Analysis and pricing of call option under the Heston model with the jump diffusion process

Abstract

The Black-Scholes-Merton model is one of the most popular asset price movement model. Because it derives a simple closed-form solution of European option price, this model has received much attention from academics and practitioners. However the volatility smile phenomenon shows that the real market doesn`t follow the Black-Scholes-Merton model. In order to make up for the critical drawbacks, the volatility should have a more complex form and the asset price movement should explain some extreme events such as collapse and sudden. In this paper we study the option pricing under the stochastic volatility model and the jump diffusion model. In particular, we study the Heston`s stochastic volatility model and the Merton`s jump diffusion model. And we will add these models to obtain more accurate price of the European call option.