Option pricing for jump-diffusion with stochastic volatility and intensity

Abstract

It is widely believed that the volatility of asset returns tends to be time varying and occasionally clustered, which leads to various stochastic volatility models. The assumption of constant intensity is relaxed to allow stochastic intensity. Combinations lead to stochastic volatility and stochastic intensity models, as well as jump-diffusion with stochastic volatility and stochastic intensity models. In this thesis, a jump-diffusion combined with stochastic volatility model and stochastic intensity is considered and its presentations include: the dynamics of asset price in which the asset price follows a geometric Brownian motion, compound Poisson processes with the stochastic volatility following Heston model, and the stochastic intensity following mean reverting process. A formula of the European option is calculated by using a technique based on the characteristic function of the underlined asset which can be expressed in an explicit formula.