This course focuses on financial mathematics and its applications to a broad array of financial derivative contracts, with emphasis on continuous time stochastic methods and their applications in modern quantitative finance. Students are expected to have a solid foundation in probability theory, calculus, ordinary and partial differential equations, and a basic familiarity with financial instruments.

Tentative topics include, but are not limited to: the no-arbitrage principle and the fundamental theorem of asset pricing; binomial pricing models and their continuous-time limits; Stochastic differential equations; Ito's Lemma; Girsanov's Theorem, the Black-Scholes model; sensitivity measures (Greeks) and hedging strategies; pricing of European, American, Asian, barrier, and other path-dependent options; short-rate models and interest rate derivatives; and stochastic volatility models.