Lecture, three hours. Limited to Master of Financial Engineering program students. Economic, statistical, and mathematical foundations of derivatives markets. Basic discrete- and continuous-time paradigms used in derivatives finance, including introduction to stochastic processes, stochastic differential equations, Ito's lemma, and key elements of stochastic calculus. Economic foundations of Black/Scholes no-arbitrage paradigm, including introduction to Girsanov's theorem and changes of measure, representation of linear functionals, equivalent martingale measures, risk-neutral valuation, fundamental partial differential equation representations of derivatives prices, market prices of risk, and Feynman/Kac representations of solutions to derivatives prices. Role of market completeness and its implications for hedging and replication of derivatives. S/U or letter grading.