news, and a habit of checking for danger, lets harsh comments outweigh silence. The lecture splits that habit into a private fear and a social one. https://zerobit-site-g094.onrender.com/research/how-a-backup-plan-changes-commitment/ https://zerobit-site-g094.onrender.com/research/how-a-backup-plan-changes-commitment/ Tue, 14 Apr 2026 00:00:00 +0000 The lecture draws more chance of quitting while a backup remains, and more chance of finishing once it is gone. The pictures are qualitative. They are not measured odds. https://zerobit-site-g094.onrender.com/research/what-to-do-after-a-bad-stretch/ https://zerobit-site-g094.onrender.com/research/what-to-do-after-a-bad-stretch/ Fri, 10 Apr 2026 00:00:00 +0000 After a cluster of bad events, the lecture judges the next action, not the stretch. Repeating a harmful action is framed as taking from your future self. https://zerobit-site-g094.onrender.com/research/why-fear-misprices-ordinary-risks/ https://zerobit-site-g094.onrender.com/research/why-fear-misprices-ordinary-risks/ Tue, 07 Apr 2026 00:00:00 +0000 People put too much probability on rare disasters, so ordinary actions look like bad bets. Someone who keeps taking the action is a sign the tail was priced too heavily. https://zerobit-site-g094.onrender.com/research/how-a-utility-function-frames-growth/ https://zerobit-site-g094.onrender.com/research/how-a-utility-function-frames-growth/ Sun, 05 Apr 2026 00:00:00 +0000 A policy maps the situation to an action. Utility scores the result, and principles draw that score. Reaching a higher peak means a temporary drop first. https://zerobit-site-g094.onrender.com/research/what-the-open-gaussian-cookbook-contains/ https://zerobit-site-g094.onrender.com/research/what-the-open-gaussian-cookbook-contains/ Fri, 03 Apr 2026 00:00:00 +0000 The open cookbook simulates Brownian motion, a bridge, fractional paths, and a Markovian lift. Extra factors track covariance. The lift is faster and still approximate. https://zerobit-site-g094.onrender.com/research/two-questions-quantitative-finance-asks/ https://zerobit-site-g094.onrender.com/research/two-questions-quantitative-finance-asks/ Tue, 31 Mar 2026 00:00:00 +0000 Quantitative finance asks what a contract is worth and which choice is better. A fair charge leaves a hedged book near zero. One path can still crown the worse forecast. https://zerobit-site-g094.onrender.com/research/how-markovian-lifting-approximates-rough-volatility/ https://zerobit-site-g094.onrender.com/research/how-markovian-lifting-approximates-rough-volatility/ Fri, 27 Mar 2026 00:00:00 +0000 Rough volatility remembers the whole path, which is slow to simulate. Markovian lifting replaces the power-law kernel with a finite stack of mean-reverting factors. https://zerobit-site-g094.onrender.com/research/what-the-sharpe-ratio-leaves-out/ https://zerobit-site-g094.onrender.com/research/what-the-sharpe-ratio-leaves-out/ Tue, 24 Mar 2026 00:00:00 +0000 Two paths can share a Sharpe ratio and still differ in return and in downside. The ratio also says nothing about whether that path was fit to old noise. https://zerobit-site-g094.onrender.com/research/why-black-litterman-weights-move-less/ https://zerobit-site-g094.onrender.com/research/why-black-litterman-weights-move-less/ Fri, 20 Mar 2026 00:00:00 +0000 Mean-variance weights jump when historical returns twitch. Black-Litterman starts from market-implied returns, then lets a stated view pull the mix away from that anchor. https://zerobit-site-g094.onrender.com/research/which-retail-trading-mistakes-matter-most/ https://zerobit-site-g094.onrender.com/research/which-retail-trading-mistakes-matter-most/ Tue, 17 Mar 2026 00:00:00 +0000 One lecture ranks account-wrecking habits from treating a signal as certain to trusting a gain screenshot. The costly ones skip statistics and chase a story. https://zerobit-site-g094.onrender.com/research/download-daily-bars-from-interactive-brokers/ https://zerobit-site-g094.onrender.com/research/download-daily-bars-from-interactive-brokers/ Fri, 13 Mar 2026 00:00:00 +0000 Daily US stock bars come from the Interactive Brokers API once socket clients are enabled in Trader Workstation. Connect on port 7497 and save each bar callback to a CSV. https://zerobit-site-g094.onrender.com/research/three-biases-that-fake-a-backtest/ https://zerobit-site-g094.onrender.com/research/three-biases-that-fake-a-backtest/ Tue, 10 Mar 2026 00:00:00 +0000 Look-ahead bias, parameter snooping, and dropped dead firms can all paint a smooth equity curve. Removing each one shows whether a signal was ever there. https://zerobit-site-g094.onrender.com/research/separate-alpha-from-market-beta/ https://zerobit-site-g094.onrender.com/research/separate-alpha-from-market-beta/ Fri, 06 Mar 2026 00:00:00 +0000 A rising equity curve can still be market beta. Compare the strategy with the market over the same dates, including a selloff, before treating leftover return as alpha. https://zerobit-site-g094.onrender.com/research/kalman-filter-for-a-changing-mean/ https://zerobit-site-g094.onrender.com/research/kalman-filter-for-a-changing-mean/ Tue, 03 Mar 2026 00:00:00 +0000 A Kalman filter mixes a fixed mean-reversion model with live prices so the level can drift. The noise setting controls speed, and faster updates bring more whipsaw. https://zerobit-site-g094.onrender.com/research/self-exciting-jumps-and-volatility-clusters/ https://zerobit-site-g094.onrender.com/research/self-exciting-jumps-and-volatility-clusters/ Fri, 27 Feb 2026 00:00:00 +0000 A Hawkes process lets each shock raise the chance of the next, then fade. It clusters jumps and cuts a three-sigma wait from about 370 days to the mid-30s. https://zerobit-site-g094.onrender.com/research/why-market-timing-breaks-on-real-data/ https://zerobit-site-g094.onrender.com/research/why-market-timing-breaks-on-real-data/ Tue, 24 Feb 2026 00:00:00 +0000 A known die lets you trade around 3.5 and compound. After it becomes ten-sided, the old quote loses, and a five can come from either die. The regime stays hidden. https://zerobit-site-g094.onrender.com/research/updating-a-volatility-model-as-quotes-arrive/ https://zerobit-site-g094.onrender.com/research/updating-a-volatility-model-as-quotes-arrive/ Fri, 20 Feb 2026 00:00:00 +0000 A badly tuned mean-reversion model can call a VIX above 60 a 65-billion-year event. A Kalman filter blends that model with new quotes. Noise sets how fast it moves. https://zerobit-site-g094.onrender.com/research/pricing-a-variance-swap-from-listed-options/ https://zerobit-site-g094.onrender.com/research/pricing-a-variance-swap-from-listed-options/ Tue, 17 Feb 2026 00:00:00 +0000 A variance swap pays realized variance minus a strike, in cash at expiry. The fair strike is a risk-neutral value replicated by a strip of puts and calls. https://zerobit-site-g094.onrender.com/research/common-mistakes-in-quant-comment-threads/ https://zerobit-site-g094.onrender.com/research/common-mistakes-in-quant-comment-threads/ Fri, 13 Feb 2026 00:00:00 +0000 A comment thread mixes backtest habits, a false résumé, and a 93 percent win rate. The replies separate political risk, sample size, and the size of the losses. https://zerobit-site-g094.onrender.com/research/what-implied-volatility-actually-measures/ https://zerobit-site-g094.onrender.com/research/what-implied-volatility-actually-measures/ Tue, 10 Feb 2026 00:00:00 +0000 Implied volatility is the input that makes a Black-Scholes price match the market. It looks forward. Realized volatility looks back. The smile runs across strikes. https://zerobit-site-g094.onrender.com/research/the-market-risk-diversification-leaves/ https://zerobit-site-g094.onrender.com/research/the-market-risk-diversification-leaves/ Fri, 06 Feb 2026 00:00:00 +0000 Nine stocks in three sectors can track the S&P 500 once firm and industry risk are diluted. Extra tech exposure that beats the index is beta, and betas jump in stress. https://zerobit-site-g094.onrender.com/research/what-quant-trading-changes-in-practice/ https://zerobit-site-g094.onrender.com/research/what-quant-trading-changes-in-practice/ Tue, 03 Feb 2026 00:00:00 +0000 Everyone sees the same past data. A quant model turns it into an expectation, such as implied volatility rich to realized, and has to be rebuilt when that gap breaks. https://zerobit-site-g094.onrender.com/research/five-projects-that-opened-quant-doors/ https://zerobit-site-g094.onrender.com/research/five-projects-that-opened-quant-doors/ Fri, 30 Jan 2026 00:00:00 +0000 A pricing library, a mortgage chain, a Gaussian cookbook, a long blog, and a volatility system are five projects credited for research and market-making interviews. https://zerobit-site-g094.onrender.com/research/simulating-memory-with-a-volterra-kernel/ https://zerobit-site-g094.onrender.com/research/simulating-memory-with-a-volterra-kernel/ Tue, 27 Jan 2026 00:00:00 +0000 A Volterra process builds a Gaussian path from past shocks only. The kernel sets the covariance, so one scheme can mimic Brownian motion, mean reversion, or a rough path. https://zerobit-site-g094.onrender.com/research/building-a-live-implied-volatility-surface/ https://zerobit-site-g094.onrender.com/research/building-a-live-implied-volatility-surface/ Fri, 23 Jan 2026 00:00:00 +0000 A Python screen pulls SPY option quotes, keeps strikes within 2 percent of spot, and draws implied volatility by strike and expiry. A lock button freezes the picture. https://zerobit-site-g094.onrender.com/research/why-option-prices-ignore-your-forecast/ https://zerobit-site-g094.onrender.com/research/why-option-prices-ignore-your-forecast/ Tue, 20 Jan 2026 00:00:00 +0000 Two traders can disagree on the drift and still share one option price. A complete-model hedge removes the drift. Live prices come from the volatility surface. https://zerobit-site-g094.onrender.com/research/counting-rare-events-in-markets/ https://zerobit-site-g094.onrender.com/research/counting-rare-events-in-markets/ Fri, 16 Jan 2026 00:00:00 +0000 A Poisson model counts rare events at a fixed rate, with exponential waits between them. Markets cluster, so the rate is allowed to move with time and with recent shocks. https://zerobit-site-g094.onrender.com/research/why-bet-size-changes-a-wealth-path/ https://zerobit-site-g094.onrender.com/research/why-bet-size-changes-a-wealth-path/ Tue, 13 Jan 2026 00:00:00 +0000 A positive average does not keep a proportional bet safe. Most paths go broke until the stake follows Kelly, and half of that fraction is the cautious version. https://zerobit-site-g094.onrender.com/research/five-papers-behind-modern-pricing/ https://zerobit-site-g094.onrender.com/research/five-papers-behind-modern-pricing/ Fri, 09 Jan 2026 00:00:00 +0000 Five results shape this map of quant finance: Bachelier, Sharpe on beta and alpha, Black-Scholes, Dupire's local volatility, and Carr-Madan pricing by Fourier transform. https://zerobit-site-g094.onrender.com/research/how-many-dice-maximize-one-six/ https://zerobit-site-g094.onrender.com/research/how-many-dice-maximize-one-six/ Tue, 06 Jan 2026 00:00:00 +0000 The chance of exactly one six is the same at five dice and at six. A continuous maximum near 5.48 sits between them, so both counts are optimal. https://zerobit-site-g094.onrender.com/research/alpha-versus-riding-the-market/ https://zerobit-site-g094.onrender.com/research/alpha-versus-riding-the-market/ Fri, 02 Jan 2026 00:00:00 +0000 Two simulated funds can share a Sharpe ratio near 2.5 while one is mostly market exposure and the other is not. Alpha is the piece left after that exposure is removed. https://zerobit-site-g094.onrender.com/research/profitable-history-versus-a-tradable-edge/ https://zerobit-site-g094.onrender.com/research/profitable-history-versus-a-tradable-edge/ Tue, 30 Dec 2025 00:00:00 +0000 A strategy can show a positive average in 2020-2023 and a negative one afterward if the gain distribution shifts. Stable regimes are what this lecture calls tradable. https://zerobit-site-g094.onrender.com/research/how-to-study-quant-topics-in-order/ https://zerobit-site-g094.onrender.com/research/how-to-study-quant-topics-in-order/ Fri, 26 Dec 2025 00:00:00 +0000 A three-level map runs from coding and algebra up to stochastic calculus. Traders stop earlier in math than researchers. Each level ends with a check. https://zerobit-site-g094.onrender.com/research/what-poker-shows-about-a-backtest/ https://zerobit-site-g094.onrender.com/research/what-poker-shows-about-a-backtest/ Tue, 23 Dec 2025 00:00:00 +0000 Pocket aces win when nobody changes behavior, then lose when opponents do. Folding big action restored a positive expectation by cutting the average loss. https://zerobit-site-g094.onrender.com/research/classifying-live-volatility-with-markov-states/ https://zerobit-site-g094.onrender.com/research/classifying-live-volatility-with-markov-states/ Fri, 19 Dec 2025 00:00:00 +0000 Three volatility states, percentile labels, and a Gaussian update turn five-second bars into a live regime. The fit uses recent bars and can be recomputed on demand. https://zerobit-site-g094.onrender.com/research/pricing-options-when-no-formula-exists/ https://zerobit-site-g094.onrender.com/research/pricing-options-when-no-formula-exists/ Tue, 16 Dec 2025 00:00:00 +0000 If a pricing equation has no closed form, the same no-arbitrage price is an expectation you can average by simulation. The paths must come from the model you claim. https://zerobit-site-g094.onrender.com/research/building-a-live-volatility-regime-feed/ https://zerobit-site-g094.onrender.com/research/building-a-live-volatility-regime-feed/ Fri, 12 Dec 2025 00:00:00 +0000 A live regime screen records five-second bars from a broker feed and refits on the last 60 bars. The first build is the data shell. The classifier comes next. https://zerobit-site-g094.onrender.com/research/why-one-backtest-mixes-different-trades/ https://zerobit-site-g094.onrender.com/research/why-one-backtest-mixes-different-trades/ Tue, 09 Dec 2025 00:00:00 +0000 The same entry at two times can draw from different gain distributions if history matters. Pooling those trades is why many backtests misread a strategy. https://zerobit-site-g094.onrender.com/research/three-steps-toward-a-quant-role/ https://zerobit-site-g094.onrender.com/research/three-steps-toward-a-quant-role/ Fri, 05 Dec 2025 00:00:00 +0000 This hiring path is skill first, a conversation that creates the interview second, and the technical round third. Freezing usually means the material is not mastered yet. https://zerobit-site-g094.onrender.com/research/how-market-makers-set-a-fair-quote/ https://zerobit-site-g094.onrender.com/research/how-market-makers-set-a-fair-quote/ Tue, 02 Dec 2025 00:00:00 +0000 A market maker quotes around an expected value, half a spread in a simple dice market. For options that value is a model price, and hedges plus a bad model consume it. https://zerobit-site-g094.onrender.com/research/which-college-majors-suit-quant-work/ https://zerobit-site-g094.onrender.com/research/which-college-majors-suit-quant-work/ Fri, 28 Nov 2025 00:00:00 +0000 On this ranking, mathematics sits alone at the top if you learn it to use it. Data science is next. Finance and computer science rank lowest for most quant seats. https://zerobit-site-g094.onrender.com/research/why-two-option-prices-agree/ https://zerobit-site-g094.onrender.com/research/why-two-option-prices-agree/ Tue, 25 Nov 2025 00:00:00 +0000 Black-Scholes hedging and the no-arbitrage expectation look like different prices. Under the model's own assumptions, a physics identity shows they are the same function. https://zerobit-site-g094.onrender.com/research/what-three-quant-interviews-showed/ https://zerobit-site-g094.onrender.com/research/what-three-quant-interviews-showed/ Fri, 21 Nov 2025 00:00:00 +0000 Three early interviews pointed to one filter: sit only for the job you want, follow what the interviewer leans into, and do the work before anyone is paying you. https://zerobit-site-g094.onrender.com/research/how-text-becomes-an-equity-signal/ https://zerobit-site-g094.onrender.com/research/how-text-becomes-an-equity-signal/ Tue, 18 Nov 2025 00:00:00 +0000 News and posts can be turned into scores, linked to a company, and sorted into a long-short equity book. The hard part is noise, negation, and a pattern that may fade. https://zerobit-site-g094.onrender.com/research/a-working-reading-list-for-quants/ https://zerobit-site-g094.onrender.com/research/a-working-reading-list-for-quants/ Fri, 14 Nov 2025 00:00:00 +0000 Treat quant books as a lab: pricing, machine learning, text, and linear algebra, plus three Stoic anchors. Read a chapter, build something, then reopen the book. https://zerobit-site-g094.onrender.com/research/what-neural-networks-learn-in-finance/ https://zerobit-site-g094.onrender.com/research/what-neural-networks-learn-in-finance/ Tue, 11 Nov 2025 00:00:00 +0000 A neural network fits an expectation, not a future price. That helps approximate a stable pricing function, and it fails when the return distribution keeps moving. https://zerobit-site-g094.onrender.com/research/learning-quant-finance-without-prestige/ https://zerobit-site-g094.onrender.com/research/learning-quant-finance-without-prestige/ Fri, 07 Nov 2025 00:00:00 +0000 A quant path can start with weak high-school math and a non-target campus if the work is pricing, probability, and projects you can explain in an interview. https://zerobit-site-g094.onrender.com/research/why-sample-means-look-normal/ https://zerobit-site-g094.onrender.com/research/why-sample-means-look-normal/ Tue, 04 Nov 2025 00:00:00 +0000 Sample averages tend toward a bell curve even when each return does not. A shifting market can still make that fixed curve understate the chance of a losing block. https://zerobit-site-g094.onrender.com/research/when-trading-is-not-a-fixed-edge-game/ https://zerobit-site-g094.onrender.com/research/when-trading-is-not-a-fixed-edge-game/ Fri, 31 Oct 2025 00:00:00 +0000 A dice market quoted at 2 and 4 expects a gain of 0.5 a trade, and paths approach it. Grocery prices and stock trades do not. There the policy has to change. https://zerobit-site-g094.onrender.com/research/brownian-motion-and-a-terminal-price/ https://zerobit-site-g094.onrender.com/research/brownian-motion-and-a-terminal-price/ Tue, 28 Oct 2025 00:00:00 +0000 Brownian motion starts at zero and spreads with time. A European call is the expected discounted payoff under that terminal law. Long samples approach the model price. https://zerobit-site-g094.onrender.com/research/why-a-fixed-return-model-breaks/ https://zerobit-site-g094.onrender.com/research/why-a-fixed-return-model-breaks/ Fri, 24 Oct 2025 00:00:00 +0000 A fixed return histogram can look like an edge and then draw down, because the generating distribution moves. A 99.8 percent game price is a quote, not a chance. https://zerobit-site-g094.onrender.com/research/casino-edge-and-a-market-makers-spread/ https://zerobit-site-g094.onrender.com/research/casino-edge-and-a-market-makers-spread/ Tue, 21 Oct 2025 00:00:00 +0000 Roulette, craps, and slots pay the house about 5.26, 1.4, and 2 to 15 percent per play. A bank's analogue is a hedged bid-ask spread, which is still not a locked gain. https://zerobit-site-g094.onrender.com/research/three-trading-myths-checked-with-expected-value/ https://zerobit-site-g094.onrender.com/research/three-trading-myths-checked-with-expected-value/ Fri, 17 Oct 2025 00:00:00 +0000 A 50.5 percent win rate can blow up while a 30 percent win rate stays stable. Roulette odds are fixed. Market odds are not, and no rule stays optimal. https://zerobit-site-g094.onrender.com/research/reading-an-earnings-volatility-crush/ https://zerobit-site-g094.onrender.com/research/reading-an-earnings-volatility-crush/ Tue, 14 Oct 2025 00:00:00 +0000 One Nvidia earnings date cut implied volatility from 43.5 to 32.1 percent while the shares barely moved. A short-volatility position would have gained that day. https://zerobit-site-g094.onrender.com/research/quant-signals-and-discretionary-policies/ https://zerobit-site-g094.onrender.com/research/quant-signals-and-discretionary-policies/ Fri, 10 Oct 2025 00:00:00 +0000 American roulette pays the player -5.26 percent a spin. An election price can read 80 percent and still be one vote. Quant and discretion differ in the actions. https://zerobit-site-g094.onrender.com/research/emoji-sentiment-and-cross-sectional-returns/ https://zerobit-site-g094.onrender.com/research/emoji-sentiment-and-cross-sectional-returns/ Tue, 07 Oct 2025 00:00:00 +0000 Emoji sentiment, after standard controls, still lines up with later returns in one campus study. One standard deviation maps to more than 5 percent a year there. https://zerobit-site-g094.onrender.com/research/why-a-trading-policy-cannot-be-handed-over/ https://zerobit-site-g094.onrender.com/research/why-a-trading-policy-cannot-be-handed-over/ Fri, 03 Oct 2025 00:00:00 +0000 Roulette's player edge is about -0.0526 per dollar. Doubling after losses is banned. Poker and trading need a changing policy, and that policy is learned. https://zerobit-site-g094.onrender.com/research/hidden-states-behind-a-return-distribution/ https://zerobit-site-g094.onrender.com/research/hidden-states-behind-a-return-distribution/ Tue, 30 Sep 2025 00:00:00 +0000 A single normal fit puts extreme Nvidia moves centuries apart. Three volatility states fatten the tails. A hidden chain learns regimes you do not name. https://zerobit-site-g094.onrender.com/research/what-poker-and-trading-both-train/ https://zerobit-site-g094.onrender.com/research/what-poker-and-trading-both-train/ Fri, 26 Sep 2025 00:00:00 +0000 Firms host poker because both games reward a policy, not one lucky hand. Roulette's edge is fixed and negative. A poker action can change that expectation. https://zerobit-site-g094.onrender.com/research/markov-chains-for-a-loan-book/ https://zerobit-site-g094.onrender.com/research/markov-chains-for-a-loan-book/ Tue, 23 Sep 2025 00:00:00 +0000 A loan cannot become 90 days late in a single month. A Markov chain allows only the steps a month can produce, and a matrix power gives the odds many months out. https://zerobit-site-g094.onrender.com/research/when-a-backtest-ratio-is-not-enough/ https://zerobit-site-g094.onrender.com/research/when-a-backtest-ratio-is-not-enough/ Fri, 19 Sep 2025 00:00:00 +0000 Win rate, monthly cash, and a high Sharpe ratio describe the past. The lecture's test is whether a live book still resembles that past before crowding or a regime shift. https://zerobit-site-g094.onrender.com/research/what-arch-and-garch-capture/ https://zerobit-site-g094.onrender.com/research/what-arch-and-garch-capture/ Tue, 16 Sep 2025 00:00:00 +0000 ARCH lets variance depend on recent squared shocks, so tails fatten and volatility clusters. GARCH adds lagged variance. A short GARCH can stand in for a very long ARCH. https://zerobit-site-g094.onrender.com/research/luck-skill-and-a-zero-edge-book/ https://zerobit-site-g094.onrender.com/research/luck-skill-and-a-zero-edge-book/ Fri, 12 Sep 2025 00:00:00 +0000 A zero-edge day-trading book still produces big winners. In one run, 7 of 100 gained over 50 percent. A positive-edge book left 11 of 100 down. https://zerobit-site-g094.onrender.com/research/repricing-a-straddle-after-volatility-falls/ https://zerobit-site-g094.onrender.com/research/repricing-a-straddle-after-volatility-falls/ Tue, 09 Sep 2025 00:00:00 +0000 A short straddle gains if implied volatility falls and the shares stay put. On one Nvidia chain, a drop to 20 percent volatility showed a gain a 10-point slide erased. https://zerobit-site-g094.onrender.com/research/what-a-time-series-forecast-is/ https://zerobit-site-g094.onrender.com/research/what-a-time-series-forecast-is/ Fri, 05 Sep 2025 00:00:00 +0000 A time-series forecast is an expectation if the recent pattern continues. It is not a call on a break. Filtering estimates the present. Smoothing estimates the past. https://zerobit-site-g094.onrender.com/research/volatility-crush-as-an-insurance-sale/ https://zerobit-site-g094.onrender.com/research/volatility-crush-as-an-insurance-sale/ Tue, 02 Sep 2025 00:00:00 +0000 Implied volatility often falls after an event, and a short option gains if spot sits still. A large share move can overwhelm that drop, as one Dell straddle showed. https://zerobit-site-g094.onrender.com/research/implied-probability-versus-a-coin-flip/ https://zerobit-site-g094.onrender.com/research/implied-probability-versus-a-coin-flip/ Fri, 29 Aug 2025 00:00:00 +0000 A coin flip's average settles on one half. An implied probability, from odds or option prices, is where the money sits. It is not a frequency from a thousand repeats. https://zerobit-site-g094.onrender.com/research/reading-a-forward-volatility-regression/ https://zerobit-site-g094.onrender.com/research/reading-a-forward-volatility-regression/ Tue, 26 Aug 2025 00:00:00 +0000 Regress next-month implied volatility on today's level. In one Nvidia window the high-vol fit was stronger, and the live reading sat near the split. https://zerobit-site-g094.onrender.com/research/retail-books-and-institutional-desks/ https://zerobit-site-g094.onrender.com/research/retail-books-and-institutional-desks/ Fri, 22 Aug 2025 00:00:00 +0000 Retail trading lives one path in liquid markets. A sell-side desk quotes both sides. A buy-side book raises capital for a signal that shrinks as that capital grows. https://zerobit-site-g094.onrender.com/research/pricing-heston-with-a-fourier-inversion/ https://zerobit-site-g094.onrender.com/research/pricing-heston-with-a-fourier-inversion/ Tue, 19 Aug 2025 00:00:00 +0000 Carr and Madan damp a call so its Fourier transform exists, swap in the Heston characteristic function, and invert. The price comes back without a new Monte Carlo run. https://zerobit-site-g094.onrender.com/research/finite-differences-for-option-pricing/ https://zerobit-site-g094.onrender.com/research/finite-differences-for-option-pricing/ Fri, 15 Aug 2025 00:00:00 +0000 Finite differences turn a pricing differential equation into a recurrence. Start from a boundary value, step with a small increment, and the grid fills in the price. https://zerobit-site-g094.onrender.com/research/solving-geometric-brownian-motion/ https://zerobit-site-g094.onrender.com/research/solving-geometric-brownian-motion/ Tue, 12 Aug 2025 00:00:00 +0000 Geometric Brownian motion is solved by a logarithm and Ito's lemma. The price is lognormal. A payoff that depends on the whole path still has to be simulated. https://zerobit-site-g094.onrender.com/research/how-the-kelly-fraction-sizes-a-bet/ https://zerobit-site-g094.onrender.com/research/how-the-kelly-fraction-sizes-a-bet/ Fri, 08 Aug 2025 00:00:00 +0000 Kelly sizing bets a fraction of the bankroll from the win rate and the payoff per unit risked. A noisy estimate of those inputs can wipe out the improvement. https://zerobit-site-g094.onrender.com/research/what-a-network-learns-from-a-dice-roll/ https://zerobit-site-g094.onrender.com/research/what-a-network-learns-from-a-dice-roll/ Tue, 05 Aug 2025 00:00:00 +0000 A network trained on dice rolls learns the mean, about 3.5, not the next face. The same object is a conditional expectation, stable for a face and unstable for a stock. https://zerobit-site-g094.onrender.com/research/what-an-edge-is-in-a-simple-market/ https://zerobit-site-g094.onrender.com/research/what-an-edge-is-in-a-simple-market/ Fri, 01 Aug 2025 00:00:00 +0000 An edge is a positive expected gain from the action you choose. A dice market has a fixed level of 3.5. Live markets move, and one path can still go broke. https://zerobit-site-g094.onrender.com/research/why-monte-carlo-estimates-settle/ https://zerobit-site-g094.onrender.com/research/why-monte-carlo-estimates-settle/ Tue, 29 Jul 2025 00:00:00 +0000 Monte Carlo works when every draw comes from one fixed distribution. The sample average then settles on the true mean, which is how a game or an option gets a price. https://zerobit-site-g094.onrender.com/research/how-a-desk-prices-a-barrier-option/ https://zerobit-site-g094.onrender.com/research/how-a-desk-prices-a-barrier-option/ Fri, 25 Jul 2025 00:00:00 +0000 A barrier option pays only if the path misses a level. Price it with a model fitted to listed options, then adjust the raw average for risk, liquidity, and margin. https://zerobit-site-g094.onrender.com/research/what-an-ito-integral-computes/ https://zerobit-site-g094.onrender.com/research/what-an-ito-integral-computes/ Tue, 22 Jul 2025 00:00:00 +0000 An Ito integral is a random variable, not one area under a curve. It adds a weight times each Brownian increment, and a closed form still contains that noise. https://zerobit-site-g094.onrender.com/research/implied-volatility-surface-and-quote-consistency/ https://zerobit-site-g094.onrender.com/research/implied-volatility-surface-and-quote-consistency/ Fri, 18 Jul 2025 00:00:00 +0000 Implied volatility is the input that makes Black-Scholes match a market price. One volatility cannot price every strike and expiry, because real surfaces are not flat. https://zerobit-site-g094.onrender.com/research/why-itos-lemma-keeps-a-second-order-term/ https://zerobit-site-g094.onrender.com/research/why-itos-lemma-keeps-a-second-order-term/ Tue, 15 Jul 2025 00:00:00 +0000 Ordinary calculus drops higher powers of a tiny step. Ito's lemma keeps one of them, because the square of a Brownian increment acts like elapsed time. https://zerobit-site-g094.onrender.com/research/gamblers-ruin-for-a-trading-system/ https://zerobit-site-g094.onrender.com/research/gamblers-ruin-for-a-trading-system/ Fri, 11 Jul 2025 00:00:00 +0000 Gambler's ruin is the chance of going broke before a wealth target. With moving win rates and payoffs, a trading system's chance is only an estimate from past trades. https://zerobit-site-g094.onrender.com/research/karhunen-loeve-series-brownian-bridge/ https://zerobit-site-g094.onrender.com/research/karhunen-loeve-series-brownian-bridge/ Tue, 08 Jul 2025 00:00:00 +0000 The Brownian bridge is a random path pinned at both ends. Its Karhunen-Loeve series builds that path from sine waves and independent normal draws. https://zerobit-site-g094.onrender.com/research/quant-trading-versus-games-of-chance/ https://zerobit-site-g094.onrender.com/research/quant-trading-versus-games-of-chance/ Fri, 04 Jul 2025 00:00:00 +0000 Roulette fixes the house edge, and one path can finish flat while the average rises. Poker and trading change the edge by acting. A good average can still lose. https://zerobit-site-g094.onrender.com/research/davies-harte-fractional-brownian-motion/ https://zerobit-site-g094.onrender.com/research/davies-harte-fractional-brownian-motion/ Fri, 27 Jun 2025 00:00:00 +0000 Fractional Brownian motion sums fractional Gaussian noise. Davies-Harte builds the noise with a Fourier embedding. At 64 steps the variance error was about 10 percent. https://zerobit-site-g094.onrender.com/research/broken-assumptions-and-risk-numbers/ https://zerobit-site-g094.onrender.com/research/broken-assumptions-and-risk-numbers/ Fri, 20 Jun 2025 00:00:00 +0000 Amazon daily returns in 2021-2022 had kurtosis 6.35, so a normal tail estimate was too thin. Correlation and a moving mean bend risk the other way. https://zerobit-site-g094.onrender.com/research/implied-versus-realized-volatility/ https://zerobit-site-g094.onrender.com/research/implied-versus-realized-volatility/ Fri, 13 Jun 2025 00:00:00 +0000 A 30-day realized volatility roughly tracks a known 20 percent level and lags if the level moves. Implied volatility is the input that matches an option's market price. https://zerobit-site-g094.onrender.com/research/trading-as-a-changing-game/ https://zerobit-site-g094.onrender.com/research/trading-as-a-changing-game/ Fri, 06 Jun 2025 00:00:00 +0000 A fair dollar coin has expected wealth of zero. Once the heads chance wanders, a 30-flip estimate can skip bad stretches. The same estimate on both sides stops the trade. https://zerobit-site-g094.onrender.com/research/why-expected-stock-returns-do-not-settle/ https://zerobit-site-g094.onrender.com/research/why-expected-stock-returns-do-not-settle/ Fri, 30 May 2025 00:00:00 +0000 A die's average settles at 3.5 because every roll shares one distribution. Nvidia's cumulative mean return does not settle across 2008, 2016, or 2024. https://zerobit-site-g094.onrender.com/research/why-mean-variance-weights-fail/ https://zerobit-site-g094.onrender.com/research/why-mean-variance-weights-fail/ Fri, 23 May 2025 00:00:00 +0000 On three games with fixed odds, an optimized mix lifted a Sharpe ratio from 1.83 to about 1.92. The same fit on stocks chases a history that will not repeat. https://zerobit-site-g094.onrender.com/research/monte-carlo-prices-match-black-scholes/ https://zerobit-site-g094.onrender.com/research/monte-carlo-prices-match-black-scholes/ Fri, 16 May 2025 00:00:00 +0000 Sample averages approach the expectation as draws accumulate. Success chance 0.7 averaged 0.711. An option simulation printed 10.4504 beside a formula price of 10.45. https://zerobit-site-g094.onrender.com/research/pricing-as-the-expected-payout/ https://zerobit-site-g094.onrender.com/research/pricing-as-the-expected-payout/ Fri, 09 May 2025 00:00:00 +0000 A coin paying 2 dollars on heads has expected payout 1 dollar. Pay 1 and average ending wealth is near zero. A die prices at 3.50. One toy option averaged about 6.70. https://zerobit-site-g094.onrender.com/research/normal-returns-portfolio-mean-annuity-due/ https://zerobit-site-g094.onrender.com/research/normal-returns-portfolio-mean-annuity-due/ Tue, 06 May 2025 00:00:00 +0000 Mean 7 percent and standard deviation 2 percent put a return below 5 percent at probability 15.87 percent. Three weights give 9.3 percent. An annuity due ends at 1,195. https://zerobit-site-g094.onrender.com/research/pca-of-stock-returns-market-industry/ https://zerobit-site-g094.onrender.com/research/pca-of-stock-returns-market-industry/ Fri, 02 May 2025 00:00:00 +0000 Four stock-return series from 2021-2022 gave a first component near 55 percent that looked like the market. Three components cleared 90 percent. https://zerobit-site-g094.onrender.com/research/fundamental-theorem-area-and-related-rates/ https://zerobit-site-g094.onrender.com/research/fundamental-theorem-area-and-related-rates/ Tue, 29 Apr 2025 00:00:00 +0000 An integral up to x squared has derivative 2 times x times sin of x squared. The area between the parabola and the line y = 4 is 32/3. A related-rate spill grows at 10 pi. https://zerobit-site-g094.onrender.com/research/lagged-returns-do-not-predict/ https://zerobit-site-g094.onrender.com/research/lagged-returns-do-not-predict/ Fri, 25 Apr 2025 00:00:00 +0000 A scatter of S&P 500 returns against the previous day is a cloud around zero. A line scored about 0.99 in sample and 33.50 later. A neural net scored 0.952 and 33.75. https://zerobit-site-g094.onrender.com/research/paper-trading-bot-with-an-llm/ https://zerobit-site-g094.onrender.com/research/paper-trading-bot-with-an-llm/ Fri, 18 Apr 2025 00:00:00 +0000 The bot stores symbols, drawdown levels, and an on-off flag, then sends one-share paper orders. A language model reads the book and answers. It does not choose entries. https://zerobit-site-g094.onrender.com/research/uniform-and-binomial-probability-practice/ https://zerobit-site-g094.onrender.com/research/uniform-and-binomial-probability-practice/ Tue, 15 Apr 2025 00:00:00 +0000 A flat density of 1/8 on 0 to 8 puts probability 1/2 on the stretch from 2 to 6. Two fair dice total 7 or 11 in 8 of 36 outcomes. Eight fair trials use a binomial count. https://zerobit-site-g094.onrender.com/research/diversify-firm-and-sector-risk/ https://zerobit-site-g094.onrender.com/research/diversify-firm-and-sector-risk/ Fri, 11 Apr 2025 00:00:00 +0000 Thirty simulated stocks had 7 percent drift and 20 percent volatility. Equal weight kept market risk and washed out single-name luck. A down market lost about 7 percent. https://zerobit-site-g094.onrender.com/research/neural-nets-that-learn-option-prices/ https://zerobit-site-g094.onrender.com/research/neural-nets-that-learn-option-prices/ Fri, 04 Apr 2025 00:00:00 +0000 A network can mimic Black-Scholes inside its training box. One row priced at 30.449 came back as 30.679. The useful case is a slow model, such as Heston, learned offline. https://zerobit-site-g094.onrender.com/research/tariff-shock-in-a-discounted-cash-flow/ https://zerobit-site-g094.onrender.com/research/tariff-shock-in-a-discounted-cash-flow/ Fri, 28 Mar 2025 00:00:00 +0000 A no-tariff cash-flow sketch values the firm at 400. Tariffs cut near-term flows, then the second sketch lets the firm reoptimize. The gap is a model, not a buy signal. https://zerobit-site-g094.onrender.com/research/option-greeks-as-linear-approximations/ https://zerobit-site-g094.onrender.com/research/option-greeks-as-linear-approximations/ Fri, 21 Mar 2025 00:00:00 +0000 Delta, theta, vega, and rho are slopes of a Black-Scholes price. Near current inputs, a one-point stock move matched a delta near 0.64. Farther away, the line missed. https://zerobit-site-g094.onrender.com/research/measure-progress-with-a-rolling-mean/ https://zerobit-site-g094.onrender.com/research/measure-progress-with-a-rolling-mean/ Fri, 14 Mar 2025 00:00:00 +0000 One score is a noisy draw around a moving level. A seven-period mean tracked the practice tests as they rose, while the full-history mean lagged and overstated downside. https://zerobit-site-g094.onrender.com/research/daily-delta-hedging-and-option-prices/ https://zerobit-site-g094.onrender.com/research/daily-delta-hedging-and-option-prices/ Fri, 07 Mar 2025 00:00:00 +0000 Delta is an option's slope against the stock. Selling a 10.45 call and hedging daily left scattered gains. More frequent hedges pulled the average toward that premium. https://zerobit-site-g094.onrender.com/research/numerical-derivative-from-the-definition/ https://zerobit-site-g094.onrender.com/research/numerical-derivative-from-the-definition/ Fri, 28 Feb 2025 00:00:00 +0000 The derivative is the limit of a rise over a small step. With a step of 0.0001, the cube x cubed at 1 gives 3.0003, against the exact slope 3. https://zerobit-site-g094.onrender.com/research/martingale-betting-and-volatility-risk/ https://zerobit-site-g094.onrender.com/research/martingale-betting-and-volatility-risk/ Fri, 21 Feb 2025 00:00:00 +0000 Doubling after each loss recovers the opening stake only with unlimited capital and no bet cap. A finite bankroll, or a short volatility bet, runs out of room first. https://zerobit-site-g094.onrender.com/research/two-digit-mental-multiplication-method/ https://zerobit-site-g094.onrender.com/research/two-digit-mental-multiplication-method/ Fri, 14 Feb 2025 00:00:00 +0000 Split one factor into tens and ones, multiply, and add. Seven products took 4 minutes 51 seconds. Six were right. One miss came from a rushed partial product. https://zerobit-site-g094.onrender.com/research/what-black-scholes-is-actually-pricing/ https://zerobit-site-g094.onrender.com/research/what-black-scholes-is-actually-pricing/ Fri, 07 Feb 2025 00:00:00 +0000 Black-Scholes returns a discounted average payoff, not a forecast. Buying the sample call at 14.10 versus a 14.23 model value still lost on single paths. https://zerobit-site-g094.onrender.com/research/three-dice-market-making-practice-game/ https://zerobit-site-g094.onrender.com/research/three-dice-market-making-practice-game/ Fri, 31 Jan 2025 00:00:00 +0000 Three dice hide part of a total while you buy, sell, or quote a spread. The rounds show how a fair price, a one-sided fill, and a balanced book each change the result. https://zerobit-site-g094.onrender.com/research/when-a-trading-edge-fades-over-time/ https://zerobit-site-g094.onrender.com/research/when-a-trading-edge-fades-over-time/ Fri, 24 Jan 2025 00:00:00 +0000 A rule with win chance 0.55, average win 10, and average loss 8 starts with a positive edge. If the win chance drifts toward 0.4, the equity curve flattens. https://zerobit-site-g094.onrender.com/research/why-a-trading-edge-is-hard-to-estimate/ https://zerobit-site-g094.onrender.com/research/why-a-trading-edge-is-hard-to-estimate/ Fri, 17 Jan 2025 00:00:00 +0000 Edge multiplies typical wins and losses by how often each occurs. Those inputs move, and a short sample estimates them badly. A positive number is not a gain promise. https://zerobit-site-g094.onrender.com/research/control-variates-for-monte-carlo-error/ https://zerobit-site-g094.onrender.com/research/control-variates-for-monte-carlo-error/ Fri, 10 Jan 2025 00:00:00 +0000 A control variate subtracts a known-mean extra from each payoff. The target price stays put, and the lecture's toy run cut variance by about three quarters. https://zerobit-site-g094.onrender.com/research/inverse-transform-sampling-from-a-cdf/ https://zerobit-site-g094.onrender.com/research/inverse-transform-sampling-from-a-cdf/ Fri, 03 Jan 2025 00:00:00 +0000 Draw a number from zero to one, then read it backward through the cumulative distribution. That map reproduces a die roll or an exponential draw when the inverse exists. https://zerobit-site-g094.onrender.com/research/gradient-descent-noise-and-annealing/ https://zerobit-site-g094.onrender.com/research/gradient-descent-noise-and-annealing/ Sat, 15 Jun 2024 00:00:00 +0000 Training walks downhill on an error surface. Plain steps stop in the nearest valley. Noise, or a cooling rule that sometimes steps uphill, can search for a deeper valley. https://zerobit-site-g094.onrender.com/research/march-2024-economy-and-yield-curve/ https://zerobit-site-g094.onrender.com/research/march-2024-economy-and-yield-curve/ Mon, 04 Mar 2024 00:00:00 +0000 Early March 2024 showed a hot stock tape, firm jobs, inflation nearer 2 percent, and an inverted Treasury curve. The lecture reads that