Option Prices in a Model with Stochastic Disaster Risk

Abstract

Contrary to well-known asset pricing models, volatilities implied by equity index options exceed realized stock market volatility and exhibit a pattern known as the volatility skew. We explain both facts using a model that can also account for the mean and volatility of equity returns. Our model assumes a small risk of economic disaster that is calibrated based on international data on large consumption declines. We allow the disaster probability to be stochastic, which turns out to be crucial to the model’s ability both to match equity volatility and to reconcile option prices with macroeconomic data on disasters. This paper was accepted by Lauren Cohen, finance.