Computational methods in finance

The overall aim of this unit is to study the fundamental computational methods for solving problems in financial mathematics. This includes a full overview of finite-difference methods for obtaining numerical solutions of partial differential equations, convergence and stability analysis of finite-difference methods, iterative techniques for solving large-scale linear systems arising from numerical solutions of PDEs, the Black-Scholes equation and stochastic volatility models, option pricing, Monte Carlo computation, and selected topics in mathematical finance.