Equilibrium Option Pricing Under Jump Diffusion

This paper mainly studies the equilibrium option pricing relating to the problems of the jump diffusion model with stochastic volatility. Using a general equilibrium pricing model with a representative investor, we obtain the expression of the risk premium, which is a function of volatility, contains the risk premium caused by a volatility and the jump risk premium. Parts of works in Zhang et al.[46] is extended. The European call option pricing formula is derived by using the Fourier transform. This paper also explains two finance empirical phenomena from the perspective of mathematics:the negative variance risk premium and implied volatility smirk.