Leonid N Vaserstein, Thesis Supervisor Dr. Victoria V Sadovskaya, Thesis Honors Advisor James Alan Miles, Thesis Honors Advisor
Keywords:
Finance Options American Put Options Binomial Pricing Model Finite Difference Methods Monte Carlo Simulations
Abstract:
Options valuation is an area of active research in financial mathematics. Fisher Black and Myron Scholes published the most popular closed-form solution for vanilla European options in their 1973 paper, ''The Pricing of Options and Corporate Liabilities.'' The Black-Scholes equation still accurately prices vanilla European options and is still widely used. However, there is no closed-form solution to the pricing of American put options. As such, several numerical methods have been proposed to approximate the price of American put options. The purpose of this paper is to analyze these methods in terms of computational speed and flexibility in adaptation to non-vanilla options. In particular, this paper will focus on the binomial asset pricing model, finite difference schemes, and Monte Carlo methods.