Closed-Form Solution of the Option Problem under the Combination of a Stochastic Volatility Process and a Jump Process

In order to generalize the Black-Scholes model, there are two ways in the literature so far. The first one assumes the volatility follows a stochastic process. The other one introduces jumps into the return process. However, neither class of models constitutes an adequate explanation of the empirical evidence, although stochastic volatility models faro somewhat better than jumps. As for this, here we propose an new model, where asset prices are given by the combination of a log-normal stochastic volatility process and an compound Poisson process. The closed-form solution to the valuation of European option has been derived.