Option pricing under a double-exponential jump-diffusion model with varying severity of jumps

Abstract

This paper extends the standard double-exponential jump-diffusion (DEJD) model to allow for successive jumps to bring about different effects on the asset price process. The double-exponentially distributed jump sizes are no longer assumed to have the same parameters; instead, we assume that these parameters may take a series of different values to reflect growing or diminishing effects from these jumps. The mathematical analysis of the stock price requires an introduction of a number of distributions that are extended from the hypoexponential (HE) distribution. Under such a generalized setting, the European option price is derived in closed-form which ensures its computational convenience. Through our numerical examples, we examine the effects on the return distributions from the growing and diminishing severity of the upcoming jumps expected in the near future, and investigate how the option prices and the shapes of the implied volatility smiles are influenced by the varying severity of jumps. These results demonstrate the benefits of the modeling flexibility provided by our extension.