FH-WORKING PAPERS

JUMP DIFFUSION MODELS FOR OPTION PRICING VS. THE BLACK SCHOLES MODEL

Authors
Patrick Burger
Marcus Kliaras
Publication date
15.05.2013
Course of studies
Banking and FinanceQuantitative Asset and Risk Management

ABSTRACT

In our complex and developed financial world the Brownian motion and the normal distribution have obtained enormous impact on the prices of option contracts traded on the stock exchange or over the counter. Due to empirical investigations during the last years two points have emerged which cannot be assumed to pertain to each option price calculation. The two points are that the return distribution of a stock does not always follow a normal distribution but has a higher peak and two heavier tails than those of the normal distribution and that there is a “volatility smile” in option pricing. The Black-Scholes approach implies that volatility is a constant function. This paper theoretically and empirically investigates three different option pricing approaches: the Black-Scholes approach, the Merton-Jump approach, and the double exponential jump diffusion model, which was proposed by Kou (2001) and Ramezani and Zeng (1998).
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