Introduction to Merton Jump Diffusion Model

This paper presents everything you need to know about Merton jump diffusion (we call it MJD) model. MJD model is one of the first beyond Black-Scholes model in the sense that it tries to capture the negative skewness and excess kurtosis of the log stock price density ( ) 0 ln( / ) T S S P by a simple addition of a compound Possion jump process. Introduction of this jump process adds three extra parametersλ , μ , and δ (to the original BS model) which give the users to control skewness and excess kurtosis of the ( ) 0 ln( / ) T S S P . Merton’s original approach for pricing is to use the conditional normality of MJD model and expresses the option price as conditional Black-Scholes type solution. But modern approach of its pricing is to use the Fourier transform method by Carr and Madan (1999) which is disccused in Matsuda (2004).