Cumulative Prospect Theory, Option Returns, and the Variance Premium

The variance premium and the pricing of out-of-the-money (OTM) equity index options are major challenges to standard asset pricing models. We develop a tractable equilibrium model with Cumulative Prospect Theory (CPT) preferences that can overcome both challenges. The key insight is that the variance premium can be written as the expected return on a portfolio of OTM call and put options, and the probability weighting feature of CPT can explain the puzzlingly low returns observed for these options. Using GMM on a sample of U.S. index option returns between 1996 and 2010, we show that the CPT model ts well observed option prices and, therefore, the 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.