Option pricing under a double exponential jump diffusion model

Analytical tractability is one of the challenges faced by many alternative models that try to generalize the Black–Scholes option pricing model to incorporate more empirical features. The aim of this paper is to extend the analytical tractability of the Black–Scholes model to alternative models with jumps. We demonstrate that a double exponential jump diffusion model can lead to an analytic approximation for finite-horizon American options (by extending the Barone–Adesi and Whaley method) and analytical solutions for popular path-dependent options (such as lookback, barrier, and perpetual American options). Numerical examples indicate that the formulae are easy to implement, and are accurate.