Theory library
Option pricing, factor models, portfolio math, market microstructure — each piece explained in plain language, with exactly the math an interviewer expects you to reproduce.
What the CLT actually guarantees, where the normal distribution comes from, and why real return distributions have fat tails that the normal badly understates.
From coin-flip walks to Brownian motion: the square-root-of-time law, where it comes from, and how it prices risk, spreads, and option value.
Markowitz portfolio math from first principles: why variances add with a covariance term, where the free lunch of diversification comes from, and what the Sharpe ratio actually measures.
The logic of the CAPM, what beta and alpha really are, and how Fama-French and modern factor models generalize the idea into the workhorse of quantitative equity.
Deriving the Kelly fraction, why over-betting is ruinous while under-betting is merely slow, and how fractional Kelly connects to real-world position sizing.
The no-arbitrage principle, forwards priced by replication, and put-call parity — the model-free backbone of every derivatives interview.
Price an option on a one-step tree with pure replication, discover risk-neutral probability, and see how the tree's limit becomes the Black-Scholes formula.
Delta, gamma, theta, and vega as a working system — including the gamma-theta trade-off that defines what it means to be long or short options.
Order books, the components of the bid-ask spread, and the Glosten-Milgrom logic of adverse selection — the theory behind every market-making interview game.
Stationarity, the Ornstein-Uhlenbeck process, pairs trading and cointegration — how stat arb works and how it fails.
What a martingale is, the optional stopping theorem, and how one theorem dissolves gambler's ruin, biased-walk, and clever-stopping-rule interview questions.