21 modules · about 348 study hours · free to read
Markets: A Rigorous Course
Equities, trading, derivatives, commodities, macro and geopolitics, from first principles.
A course for readers who want the models behind markets and the evidence for them. Every result is derived, every model is worked in numbers, and every module ends with problems you can check and code you can test.
Who it is for
- Readers with university mathematics (calculus, linear algebra, probability) who want to trade or invest knowing why a method works and when it fails.
- Practitioners who know the mechanics and want the derivations, the statistics and the base rates behind them.
- Newcomers: the on-ramp module and the sections marked Foundation need only light maths and cover the accounts, orders, instruments and tax you meet first.
- Foundation
- Needed by everyone. Practical, light on maths.
- Core
- The main material: models and derivations a serious trader or investor should know.
- Advanced
- Research-level proofs and extensions. Skippable on the practitioner track; revisit later.
How it is taught
Derivations, not rules of thumb
Results are stated and proved: no-arbitrage pricing, the Kelly criterion, Black–Scholes, the statistics of a backtest. Research-level proofs are marked Advanced and can be skipped on a first reading.
Worked examples in numbers
Each model is worked through on real instruments from Indian and global markets, with costs, margins and tax where they change the answer.
393 problems
Numeric answers are checked as you enter them. Full solutions sit behind a deliberate step, so you try first.
69 Python exercises
Each comes with starter code and a test suite. Write the function, run the tests in a sandbox and read what failed.
74 figures and 29 labs
Interactive figures show a model respond as you move its parameters; the labs apply the methods to market data.
A plan, two journals and a simulator
With a free account: a day-by-day study plan, a forecast journal scored by the Brier score, a paper-trade journal in R-multiples, and an order simulator for paper trading.
Tracks
Three ways through the same material. Each track is a day-by-day plan of sections, problems and exercises.
Practitioner track
8 weeks · about 20 h a week
From zero to confident paper trading: the whole on-ramp, then foundation and core sections, risk limits and the trading plan early, each playbook after its essential reading, and the simulator. Advanced sections and the derivations of the stat-arb tests are skipped; C1 and C4 are started.
Core track
8 weeks · about 25 h a week
Foundation and core sections of every module (advanced sections skipped), all ★ and ★★ problems, one exercise per module, the playbooks; C1 and C4 are started.
Full track
17 weeks · about 25 h a week
Everything, including every problem, exercise and lab, and all four capstones at their minimum viable scope (about 80 hours of capstone work; the full scope of each capstone takes longer, as its brief states).
Parts and modules
334 sections in 21 modules, and 4 capstone projects. Every module is open to read.
Part IFoundations
- M01 Market structure, microstructure and costs 12 h · 15 sections How Indian markets are built: exchanges, clearing, depositories and SEBI; the trading day and the call auctions; the limit order book; circuit breakers; T+1 settlement; the full algebra of costs and taxes; index construction and corporate-action adjustments.
- M02 Statistics of returns 16 h · 15 sections Returns as the object of study: aggregation rules, volatility drag, horizon scaling and variance ratios, what sampling error lets you estimate, the stylized facts, heavy tails and the Hill estimator, volatility clustering, VaR, and dependence between assets.
- M03 The mathematics of betting: expectancy, Kelly, ruin 14 h · 14 sections Expectancy and R-multiples, the Kelly criterion from log utility, overbetting, fractional Kelly, estimation risk, gambler's ruin, drawdown distributions and position sizing in practice.
Part IITrading equities
- M04 Systematic trading research and swing trading 14 h · 11 sections Technical analysis restated as testable hypotheses; swing frameworks (Weinstein, Minervini, O'Neil, Darvas) as rule sets; momentum and reversal evidence; backtesting without bias; the statistics of the Sharpe ratio; multiple testing and the deflated Sharpe ratio.
- M04A Reading markets: charts, volume, breadth and trade management 14 h · 16 sections The practitioner's eye, made rigorous: candlesticks and timeframes, support and resistance, volume, gaps, market breadth and participant data; stops, trailing stops, scaling and time stops derived from first principles; the daily routine and the event calendar.
