Mathematics in Financial Engineering

Catalog description

This course introduces the mathematical foundations of modern financial engineering through the discrete-time binomial asset-pricing model. We develop the key ideas of no-arbitrage, replication, risk-neutral pricing, state prices, and martingales in a rigorous but accessible discrete-time setting. Topics include the one-period and multiperiod binomial models, probability theory on coin-toss spaces, state-price deflators and change of measure, pricing and optimal exercise of American options, random walks and first-passage times, and interest-rate-dependent securities such as bonds and interest-rate derivatives. The course is designed for undergraduates in mathematics, statistics, or engineering with an interest in financial engineering, and it provides a solid conceptual and mathematical bridge to continuous-time models and stochastic calculus. Knowledge of Python proficiency required. | Prerequisites: One of (MA-UY.2114, MATH-UA.123, MATH-UA.133) AND (MA-UY.1044, MA-UY.2034, MA-UY.3054, MATH-UA.140, MATH-UA.148) AND One of (MA-UY.2224, MA-UY.3014, MA-UY. 3514, MATH-UA.333, MATH-UA.338)