mix as a snapshot, not a signal. https://zerobit-site-g094.onrender.com/research/expected-tosses-until-three-heads/ https://zerobit-site-g094.onrender.com/research/expected-tosses-until-three-heads/ Tue, 27 Feb 2024 00:00:00 +0000 First-step analysis gives the mean wait for three heads as 1/p plus 1/p squared plus 1/p cubed. A fair coin gives 14, and 10,000 trials averaged about 13.87. https://zerobit-site-g094.onrender.com/research/markov-chains-three-heads-coin-questions/ https://zerobit-site-g094.onrender.com/research/markov-chains-three-heads-coin-questions/ Tue, 20 Feb 2024 00:00:00 +0000 Four streak states turn coin-run questions into matrix powers. Those powers separate ever seeing three heads, ending on them, and first hitting them at toss n. https://zerobit-site-g094.onrender.com/research/n-step-odds-in-a-two-coin-markov-chain/ https://zerobit-site-g094.onrender.com/research/n-step-odds-in-a-two-coin-markov-chain/ Mon, 12 Feb 2024 00:00:00 +0000 Two coins plus a heads-or-tails switch form a Markov chain. Coin one on day two has probability 0.65. Longer dates use powers of the one-step matrix. https://zerobit-site-g094.onrender.com/research/when-expected-value-is-infinite/ https://zerobit-site-g094.onrender.com/research/when-expected-value-is-infinite/ Fri, 09 Feb 2024 00:00:00 +0000 A fair game that pays two to the power of the first tails has infinite expected payout. Repeated averages wander, so the usual limit theorems do not apply. https://zerobit-site-g094.onrender.com/research/price-of-a-consecutive-heads-game/ https://zerobit-site-g094.onrender.com/research/price-of-a-consecutive-heads-game/ Fri, 02 Feb 2024 00:00:00 +0000 Pay D each time heads follows heads in n flips. Expected payout is (n minus 1) times p squared times D. A fair coin and a one-dollar prize pays 0.25 on two flips. https://zerobit-site-g094.onrender.com/research/density-of-a-minimum-of-three-uniforms/ https://zerobit-site-g094.onrender.com/research/density-of-a-minimum-of-three-uniforms/ Fri, 26 Jan 2024 00:00:00 +0000 When three independent uniform returns sit on zero to one, the minimum has distribution function 1 minus (1 minus z) cubed, and density 3 times (1 minus z) squared. https://zerobit-site-g094.onrender.com/research/executive-pay-and-2021-prices/ https://zerobit-site-g094.onrender.com/research/executive-pay-and-2021-prices/ Mon, 22 Jan 2024 00:00:00 +0000 In one 2021 large-cap cut, top stock awards did not track that year's return. Log awards tilted up with price, and total pay stayed mostly flat across the price range. https://zerobit-site-g094.onrender.com/research/brownian-paths-from-normal-draws/ https://zerobit-site-g094.onrender.com/research/brownian-paths-from-normal-draws/ Fri, 19 Jan 2024 00:00:00 +0000 A Brownian path is a running sum of normal steps. Over 252 unit days, many paths end near mean zero and variance 252. An array build is the practical way to make them. https://zerobit-site-g094.onrender.com/research/what-a-large-tweet-panel-shows/ https://zerobit-site-g094.onrender.com/research/what-a-large-tweet-panel-shows/ Mon, 15 Jan 2024 00:00:00 +0000 A Russell 3000 tweet panel of about 100 million posts shows longer messages over time, a duplicate share near 15 percent, and about 55 to 60 percent naming one ticker. https://zerobit-site-g094.onrender.com/research/normal-moments-from-one-function/ https://zerobit-site-g094.onrender.com/research/normal-moments-from-one-function/ Mon, 08 Jan 2024 00:00:00 +0000 A normal moment generating function is an exponential. Derivatives at zero are the moments. Brownian motion then has mean zero and variance equal to elapsed time. https://zerobit-site-g094.onrender.com/research/what-a-critical-value-is/ https://zerobit-site-g094.onrender.com/research/what-a-critical-value-is/ Fri, 05 Jan 2024 00:00:00 +0000 A critical value is the cutoff with a chosen left-tail probability. On the standard normal curve, the cutoff for 95 percent to the left is about 1.65. https://zerobit-site-g094.onrender.com/research/mean-variance-and-correlation/ https://zerobit-site-g094.onrender.com/research/mean-variance-and-correlation/ Fri, 29 Dec 2023 00:00:00 +0000 A mean is a probability-weighted sum, not the most common outcome. Shifts move the mean and leave variance alone. Correlation rescales covariance onto minus one to one. https://zerobit-site-g094.onrender.com/research/test-a-mean-without-the-full-distribution/ https://zerobit-site-g094.onrender.com/research/test-a-mean-without-the-full-distribution/ Mon, 18 Dec 2023 00:00:00 +0000 A hypothesis test can ask which side of a field holds the ball without knowing the raw distribution. A large sample makes the average nearly normal. https://zerobit-site-g094.onrender.com/research/poisson-maximum-likelihood-estimate/ https://zerobit-site-g094.onrender.com/research/poisson-maximum-likelihood-estimate/ Mon, 11 Dec 2023 00:00:00 +0000 For Poisson counts, maximum likelihood picks the sample average. A simulated hospital with true rate 85 recovered about 84.8, and a full-bed chance near 5 percent. https://zerobit-site-g094.onrender.com/research/stocktwits-and-analyst-spreads/ https://zerobit-site-g094.onrender.com/research/stocktwits-and-analyst-spreads/ Mon, 04 Dec 2023 00:00:00 +0000 On rating day, StockTwits tone and the buy-minus-sell spread sloped up together. The fit was statistically detectable and still weak. It is a lead, not a cause. https://zerobit-site-g094.onrender.com/research/same-day-sentiment-and-returns/ https://zerobit-site-g094.onrender.com/research/same-day-sentiment-and-returns/ Fri, 01 Dec 2023 00:00:00 +0000 Same-day StockTwits tone and same-day returns lined up across daily quartiles. One long-short book in the lecture had a Sharpe near 2.3, and it was not tradable. https://zerobit-site-g094.onrender.com/research/what-a-95-percent-interval-means/ https://zerobit-site-g094.onrender.com/research/what-a-95-percent-interval-means/ Mon, 27 Nov 2023 00:00:00 +0000 A 95 percent interval is not a 95 percent chance that the mean lies between two fixed ends. About 95 of 100 intervals built the same way would cover the fixed mean. https://zerobit-site-g094.onrender.com/research/law-of-large-numbers-and-sampling-means/ https://zerobit-site-g094.onrender.com/research/law-of-large-numbers-and-sampling-means/ Wed, 22 Nov 2023 00:00:00 +0000 Averages of uniform, normal, or Poisson draws lock onto the true mean as samples grow, and those averages form a bell. That is why a text sample can still be tested. https://zerobit-site-g094.onrender.com/research/pass-by-value-versus-reference/ https://zerobit-site-g094.onrender.com/research/pass-by-value-versus-reference/ Fri, 14 Apr 2023 00:00:00 +0000 Copies passed into a function cannot swap the caller's numbers. A pointer or a C++ reference reaches the originals, and the same three assignments then exchange them. https://zerobit-site-g094.onrender.com/research/what-a-cpp-pointer-stores/ https://zerobit-site-g094.onrender.com/research/what-a-cpp-pointer-stores/ Fri, 07 Apr 2023 00:00:00 +0000 A C++ pointer holds an address, not a second copy of the integer. Reading it shows the value. Writing through it changes the original, because both names share one slot. https://zerobit-site-g094.onrender.com/research/why-option-prices-need-a-stock-process/ https://zerobit-site-g094.onrender.com/research/why-option-prices-need-a-stock-process/ Thu, 05 Jan 2023 00:00:00 +0000 Strike and expiry of a European call are known today. The stock at expiry is not, so a price process is how today's information becomes a distribution you can price. https://zerobit-site-g094.onrender.com/research/java-interactive-brokers-connection/ https://zerobit-site-g094.onrender.com/research/java-interactive-brokers-connection/ Mon, 28 Nov 2022 00:00:00 +0000 A Java bot reaches Interactive Brokers through a gateway, a jar on the classpath, and callbacks. A reader thread holds the socket. Crypto needs API version 10.2 or newer. https://zerobit-site-g094.onrender.com/research/pytorch-gpu-matrix-speedup/ https://zerobit-site-g094.onrender.com/research/pytorch-gpu-matrix-speedup/ Wed, 23 Nov 2022 00:00:00 +0000 A huge matrix product took about 23 seconds on a CPU and about 3 seconds on a free GPU, once the clock waited for the device. Training a network speeds up the same way. https://zerobit-site-g094.onrender.com/research/tetlock-pessimism-factor-and-costs/ https://zerobit-site-g094.onrender.com/research/tetlock-pessimism-factor-and-costs/ Wed, 12 Oct 2022 00:00:00 +0000 A pessimism score from one news column lined up with 8.1 basis points of next-day index return. The 7.3 percent strategy did not survive modest trading costs. https://zerobit-site-g094.onrender.com/research/deep-learning-for-rough-volatility/ https://zerobit-site-g094.onrender.com/research/deep-learning-for-rough-volatility/ Wed, 05 Oct 2022 00:00:00 +0000 Rough-volatility prices are slow to simulate. A small network can learn the map first, and a barrier-option check in the paper stayed under 10 basis points of error. https://zerobit-site-g094.onrender.com/research/workshop-or-project-deep-dive/ https://zerobit-site-g094.onrender.com/research/workshop-or-project-deep-dive/ Wed, 03 Aug 2022 00:00:00 +0000 Use one workshop for a single technique. Use a deep dive when you can name a public repo, such as a trading system or qfin, and the behavior you want to change. https://zerobit-site-g094.onrender.com/research/compound-interest-and-time-value/ https://zerobit-site-g094.onrender.com/research/compound-interest-and-time-value/ Mon, 01 Aug 2022 00:00:00 +0000 Money now can earn interest that money later misses. Compounding more often in the year raises the ending amount, and the continuous limit of that amount stays finite. https://zerobit-site-g094.onrender.com/research/two-ways-to-fit-a-line-in-python/ https://zerobit-site-g094.onrender.com/research/two-ways-to-fit-a-line-in-python/ Wed, 27 Jul 2022 00:00:00 +0000 Least squares has one best line. A matrix formula and a library fit, run on the same ten noisy points, agreed once both answers were rounded to five decimals. https://zerobit-site-g094.onrender.com/research/european-call-and-put-payoffs/ https://zerobit-site-g094.onrender.com/research/european-call-and-put-payoffs/ Mon, 25 Jul 2022 00:00:00 +0000 A European call pays at expiry only when the stock beats the strike. Puts reverse that gap. The premium is paid up front and changes gain, not the payoff. https://zerobit-site-g094.onrender.com/research/sample-a-normal-curve-in-python/ https://zerobit-site-g094.onrender.com/research/sample-a-normal-curve-in-python/ Wed, 20 Jul 2022 00:00:00 +0000 NumPy can draw standard normal numbers, a short function can trace the bell, and a library call can return the chance of falling below a cutoff. https://zerobit-site-g094.onrender.com/research/what-a-normal-curve-tells-you/ https://zerobit-site-g094.onrender.com/research/what-a-normal-curve-tells-you/ Mon, 18 Jul 2022 00:00:00 +0000 A normal curve is set by its mean and variance. Roughly 68, 95, and 99.7 percent of outcomes fall inside one, two, and three standard deviations. https://zerobit-site-g094.onrender.com/research/linear-independence-for-model-features/ https://zerobit-site-g094.onrender.com/research/linear-independence-for-model-features/ Wed, 13 Jul 2022 00:00:00 +0000 Vectors are linearly independent when only zero weights sum them to zero. Dependent features repeat each other and cannot cover the space a model needs. https://zerobit-site-g094.onrender.com/research/python-threads-for-market-checks/ https://zerobit-site-g094.onrender.com/research/python-threads-for-market-checks/ Wed, 06 Jul 2022 00:00:00 +0000 A price check that loops forever blocks later code. Threads run two checks on separate clocks, and a flag stops them without restarting the program. https://zerobit-site-g094.onrender.com/research/learn-python-with-one-stock-chart/ https://zerobit-site-g094.onrender.com/research/learn-python-with-one-stock-chart/ Wed, 29 Jun 2022 00:00:00 +0000 Learn Python by finishing one interactive stock app: charts, indicators, and a date window. Beginners start at the base; people who already code skip ahead. https://zerobit-site-g094.onrender.com/research/simulate-correlated-brownian-paths/ https://zerobit-site-g094.onrender.com/research/simulate-correlated-brownian-paths/ Wed, 22 Jun 2022 00:00:00 +0000 Give two Brownian paths a chosen correlation with a matrix factor or with one formula. A finite sample landed near the target, not exactly on it. https://zerobit-site-g094.onrender.com/research/five-python-habits-for-quant-code/ https://zerobit-site-g094.onrender.com/research/five-python-habits-for-quant-code/ Wed, 15 Jun 2022 00:00:00 +0000 Slice notation, string splits, column filters, least squares, and saved objects cover most daily quant Python. Here is what each does and where it breaks. https://zerobit-site-g094.onrender.com/research/back-out-implied-volatility-from-price/ https://zerobit-site-g094.onrender.com/research/back-out-implied-volatility-from-price/ Wed, 08 Jun 2022 00:00:00 +0000 Implied volatility is the Black-Scholes input that matches a traded option price. One Apple call solves near 31.38 percent and reprices the three-dollar quote. https://zerobit-site-g094.onrender.com/research/approximate-an-integral-with-random-samples/ https://zerobit-site-g094.onrender.com/research/approximate-an-integral-with-random-samples/ Wed, 01 Jun 2022 00:00:00 +0000 Monte Carlo integration averages a function on uniform draws and multiplies by the interval length. For 4x cubed from 0 to 2, 10,000 draws give about 15.985 versus 16. https://zerobit-site-g094.onrender.com/research/derive-the-black-scholes-merton-pde/ https://zerobit-site-g094.onrender.com/research/derive-the-black-scholes-merton-pde/ Wed, 25 May 2022 00:00:00 +0000 Hedging a call with delta shares removes the random term under geometric Brownian motion. The lesson sets that riskless change equal to the riskless return. https://zerobit-site-g094.onrender.com/research/fit-a-line-with-the-matrix-formula/ https://zerobit-site-g094.onrender.com/research/fit-a-line-with-the-matrix-formula/ Wed, 18 May 2022 00:00:00 +0000 Least squares picks the intercept and slope that minimize squared errors. In matrix form the coefficients are the inverse of X transpose X, times X transpose y. https://zerobit-site-g094.onrender.com/research/read-a-linear-subscriber-growth-chart/ https://zerobit-site-g094.onrender.com/research/read-a-linear-subscriber-growth-chart/ Wed, 11 May 2022 00:00:00 +0000 A subscriber series in this session looks nearly straight, and the average daily gain is about 1.88. A two-point slope check is about 2. No 2023 total is fitted. https://zerobit-site-g094.onrender.com/research/why-portfolio-weights-drift-apart/ https://zerobit-site-g094.onrender.com/research/why-portfolio-weights-drift-apart/ Wed, 04 May 2022 00:00:00 +0000 A 50-50 Amazon and Apple book bought in 2020 and never reset ends near 40 percent Amazon and 60 percent Apple. The one-time value is about 18,552 from 10,000. https://zerobit-site-g094.onrender.com/research/see-why-option-delta-is-a-tangent/ https://zerobit-site-g094.onrender.com/research/see-why-option-delta-is-a-tangent/ Wed, 27 Apr 2022 00:00:00 +0000 Delta is the slope of a Black-Scholes call against the spot. At spot 85 the lesson's call is about 5.0931 with delta about 0.3476, and the line peels away later. https://zerobit-site-g094.onrender.com/research/why-a-unit-root-fools-a-price-regression/ https://zerobit-site-g094.onrender.com/research/why-a-unit-root-fools-a-price-regression/ Wed, 20 Apr 2022 00:00:00 +0000 Regressing Apple's next close on today's close gives an R-squared near 0.998. The same fit on returns falls to about 0.015 because the price has a unit root. https://zerobit-site-g094.onrender.com/research/plot-price-paths-with-streamlit/ https://zerobit-site-g094.onrender.com/research/plot-price-paths-with-streamlit/ Wed, 13 Apr 2022 00:00:00 +0000 Streamlit sliders can drive a qfin geometric Brownian motion simulator and redraw a line chart. The lesson's price slider runs from 0 to 100 and starts at 50. https://zerobit-site-g094.onrender.com/research/what-an-empty-intro-recording-contains/ https://zerobit-site-g094.onrender.com/research/what-an-empty-intro-recording-contains/ Wed, 06 Apr 2022 00:00:00 +0000 The April 6, 2022 recording is only a greeting. It has no lesson, no formulas, and no market result to report. https://zerobit-site-g094.onrender.com/research/simulate-the-bachelier-model-in-python/ https://zerobit-site-g094.onrender.com/research/simulate-the-bachelier-model-in-python/ Fri, 25 Mar 2022 00:00:00 +0000 A Bachelier path adds volatility times a normal shock times the square root of the step. The lesson draws 