Option Prices in a Model with Stochastic Disaster Risk

Recent work suggests that the consumption disaster-based explanation of the equity premium is inconsistent with the average implied volatilities from option data. We resolve this inconsistency in a model with stochastic disaster risk (SDR). The SDR model explains average implied volatilities, even when calibrated to consumption and aggregate market data alone. We extend the benchmark SDR model to one that allows for variation in the risk of disaster at different time scales. This extension can match both the time series of implied volatilities, as well as the average implied volatility curve.