Numerical Methods in Finance

Prerequisites: some familiarity with the basic principles of partial differential equations, probability and stochastic processes, and of mathematical finance as provided, e.g. in MATH W5010. Prerequisites: some familiarity with the basic principles of partial differential equations, probability and stochastic processes, and of mathematical finance as provided, e.g. in MATH W5010. Review of the basic numerical methods for partial differential equations, variational inequalities and free-boundary problems. Numerical methods for solving stochastic differential equations; random number generation, Monte Carlo techniques for evaluating path-integrals, numerical techniques for the valuation of American, path-dependent and barrier options.