Numerical Valuation of American Options under Exponential Levy Processes
Xinzheng Huang

Site of the project:
TU Delft

start of the project: February 2005

The Master project has been finished in August 2005 ( Masters Thesis). This master project leads to a journal article.

Summary of the master project:
The valuation of American options is of practical importance because the majority of exchange-traded options is American. We focus on numerical issues related to American options since there are no closed form solutions available. We investigate the option price, the optimal exercise boundary and the Greeks (partial derivatives of the option prices). Two models for the dynamics of stock prices are considered: the Black-Scholes model and the variance gamma model. The Black-Scholes model, which marks the beginning of the modern era of financial derivatives and remains dominant in option trading assumes that the log-price of stocks follows a geometric Brownian motion. The variance gamma model is a three parameters model that is obtained by evaluating a Brownian motion at random times given by a gamma process. We deal with the numerical evaluation of partial differential equations and partial integro-differential equations with a coordinate transformation that can be made time-dependent in order to follow the optimal exercise boundary.

Contact information: Kees Vuik

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