Quant
Quantitative finance: corporate finance, equities, bonds and derivatives, the mathematics of pricing, and the engineering and risk management built on it. Quant has 3 parts, grouped by field. Each subject page lists the subjects it builds on.
Part 1 of 3
Finance foundations
How money, stocks, bonds and derivatives work before any stochastic calculus: discounting, valuation, yields and payoffs.
4 subjects · 5 lessons open · 55 planned
- Corporate finance Time value of money, capital budgeting, capital structure, the cost of capital and real options. 1 lesson open · 9 plannedOpen now: Compounding and discounting
- Equities and portfolios Stock valuation, portfolio choice, the efficient frontier, CAPM and factor models. 10 planned
- Bonds and interest rates Yields, discount curves, duration, convexity and credit spreads. 16 planned
- Derivatives Options, forwards, futures, swaps and their no-arbitrage relations. 4 lessons open · 20 plannedOpen now: Option payoffs and put-call parity, Forward prices by cash-and-carry, No-arbitrage bounds on option prices, When early exercise pays
Part 2 of 3
Financial mathematics
The theory behind pricing: replication and risk-neutral measures, Itô calculus, PDEs, and models for rates and volatility.
5 subjects · 5 lessons open · 24 planned
- Arbitrage and risk-neutral pricing Replication, state prices, self-financing strategies, risk-neutral measures, Girsanov and change of numeraire. 3 lessons open · 7 plannedOpen now: Pricing by replication: one period, State prices and no-arbitrage, Backward induction on a binomial tree
- Stochastic calculus and SDEs The Itô integral, Itô's lemma, local time and stochastic differential equations such as geometric Brownian motion. 1 lesson open · 5 plannedOpen now: The Itô integral
- PDE methods The Black–Scholes PDE, the Feynman–Kac link between PDEs and expectations, and free boundaries. 1 lesson open · 2 plannedOpen now: Delta hedging and the Black–Scholes PDE
- Interest-rate models Short-rate models and forward-rate models: Vasicek, CIR, Hull–White, HJM and the LIBOR market model. 5 planned
- Volatility and jump models Local and stochastic volatility, jumps, SABR and how the smile moves with spot. 5 planned
Part 3 of 3
Financial engineering and risk management
Turning models into numbers: pricing algorithms, hedging and calibration, then measuring market and credit risk.
4 subjects · 33 lessons planned
Pricing and hedging
- Option pricing path A course in 22 steps, in order: discounting, replication, the binomial tree, Brownian motion and Itô calculus, then Black–Scholes and Monte Carlo. 13 of 22 steps open
- Monte Carlo and numerical pricing Monte Carlo, variance reduction, finite differences, Fourier pricing with characteristic functions, American options by regression and simulated Greeks. 8 planned
- Hedging and calibration Discrete hedging error, volatility surfaces, calibration, portfolio insurance and transaction costs. 7 planned