“Asset Pricing under Jump Diffusion” by Jin ZHANG
University of Hong Kong
In this paper, we model a stock price as a production process in a production economy with jump diffusion and establish a general equilibrium model for the equity premium. We propose a pricing kernel and use it to price options. We prove that the modified Merton's (1976) summation series formula for the option price is equivalent to Bakshi and Madan's (2000) inverse Fourier transformation formula. We then present analytical expressions for the return distributions in the physical and the risk-neutral measures. We find out that our model explains very well the empirical evidence on the risk-neutral skewness and the relation between the moments of the risk-neutral and physical distributions. The model also explains the empirical evidence on the negative excess return of a Delta-hedged option portfolio.