University of Houston
Department of Computer Science

In partial fulfillment of the Requirements for the Degree of
Master of Science


Guowei Zhang
will defend his thesis

Study of the Pricing Methods for Standard European Stock 0ptions:

Dynamic Programming and Monte-Carlo Simulation


Abstract

Dynamic Programming (DP) and Monte-Carlo (MC) simulation are two of the popular numerical methods for pricing financial derivatives used in both financial literature and industry. We carried out these two methods to study the pricing of standard European stock options when their underlying stock price obeys both Hull and White (1987) stochastic volatility process and Merton (1976) jump-diffusion process. We studied the dependence of options price on different parameters in each case. We also compared DP and MC results in both cases. We conformed previous results in the literature about the effects of correlation coefficient between stock price and its volatility in Hull and White’s model and mean return rate, stock price volatility, volatility of jump magnitudes, Poisson arrival rate constant in Merton’s model on corresponding options’ price. We contribute to the literature by studying the effects of mean-reverting constant, stock price’s initial volatility, volatility of variance on options’ price in Hull and White model and giving a quantitative comparison between DP and MC methods by comparing both of the pricing results and the computation time.

Date: Friday, September 6, 2002
Time: 4:00 PM
Place: 550-PGH


Faculty, students, and the general public are invited.
Thesis Advisor: Dr. Stephen Huang