Equilibrium Option Pricing Research Under The Production-Based SVCJ Model

This paper constructs a production-based equilibrium model starting from the index level(e.g.,S&P 500).Based on a sample of the U.S.economy from 1889 to 1978,Mehra and Prescott find that the production-based equilibrium model works so well in explaining in the equity premium puzzle.The production-based equilibrium model is easier than the consumption-based model.So in this paper,we use the production-based model to study the the equity premium and option price.In this paper,we consider the jump diffusion of assets return and volatility,i.e.stochastic volatility with contemporaneous jumps in price and variance process models.The model can well reflect the large changes of asset price influenced by the politics,economics and disasters.We use the production-based SVCJ model to study the the equity premium and option price.In the SVCJ model,the volatility of stock returns is stochastic and with jump diffusion,so we use the general equilibrium framework methods to study the equity premium and option price under SVCJ model.We use the pricing kernel to provides a transition for parameters between the risk-neutral measure and the physical probability measure.Then,we use the Fourier transformation methods to obtain the exact expression of option value.In existing papers about the production-based equilibrium model,the volatility of the stock return is a constant in Zhang et al.the volatility of the stock return is stochastic but with no jumps in Ruan et al.We extend the production-based equilibrium model studied by Zhang et al,in which the stock return has a constant volatility and the investor has a constant relative risk aversion(CRRA)utility function,into more general settings where the volatility of the stock return is stochastic and with jumps.In incomplete markets,where risks are more than tradable risky assets,there are several methods to deal with those pricing and portfolio problems.We use general equilibrium framework methods to study the equity premium and option price under stochastic volatility with correlated jumps models.We use the pricing kernel to provides a transition for parameters between the risk-neutral measure Q and the physical probability measure P.Then we use the fourier transformation methods to obtain the exact expression of the option value.