Masters Oral Defense: "Statistical Analysis of Short-time Option Prices Based on a L´evy Model"

Weiliang Wang, Washington University in Saint Louis

Abstract: The Black-Scholes model has been widely used to find the price of options, while several generalizations have been made due to its limitation. In this thesis, we consider one of the generalizations—the exponential L´evy model with a mix of CGMY process and Brownian motion. We state the main results of the first, second and third order expansions for close-to-the-money call option price under this model. Using importance sampling based on Monte Carlo method, a dataset of the call option prices can be simulated. Comparing the true value with three difference order approximations, we find that the higher order approximation is more accurate than lower order in most cases, which can be used for calibrating the parameters in the model. We use the Standard & Poor’ s 500 index options price to verify these results.

Hosts: Jimin Ding & Jose Figueroa-Lopez