IE 525

Basic theory of stochastic differential equations and numerical techniques for their analysis with applications to financial modeling. Brownian motion, martingales, stochastic integration, Ito's formula, stochastic differential equations, partial differential equations, simulation methods for derivatives pricing, finite-difference techniques for Black-Scholes equations and options pricing, Monte Carlo methods, variance reduction techniques, and sensitivity calculations. Course Information: 2 graduate hours. No professional credit. May be repeated if topics vary to a maximum of 4 hours. Prerequisite: IE 523.

The course focuses on numerical methods for modeling, pricing and risk management of financial instruments, including derivatives. It covers deterministic methods, such as finite difference methods for ordinary and partial differential equations, explicit and implicit schemes, and free boundary problems for American options. It also examines stochastic methods, such as randomization and anti-gaming, Monte Carlo simulation, including variance reduction and quasi-Monte Carlo. It also studies data-driven financial model calibration and optimization, financial data pattern analysis and synthesis, filtering and machine learning, analytics in high-frequency data environment. Prerequisite: FIN 500.

8/23/2016