Course map
Twenty lessons, one path
From conditional probability to quoting markets against an informed trader: 21 lessons, about 4 hours, then a bank of 50 interview questions from 9 firms. Go in order, or jump to what your next interview needs.
Part 1
Probability
Conditional probability, expectation, variance, the classic distributions and how two random things move together.
- 01Conditional probability and Bayes’ theoremUpdating a belief when evidence arrives, and why a rare base rate beats a convincing witness.
Figures: 3D population model, Bayes square · 12 min · used for: Updating fair value when an order hits you - 02Expected value and linearityThe weighted average that prices every game, and the linearity trick that solves half of all interview questions.
Figures: 3D dice game, Strategy lab, Line-up simulator · 12 min · used for: Pricing any payoff: options, bets, games - 03Variance, and why diversification worksHow spread adds up, the √n rule for averages, and standard deviations as arrows.
Figures: 3D volatility arrows, The √n rule · 10 min · used for: Portfolio risk and diversification - 04The seven distributions you must knowBernoulli, binomial, Poisson, geometric, uniform, normal and exponential: shape, mean, variance and where each one shows up.
Figures: 3D distribution explorer, Cumulative view · 14 min · used for: Order arrivals, defaults, returns, waiting times - 05Joint distributions, covariance and correlationHow two random variables move together, what correlation can’t see, and the three-correlations puzzle.
Figures: 3D joint density, Correlation scatter, Three-correlations bound · 12 min · used for: Hedging, pairs trading, risk models
Part 2
Statistics
Why averages settle down, why they look normal, and how sure you can be about a number you estimated.
- 06The law of large numbers and the central limit theoremAverages converge to the truth, and their errors always look normal, whatever you started with.
Figures: 3D Galton board, CLT sampler, Running averages · 12 min · used for: Trusting a backtest; sizing a sample - 07Confidence intervalsWhat “95% confident” really promises, watched across a hundred repeated experiments.
Figures: Coverage machine · 10 min · used for: Error bars on Sharpe ratios and signal strength
Part 3
Quant research: data science
Least squares, nearest neighbours, bias and variance, regression inference, ridge, lasso, PCA and causality.
- 08Least squares versus nearest neighboursThe two simplest predictors, one rigid and one flexible, and the decision boundaries they draw.
Figures: 3D classifier terrain, Decision-boundary painter · 12 min · used for: Baseline models for any prediction task - 09The bias–variance trade-off and the curse of dimensionalityWhy a model that fits the past perfectly predicts the future badly, and why high dimensions are lonely.
Figures: Overfitting lab, 3D neighbourhood cube · 12 min · used for: Avoiding overfit alpha signals - 10Linear regression: β, the hat matrix, t and FThe one formula to know by heart, what the residual squares are, and how to tell a real coefficient from noise.
Figures: 3D regression plane, Drag-the-points regression · 16 min · used for: Factor models, hedge ratios, beta - 11Ridge, lasso and elastic netShrinking coefficients on purpose, and the geometry that makes lasso set some of them to exactly zero.
Figures: 3D RSS bowl, Constraint geometry, Coefficient paths, Thresholds · 14 min · used for: Combining hundreds of noisy signals - 12Principal componentsRotating the data to the directions where it actually varies, then keeping only the important ones.
Figures: 3D principal components, PCA rotator · 10 min · used for: Yield-curve factors, stat-arb residuals - 13Causality: selection bias, randomisation and omitted variablesWhy correlation isn’t causation, how a coin flip fixes it, and how to size the bias you couldn’t remove.
Figures: Selection-bias simulator, Omitted-variable bias · 14 min · used for: Telling a real effect from a confound
Part 4
Quant research: case studies
Three open-ended modelling questions in the style of Two Sigma and QuantCo, worked end to end.
- 14Case: predicting New York housing pricesA Two Sigma-style case: encode, normalise, log-transform and regress, then deal with correlated inputs.
Figures: Log-transform lab · 10 min · used for: Feature engineering on skewed data - 15Case: pricing seats at an opera houseA QuantCo-style case: nearest neighbours over the seat map, time to the show, and scarcity.
Figures: 3D opera house · 10 min · used for: Dynamic pricing and spatial models - 16Case: forecasting CitiBike demandAn open-ended Two Sigma case: brainstorm inputs, encode time as a circle, and tame correlated weather.
Figures: 3D demand clock, Clock encoder · 10 min · used for: Seasonality in volume and volatility
Part 5
Quant trading: market making
Quoting a bid and an ask, reacting to trades, keeping score of position and PnL, and sizing a bet.
- 17What a market maker doesBid, ask, spread and edge, and the three inputs behind every quote: value, last trade and position.
Figures: 3D order book, Quote builder · 12 min · used for: The day job at Jane Street, Optiver, SIG, IMC - 18Market-making cases, trade by tradeReplay the Red Sox, Tanzania and trade-or-tighten games, and keep score of position and PnL.
Figures: Case replayer · 14 min · used for: The trading interview round - 19Play: make a market on five diceQuote a market while dice are revealed, against a trader who knows more than you do.
Figures: 3D dice market game · 10 min · used for: Practice for the live market-making round - 20Sizing a bet: the Kelly criterionHow much of your bankroll to stake when you have an edge, and why betting twice Kelly gets you nowhere.
Figures: Kelly simulator · 10 min · used for: Position sizing and risk limits - 21Inside high-frequency tradingThe limit order book, queue priority, the economics of a market maker, and why microseconds and the speed of light matter.
Figures: Live 3D order book, Latency ladder · 14 min · used for: The core business of electronic market makers
Part 6
Interview prep
Questions reported from Jane Street, Citadel, Two Sigma, HRT, Optiver, SIG and more, with checked solutions.