Cumulative Prospect Theory, Option Returns, and the Variance Premium

Abstract

We develop a tractable equilibrium asset pricing model with Cumulative Prospect Theory (CPT) preferences. Using GMM on a sample of U.S. equity index option returns, we show that by introducing a single common probability weighting parameter for both tails of the return distribution, the CPT model can simultaneously generate the otherwise puzzlingly low returns on both out-of-the-money (OTM) put and OTM call options. Since the variance premium can be written as the expected return on a portfolio of OTM call and put options, the CPT model also fits the high observed variance premium. In a dynamic setting, probability weighting and time-varying equity return volatility combine to match the observed time-series pattern of the variance premium.

Keywords: Cumulative prospect theory, variance risk premium, probability weighting

JEL Classification: C15, G11, G13