OPTION PRICING UNDER JUMP-DIFFUSION MODEL WITH Q PROCESS VOLATILITY

Abstract

In this paper, a financial market model is presented, where the underlying asset price is given by the combination of a two state Q process volatility and a compound Poisson process. The formula of European call option price under this model is derived. It generalizes the results of Hull and White (1987). At last an empirical examination on the Shanghai Stock Exchange Index is done to prove that the volatility described by two states Q process satisfies the features of fat tails and volatility clustering of financial data. And the numerical simulation results show that the option price is related to the volatility of initial time.
Key words: European option, jump-diffusion model, compound Poisson process, finite state Q process