The Pricing Of Options In A Jump-Diffusion Model With Stochastic Volatility

The aim of this paper is to study jump-di?usion model with stochasticvolatility for option pricing. We get a jump-di?usion option pricing modelwith stochastic volatility by adding a compound Poisson process to stockprice process based on the Heston stochastic volatility model. We derivedthe European call option pricing formula using Fourier inverse transforma-tion and change of measure under the assumption of exist of risk-neutralmeasure,then we get two inferences. Finally,We derived the actuarial pric-ing formula and two inferences of European call option by using Fourierinverse transformation and Mathematical expectation under no economicassumptions.