Articles
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.
Vectors as portfolios, matrices as risk models, eigenvalues as factors — the linear algebra quant finance actually uses, with the interview questions it powers.
The two calculus ideas quant interviews live on — second-order Taylor expansions and Jensen's inequality — and how they become duration, gamma, and volatility drag.
Asymptotic complexity from a practitioner's angle: the growth-rate ladder, why hash maps and sorting dominate interview answers, and the classic quant-dev prompts.
The Python that quant screens actually test — comprehensions, generators, vectorized thinking, and the standard-library tools that solve interview problems in three lines.
The bias-variance trade-off, why in-sample performance lies, regularization, and the validation discipline that separates research from curve-fitting.
Trees, ensembles, and neural nets through a market lens — non-stationarity, tiny signal-to-noise, feature engineering, and why simple often wins.
The handful of closed-form sums and approximations — geometric series, Gauss sums, e and log tricks, the rule of 72 — that power fast quant arithmetic.
Permutations, combinations, stars and bars, inclusion-exclusion, and derangements — the counting toolkit behind a huge share of probability questions.
Binomial, Poisson, geometric, exponential, normal, lognormal — what each distribution models, its key numbers, and how to pick the right one instantly.
States, transition matrices, stationary distributions, and first-step analysis — the general machine behind coin-pattern and random-walk interview questions.
Stacks, queues, heaps, hash maps, and trees — what each is actually for, their costs, and the quant-flavored problems each one unlocks.
Overlapping subproblems, memoization vs tabulation, and the four classic DP patterns — with the buy-low-sell-high problem every finance-adjacent interview asks.
What implied volatility actually is, why the smile and skew exist, and how vol surfaces turn Black-Scholes from a model into a language.
Straddles, spreads, butterflies, calendars, and risk reversals — reading each standard option structure as a precise statement about the return distribution.
Logistic regression, precision vs recall, ROC/AUC, and calibration — the classification toolkit, taught through the imbalanced problems finance actually has.
K-means, hierarchical clustering, and PCA as market tools — regime detection, factor extraction, covariance denoising — and the validation problem no labels can solve.
The decomposition method for estimating anything — piano tuners, market sizes, order flow — and the habits that make estimates land within a factor of two.
The general method behind gambler's ruin, expected hitting times, and pattern-waiting problems — solving linear recurrences instead of re-deriving each puzzle.
Dominant strategies, Nash equilibrium, backward induction, and the winner's curse — the strategic reasoning layer under pirate puzzles and market games.
E[X] = E[E[X|Y]] — the law of total expectation, Wald's identity, and the conditioning habit that cracks multi-stage problems in one line.
Distributions of the max and min, uniform spacings, and expected records — the machinery behind best-of-n questions and tail-aware quoting.
Beyond finding elements in sorted arrays: binary search on answers, bisection on monotone conditions, and the off-by-one discipline that interviews test.
Representations, the two traversals and what each is for, topological sort, and Dijkstra — plus the arbitrage-detection question that makes graphs a quant topic.
The latency ladder from L1 cache to cross-ocean networks, queues and backpressure, and the systems intuition trading-firm interviews probe.
When exercising early is optimal and when it never is — dividends, deep-in-the-money puts, and pricing the early-exercise right on a binomial tree.
What happens to the textbook hedge when you rebalance discretely — the gamma-theta P&L identity, hedging error, and the realized-vs-implied bet made explicit.
Autocorrelation, AR and MA models, GARCH volatility — the time-series toolkit, and the honest reason it forecasts volatility well and returns barely.
Layers, activations, gradient descent, and backpropagation without mysticism — plus the honest assessment of where deep learning earns its keep in finance.
Lookahead, survivorship, overfitting, costs, capacity — the complete checklist of ways backtests lie, and the discipline that keeps a strategy honest.
Why big orders move prices against you, the square-root impact law, TWAP/VWAP and implementation shortfall — the cost side of every strategy.
Value-at-Risk and its blind spots, expected shortfall, drawdown math, and the position-limit logic that keeps edges alive long enough to compound.
Remainders as a first-class tool: last digits of huge powers, divisibility rules, and the parity arguments that crack brainteasers instantly.
The three inequalities that answer optimization questions without calculus, and the bounding habits that make estimates rigorous.
The three argument patterns interviews actually test — with the islanders, chessboard, and pigeonhole classics as worked demonstrations.
The law of large numbers with error bars: standard errors, convergence at 1/√n, variance reduction, and when simulating beats solving.
The model of random arrivals in continuous time — superposition, thinning, conditional uniformity, and the waiting-time paradox that fools intuition.
Bayes' theorem rebuilt for streams of evidence — odds form, log-odds addition, and calibrated updating as the core trading skill.
The structure of random orderings — cycle decomposition, the 1/e of derangements, records, and why seven riffle shuffles randomize a deck.
Designing recursive solutions that don't blow up — base cases, state, and the choose-explore-unchoose pattern behind subsets, permutations, and N-Queens.
The bitwise toolkit — masks, shifts, XOR identities, and bitsets — plus the classic find-the-missing-number problems they crack in one line.
The SQL that data-facing quant screens test — aggregation, join semantics, and the window functions that compute returns and rolling stats in-database.
Breeden-Litzenberger — reading the market's probability distribution out of the option chain, and what butterflies, digitals, and the smile say about it.
Trading volatility directly — variance swap mechanics, the log-contract replication idea, how the VIX is built, and the vol risk premium.
Pricing binary and barrier payoffs by building them from vanillas — static replication, reflection tricks, and why discontinuous payoffs make traders nervous.
Ranks, z-scores, neutralization, decay, and point-in-time hygiene — the transformations that turn raw market data into features a model can actually learn from.
MDPs, value functions, and Q-learning in one lesson — plus the honest assessment of where RL genuinely fits in trading and where it's rebranded DP.
From word counts to LLM embeddings, and from satellite images to card panels — how text and alt data become signals, and the pitfalls unique to them.
Discounting, yield to maturity, the price-yield seesaw, duration and convexity — fixed-income fundamentals every quant interview assumes.
Cost-of-carry pricing, contango and backwardation, roll yield, and basis risk — the mechanics of the contracts most trading firms live in.
Loss aversion, anchoring, overconfidence, and the limits of arbitrage — the human regularities behind factor premia, and the interview's favorite mirror.
Market vs funding liquidity, margin spirals, fire sales, and the case studies — LTCM, 2008, March 2020 — that every risk conversation assumes you know.