Option Pricing Under a Double Exponential Jump Diffusion Model

The double exponential jump diffusion model is one of the models that has been proposed to incorporate the leptokurtic feature (meaning having both high peak and heavy tails in asset return distributions) and the volatility smile. This paper demonstrates that, unlike many other models, the double exponential jump diffusion model can lead to analytical tractability for path-dependent options. Obtained are closed form solutions for perpetual American options, as well as the Laplace transforms of lookback options and barrier options. Numerical examples indicate that the formulae are easily implemented