AMS 514, Computational Finance
Review of foundations: stochastic calculus, martingales, pricing, and arbitrage. Basic principles of Monte Carlo and the efficiency and effectiveness of simulation estimators. Generation of pseudo- and quasi-random numbers with sampling methods and distributions. Variance reduction techniques such as control variates, antithetic variates, stratified and Latin hypercube sampling, and importance sampling. Discretization methods including first and second order methods, trees, jumps, and barrier crossings. Applications in pricing American options, interest rate sensitive derivatives, mortgage-backed securities and risk management. Whenever practical, examples will use real market data. Extensive numerical exercises and projects in a general programming environment will also be assigned.
Prerequisite: AMS 512 and 513
3 credits, ABCF grading

Text: A Mathematics of Financial Derivatives: A Student Introduction, by Paul WIlmott, Sam Howison and Jeff Dewynne, most recent ediiton
Cambridge University Press ISBN#0521497892 - Required

Computation Methods for Option Pricing, by Yves Achdou, Olivier Pironneau., most recent edition, SIAM
ISBN#: 9750898715736 - Recommended