Abstract

The Black-Scholes model has been widely used to find the prices of option, while several generalizations have been made due to its limitation. In this thesis, we consider one of the generalizations---the exponential Levy model with a mixture 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 prices under this model. Using importance sampling based on Monte Carlo method, a dataset of call option prices can be simulated. Comparing the simulated true prices with the three different order approximations, we find that the higher-order approximation is more accurate than the lower-order in most cases, which can be used for calibrating the parameters in the model. In order to verify these results, we use call option prices obtained from the Standard & Poor's 500 index options. The third-order approximation of this real dataset is not as accurate as before.

Committee Chair

Jose E. Figueroa-Lopez

Committee Members

Todd Kuffner, Jimin Ding

Comments

Permanent URL: https://doi.org/10.7936/K74Q7TF4

Degree

Master of Arts (AM/MA)

Author's Department

Mathematics

Author's School

Graduate School of Arts and Sciences

Document Type

Thesis

Date of Award

Spring 5-2018

Language

English (en)

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Mathematics Commons

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