Topics in Mathematics with Applications in Finance (MIT 18.S096)
by Peter Kempthorne, Choongbum Lee, Vasily Strela et al. · MIT OpenCourseWare
Pairs mathematics lectures by MIT faculty with lectures from industry practitioners: linear algebra, probability, time series, volatility modeling, portfolio theory, stochastic calculus and Black-Scholes pricing. Includes 24 lecture videos, lecture slides and problem sets, showing how these quantitative tools are used in finance.
More resources on Financial Mathematics
46-944 Stochastic Calculus for Finance — CMU Course Notes
Free lecture notes and scanned board notes from Carnegie Mellon's graduate stochastic calculus course. Covers martingales, Brownian motion, Itô integrals, Girsanov's theorem, and risk-neutral measures, with homework, exams, and full solutions. Creative Commons licensed.
The Pricing of Options and Corporate Liabilities (1973)
The 1973 Journal of Political Economy paper deriving the option pricing formula from a riskless hedged portfolio argument. Scanned original, hosted by Princeton. Also shows how corporate bonds, stock, and warrants can be valued as options.
Stochastic Calculus for Finance II: Continuous-Time Models
Grew out of Carnegie Mellon's computational finance master's program. Builds measure-theoretic probability, Brownian motion, Itô integration, and risk-neutral pricing, then applies them to exotic options, term structure models, foreign exchange, and jump-diffusion processes.
Financial Calculus: An Introduction to Derivative Pricing
A compact bridge from binomial trees to continuous-time martingale pricing. Develops change of measure, the Girsanov theorem, and the Heath-Jarrow-Morton interest rate framework without heavy measure-theoretic machinery, favoring financial intuition over formal proof. Fills the level gap that otherwise kills people: Hull is too light on theory, Shreve demands measure theory.
Options, Futures, and Other Derivatives (11th Edition)
The standard derivatives reference across trading desks and MFE programs. Covers forwards, futures, swaps, option pricing, the Greeks, volatility smiles, interest rate derivatives, and credit risk, using minimal stochastic calculus before introducing the Black-Scholes-Merton framework. The prerequisite layer for everything else in this topic: you cannot price a derivative with stochastic calculus until you know what the instruments are.