Market excess returns, variance and the third cumulant

Abstract

In this paper, we develop an equilibrium asset pricing model for the market excess return, variance and the third cumulant by using a jump-diffusion process with stochastic variance and jump intensity in Cox, Ingersoll and Ross' (1985) production economy. Empirical evidence with S&P 500 index and options from January 1996 to December 2005 strongly supports our model prediction that lower the third cumulant, higher the market excess returns. Consistent with existing literature, the theoretical mean-variance relation is supported only by regressions on risk-neutral variance. We further demonstrate empirically that the third cumulant explains significantly the variance risk premium.