Jump‐Diffusion Models

Abstract Jump‐diffusion option pricing models are generalizations of the Black–Scholes model, generalizations in which the underlying asset price can jump. The dynamics of the log‐price is given by the sum of Brownian motion and an independent compound Poisson process. Some examples of jump size distributions, such as normal or double exponential, lead to analytically tractable option pricing models that can generate implied volatility smiles.