%0 Journal Article
%T Equilibrium Asset and Option Pricing under Jump-Diffusion Model with Stochastic Volatility
%A Xinfeng Ruan
%A Wenli Zhu
%A Shuang Li
%A Jiexiang Huang
%J Abstract and Applied Analysis
%D 2013
%I Hindawi Publishing Corporation
%R 10.1155/2013/780542
%X We study the equity premium and option pricing under jump-diffusion model with stochastic volatility based on the model in Zhang et al. 2012. We obtain the pricing kernel which acts like the physical and risk-neutral densities and the moments in the economy. Moreover, the exact expression of option valuation is derived by the Fourier transformation method. We also discuss the relationship of central moments between the physical measure and the risk-neutral measure. Our numerical results show that our model is more realistic than the previous model. 1. Introduction Option pricing problem is one of the predominant concerns in the financial market. Since the advent of the Black-Scholes option pricing formula in [1], there has been an increasing amount of literature describing the theory and its practice. Due to drawbacks of the Black-Scholes model which cannot explain numerous empirical facts such as large and sudden movements in prices, heavy tails, volatility clustering, the incompleteness of markets, and the concentration of losses in a few large downward moves, many option valuation models have been proposed and tested to fit those empirical facts. Jump-diffusion models with stochastic volatility could overcome these drawbacks of the Black-Scholes model in [2¨C21]. Based on those advantages, in this paper, we focus on studying the jump-diffusion model with stochastic volatility. Different from the Black-Scholes framework, we use jump diffusion to describe the price dynamics of underlying asset. The market of our model is incomplete; that is, it is not possible to replicate the payoff of every contingent claim by a portfolio, and there are several equivalent martingale measures. How to choose a consistent pricing measure from the set of equivalent martingale measures becomes an important problem. This means that we need to find some criteria to determine one from the set of equivalent martingale measures in some economically or mathematically motivated fashion. A unique martingale measure was found by various researchers via using optimal criteria, for instance, minimal martingale criterion, minimal entropy martingale criterion, and utility maximization criterion [22¨C31]. General equilibrium framework method is also a popular method to deal with the option pricing in an incomplete market. General equilibrium framework is initially introduced by Lucas Jr. (1978) [32], Cox et al. (1985) [33] and developed by Vasanttilak and Lee (1990) [34], Pan (2002) [35], Liu and Pan (2003) [36], Liu et al. (2005) [37], Bates (2008) [38], Santa-Clara and Yan (2004) [12],
%U http://www.hindawi.com/journals/aaa/2013/780542/