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The Black-Scholes based model has been a useful tool for option pricing in the stock market. Yet there are two phenomena the leptokurtic feature and the implied volatility curve which naturally occur in asset pricing. The model proposed by S. G. Kou not only offers an explanation of the leptokurtic feature and the volatility smile, but also leads to analytical solutions to many option pricing problems such as European call and put options. Our research focuses mainly on the analytical solution of the Kou model in MATlab for the European option using what Kou defines as the Hh function. This function can be viewed as a generalization of the cumulative normal distribution function. More precisely the left tail of the Hh function has a polynomial growth rate, and the right tail has an exponential decay. We also evaluate the integral Kou defines as I_n which is important in option pricing to determine the arbitrary constants alpha, lambda and beta. For our research, we determine these constants in a MATlab code and then use them in Kou's Upsilon function to determine the value of the European option.

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Graduate Research

Primary Advisor

Ruihua Liu

Primary Advisor's Department



Stander Symposium poster

The Kou Jump-Diffusion Model for Option Pricing