Risk-Neutral Option Pricing for Log-Uniform Jump-Amplitude Jump-Diffusion Model

Reduced European call and put option formulas by risk-neutral valuation are given. It is shown that the European call and put options for log-uniform 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 tractable. Instead, a Monte Carlo algorithm is used to compute European option prices. Monte Carlo variance reduction techniques such as both antithetic and optimal control variates are used to accelerate the calculations by allowing smaller sample sizes. The numerical results show that this is a practical, efficient and easily implementable algorithm