Equilibrium Asset and Option Pricing under Jump-Diffusion Model with Stochastic Volatility

Abstract

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.

Equilibrium approach of asset and option pricing under Lévy process and stochastic volatility

“…Proof. Based on the expression for R t under the physical measure and the risk-neutral measure respectively in proposition 12 in Ruan (2013), the results can be obtained immediately.…”

“…In the general equilibrium framework, it is assumed that there is a representative investor who wants to maximize an objective function in a rational expectation economy where there are one risk-free asset and one risky asset. In this work, we model the risky asset as an exponential of a Lévy process with stochastic volatility, which extends the work of Santa-Clara and Yan (2004), Fu and Yang (2012) and Ruan et al (2013). Then we develop exact expressions of the equity premium and pricing kernel in a general equilibrium economy.…”

“…Moreover, Fu and Yang (2012) also relaxes those restrictions and uses a general Lévy process, but a constant volatility is assumed. Ruan et al (2013) considers stochastic volatility, but only with Poisson distribution for the jump component. Aase (2000) establishes an equilibrium asset pricing model based on the Lévy process, which is an important contribution to the field; however, the volatility is modeled by the aggregate consumption process based on some assumptions.…”