Risk-Neutral Option Pricing for Jump-Diffusion Processes

Abstract

A reduced European call option pricing formula by risk-neutral valuation is given. It is shown that the European call and put options for jump-diffusion models are worth more than that for the Black-Scholes (diffusion) model with the common parameters. Due to the complexity of the risk-neutral jump-diffusion results, obtaining a closed option pricing formula like that of Black-Scholes is not viable. Instead, a Monte Carlo algorithm, including optimal control variates, is used to compute European option prices. Monte Carlo variance reduction techniques are enhanced by the use antithetic random variates. The numerical results show that this is practical, efficient and easily implementable algorithm. This is joint work with Zongwu Zhu.