Advanced Topics in Mathematical Finance

3 credits · Graduate Programs

Topics include specific areas of mathematical finance and build on Mathematics 681 and 683. Monte Carlo Methods for Quantitative Finance: random number generation, simulation of stochastic differential equations, option valuation, variance reduction techniques, quasi-Monte Carlo methods, computing `greeks', valuation of path-dependent and early-exercise options; applications to risk management; Markov Chain Monte Carlo methods. Energy, Commodity and Environmental Finance: energy and commodity markets; spot, futures, forwards and swap contracts; the theory of storage; stochastic models for energy prices; model calibration; emissions market modelling; weather derivatives; energy risk management; energy option valuation. Advanced Topics in Mathematical Finance: An introduction to some of the main ideas in mathematical and computational finance through a guided reading of some seminal papers from the last 100 years, starting with Bachelier's 1900 thesis, and including papers by Samuelson, Markowitz, Black & Scholes, Merton, Hull & White, Schwartz, Glasserman, and others. Prerequisite(s): Mathematics 681 and 683 and admission to a graduate program in Mathematics and Statistics.