100 of those driftless paths across one year with 252 steps. https://zerobit-site-g094.onrender.com/research/derive-the-bachelier-call-price/ https://zerobit-site-g094.onrender.com/research/derive-the-bachelier-call-price/ Wed, 23 Mar 2022 00:00:00 +0000 The Bachelier forward is a driftless Brownian move, and it is a martingale. The call price is the expected positive payoff, reduced to normal probabilities. https://zerobit-site-g094.onrender.com/research/three-properties-of-brownian-motion/ https://zerobit-site-g094.onrender.com/research/three-properties-of-brownian-motion/ Mon, 21 Mar 2022 00:00:00 +0000 Brownian motion starts at zero, is almost surely continuous, and has independent normal increments. A five-day sketch shows the cloud, and the integral is the end value. https://zerobit-site-g094.onrender.com/research/compare-p-quants-and-q-quants/ https://zerobit-site-g094.onrender.com/research/compare-p-quants-and-q-quants/ Fri, 18 Mar 2022 00:00:00 +0000 Q quants calibrate continuous models to today's listed prices. P quants forecast with large discrete data sets. A rich option versus a model price sits on the border. https://zerobit-site-g094.onrender.com/research/code-geometric-brownian-motion-paths/ https://zerobit-site-g094.onrender.com/research/code-geometric-brownian-motion-paths/ Wed, 16 Mar 2022 00:00:00 +0000 A Python loop samples geometric Brownian motion by multiplying the last price by an exponential step. A demo starts at 100, with 30 percent volatility and 100 paths. https://zerobit-site-g094.onrender.com/research/solve-geometric-brownian-motion/ https://zerobit-site-g094.onrender.com/research/solve-geometric-brownian-motion/ Mon, 14 Mar 2022 00:00:00 +0000 Geometric Brownian motion solves through a log transform and Ito's lemma. The later price equals the start times an exponential of drift and a Brownian move. https://zerobit-site-g094.onrender.com/research/price-a-call-with-a-one-step-tree/ https://zerobit-site-g094.onrender.com/research/price-a-call-with-a-one-step-tree/ Wed, 21 Jul 2021 00:00:00 +0000 A one-step tree prices a call by holding delta shares so both branches match. The lesson's numbers give delta of one third and a call price of about 4.70. https://zerobit-site-g094.onrender.com/research/read-call-and-put-payoff-at-expiry/ https://zerobit-site-g094.onrender.com/research/read-call-and-put-payoff-at-expiry/ Thu, 15 Jul 2021 00:00:00 +0000 At expiration a call pays the positive gap between spot and strike, and a put pays the gap the other way. Two XYZ cases and a 50-50 example show the arithmetic. https://zerobit-site-g094.onrender.com/research/backtest-a-moving-average-crossover/ https://zerobit-site-g094.onrender.com/research/backtest-a-moving-average-crossover/ Sat, 26 Jun 2021 00:00:00 +0000 A pandas backtest of SPY goes long when the 7-day average exceeds the 14-day average and short otherwise. The lesson's Sharpe for that test prints near 0.697. https://zerobit-site-g094.onrender.com/research/what-the-qfin-python-library-prices/ https://zerobit-site-g094.onrender.com/research/what-the-qfin-python-library-prices/ Thu, 24 Jun 2021 00:00:00 +0000 qfin prices European calls and puts with Black-Scholes and runs Monte Carlo on several exotic payoffs. Geometric Brownian motion or the Heston model drives the paths. https://zerobit-site-g094.onrender.com/research/why-money-today-differs-from-later/ https://zerobit-site-g094.onrender.com/research/why-money-today-differs-from-later/ Sun, 31 Jan 2021 00:00:00 +0000 A sum today and a sum later differ because interest connects them across time. This first session frames present value, continuous time, and a spreadsheet comparison. https://zerobit-site-g094.onrender.com/research/hedge-delta-gamma-and-vega-together/ https://zerobit-site-g094.onrender.com/research/hedge-delta-gamma-and-vega-together/ Sat, 16 Jan 2021 00:00:00 +0000 Shares can flatten delta, but gamma and vega need other options. A short Nvidia call book is offset with two listed calls, then about 46 shares clear the leftover delta. https://zerobit-site-g094.onrender.com/research/apply-itos-lemma-to-an-option-portfolio/ https://zerobit-site-g094.onrender.com/research/apply-itos-lemma-to-an-option-portfolio/ Mon, 06 Jul 2020 00:00:00 +0000 Ito's lemma gives the change in an option value that depends on time and a random price. A fixed contract count scales that change into the portfolio. https://zerobit-site-g094.onrender.com/research/show-live-broker-data-in-flask/ https://zerobit-site-g094.onrender.com/research/show-live-broker-data-in-flask/ Thu, 18 Jun 2020 00:00:00 +0000 A Flask page can show a live broker cache by reading the trading object's lists on a POST route. Ajax refreshes that HTML about once a second while the feed runs. https://zerobit-site-g094.onrender.com/research/refresh-a-flask-page-with-ajax/ https://zerobit-site-g094.onrender.com/research/refresh-a-flask-page-with-ajax/ Wed, 10 Jun 2020 00:00:00 +0000 Ajax can replace one HTML fragment on a timer by posting to a Flask route. The lesson redraws a random number every second without reloading the whole page. https://zerobit-site-g094.onrender.com/research/show-python-results-with-flask/ https://zerobit-site-g094.onrender.com/research/show-python-results-with-flask/ Tue, 02 Jun 2020 00:00:00 +0000 Flask serves a small Python web app on port 5000 and renders an HTML file. Jinja drops a Python variable into that page so a browser can show server-side results. https://zerobit-site-g094.onrender.com/research/cache-live-option-ticks-in-python/ https://zerobit-site-g094.onrender.com/research/cache-live-option-ticks-in-python/ Mon, 01 Jun 2020 00:00:00 +0000 Live option ticks disappear unless the callback stores them. Three lists on the wrapper keep delta, the option price, and the underlying price when a field changes. https://zerobit-site-g094.onrender.com/research/stream-live-option-quotes-in-python/ https://zerobit-site-g094.onrender.com/research/stream-live-option-quotes-in-python/ Fri, 29 May 2020 00:00:00 +0000 A live option stream starts with a contract plus a market-data request. The wrapper callback prints the option price and the underlying price as ticks arrive. https://zerobit-site-g094.onrender.com/research/connect-python-to-interactive-brokers/ https://zerobit-site-g094.onrender.com/research/connect-python-to-interactive-brokers/ Thu, 28 May 2020 00:00:00 +0000 An Interactive Brokers session in Python pairs a request client with a callback wrapper. A paper-trading login on the local gateway is enough to prove the link. https://zerobit-site-g094.onrender.com/research/build-a-delta-neutral-volatility-position/ https://zerobit-site-g094.onrender.com/research/build-a-delta-neutral-volatility-position/ Wed, 27 May 2020 00:00:00 +0000 A short call hedged with shares can isolate a volatility view from the stock's direction. Delta sets the share count, and that hedge must be reset as the spot moves. https://zerobit-site-g094.onrender.com/research/price-a-european-call-with-monte-carlo/ https://zerobit-site-g094.onrender.com/research/price-a-european-call-with-monte-carlo/ Tue, 26 May 2020 00:00:00 +0000 Monte Carlo prices a European call by averaging discounted payoffs across simulated paths. One worked case uses 1,000 paths and prints 160.75 against a 154.46 quote. https://zerobit-site-g094.onrender.com/research/estimate-a-probability-with-monte-carlo/ https://zerobit-site-g094.onrender.com/research/estimate-a-probability-with-monte-carlo/ Mon, 25 May 2020 00:00:00 +0000 Monte Carlo estimates a probability by repeating a random trial and averaging the successes. A 70 percent shooter and 10,000 rounds of 100 shots show the method. https://zerobit-site-g094.onrender.com/research/simulate-geometric-brownian-motion-paths/ https://zerobit-site-g094.onrender.com/research/simulate-geometric-brownian-motion-paths/ Sun, 24 May 2020 00:00:00 +0000 A geometric Brownian motion path steps a price by drift and a volatility-scaled normal shock. This page shows the class, the one-year loop, and the plot. https://zerobit-site-g094.onrender.com/research/run-python-work-on-several-threads/ https://zerobit-site-g094.onrender.com/research/run-python-work-on-several-threads/ Sun, 24 May 2020 00:00:00 +0000 Python threads let several waits run together. A two-second task done four times in a line takes four waits; started on four threads, it finishes in one.