A Monte-Carlo Option-Pricing Algorithm for Log-Uniform Jump-Diffusion Model

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 jump-diffusion models, obtaining a closed option pricing formula like that of Black-Scholes is not viable. Instead, a Monte Carlo algorithm is used to compute European option prices. Monte Carlo variance reduction techniques such as both antithetic and control variates are used. The numerical results show that this is a practical, efficient and easily implementable algorithm.