- M05 Intraday trading and execution 16 h · 15 sections Microstructure models (Roll, Glosten–Milgrom, Kyle), price impact, execution benchmarks and Almgren–Chriss optimal execution; the evidence on intraday strategies, the mathematics of cost drag and why most retail day traders lose.
Part IIIInvesting
- M06 Fundamental analysis and valuation 20 h · 16 sections Reading Indian listed companies; the three statements as one system; DCF and the value-driver formula; cost of capital for India; multiples and reverse DCF; margin of safety as a distribution; forensic accounting; quality frameworks; sector cycles; the Jhunjhunwala, Satyam and Yes Bank cases.
- M06A Corporate events, earnings, sectors and factors 14 h · 19 sections Results season and post-earnings drift; buybacks, demergers, open offers, IPOs and their evidence; promoter and insider disclosures as signals; valuing banks and cyclicals; factor investing in India.
- M06B Funds: mutual funds, ETFs and the asset-management business 16 h · 17 sections How an Indian mutual fund is built (the trust, the AMC, the custodian), how a unit is priced (NAV, cut-offs, stale-price transfers, swing pricing), what it costs under the 2026 regulations and how fee drag compounds, how fund houses make money, SIP arithmetic, measuring skill against luck (Berk–Green), index-fund tracking, ETF creation units and premiums, debt funds and runs, fund taxation, and how to build a fund portfolio.
Part IVDerivatives
- M07 Forwards and futures 16 h · 13 sections The no-arbitrage forward price, futures versus forwards, basis and convergence, Indian index futures and margins, open interest, minimum-variance hedging, and a preview of commodity carry.
- M08 Option pricing: from replication to Black–Scholes 32 h · 16 sections No-arbitrage bounds and parity, binomial replication and the risk-neutral measure, Brownian motion and Itô's lemma, the Black–Scholes PDE and formula, Black-76, the Greeks and implied volatility, with Indian contract specifics.
- M09 Volatility and option trading 18 h · 16 sections Realised-volatility estimators, the P&L of a delta-hedged option, the variance risk premium, the smile, variance swaps and VIX, option strategies with exact profit conditions, expiry-day gamma and why short volatility has negative skew.
- M09A The Indian options desk 14 h · 20 sections The daily instruments of an Indian options trader, with their statistics: the option chain, OI build-up, PCR and max pain, IV rank, event implied moves, participant-wise OI, margins for hedged positions, adjustments and the stock-option settlement trap.
Part VCommodities, macro and geopolitics
- M10 Commodities: gold, silver, crude 16 h · 19 sections Storage theory and convenience yield, roll yield, Hotelling and gold as a durable asset, Indian gold import parity, what drives gold and silver, crude market structure and India's exposure, and MCX contracts.
- M11 Macro: rates, FX and flows 22 h · 21 sections Bond maths, duration and convexity, real rates and the yield curve, the Taylor rule, RBI and Fed transmission, interest parity and the carry trade, the dollar and the rupee, foreign flows, and regimes.
- M12 Geopolitics and event studies 18 h · 12 sections Event-study econometrics, the geopolitical risk index, scenario trees with Bayesian updating, options as geopolitical hedges, transmission channels into Indian prices, and seven case studies from 1990 to 2026.
Part VIPrediction and synthesis
- M13 Forecasting and market prediction 16 h · 13 sections What prediction can mean in near-efficient markets, ARMA, out-of-sample R², GARCH by maximum likelihood, regime switching, machine-learning pitfalls, proper scoring rules and the forecast journal.
- M13A Cointegration, pairs and statistical arbitrage 14 h · 17 sections Unit roots and spurious regression, Engle–Granger and Johansen, Ornstein–Uhlenbeck estimation and optimal bands, Kalman-filter hedge ratios, structural breaks, and Indian pairs and parity trades.
- M14 Portfolio construction, risk, psychology and going live 20 h · 23 sections Mean–variance and its failure, shrinkage, risk parity, volatility targeting, combining strategies, expected shortfall and stress tests, prospect theory and trading psychology, the written trading plan, and the Jhunjhunwala playbook.
Reading is open; an account keeps your work
Every section, problem, exercise and reference page can be read without signing in. A free account keeps your progress, answers, notes and code drafts, and adds the study plan, the journals and the simulator. Running code needs an account approved for it.
Written by Gaurav.