Options Pricing & Stochastic Calculus

Catalog description

This course provides the mathematical foundations of Option Pricing models. The techniques covered include arithmetic and geometric Brownian motion, first passage time, the reflection principle, the stochastic Ito integral, Ito differential Calculus, change of probability measure, martingales, Stochastic Differential Equations and Partial Differential Equations. Some of the pricing models considered are the European, Barrier, Asian and American options. These problems are either solved analytically by the martingale approach or numerically, by applying approximation and simulation methods. Since the same techniques allow the treatment of more complex financial products, examples of credit derivatives will be also presented. This course is a requirement in the Computational Finance Track | Prerequisite: FRE-GY 6083 and matriculation into a master or doctoral program