Option pricing model about stock pricing jump process with compound Poisson process

The behavior model of stock price is studied. The results of Merton on European option pricing by martingale method are given. By changing basic assumption of Merton option pricing model to the assumption that jump process is a kind of special compound Poisson process and volatility without jump is the function of time, it is established that the behavior model of the stock pricing process is jump-diffusion process. The formula of European option whose stock price with jump process is a compound Poisson process is deduced under the risk-neutral hypothesis, and it is extended that Merton option pricing model.