The Probability of Rare Disasters: Estimation and Implications

Abstract

I analyze a rare disasters economy that yields a measure of the risk neutral probability of a macroeconomic disaster, p*t . A large panel of options data provides strong evidence that p*t is the single factor driving option-implied jump risk measures in the cross section of firms. This is a core assumption of the rare disasters paradigm. A number of empirical patterns further support the interpretation of p*t as the risk-neutral likelihood of a disaster. First, standard forecasting regressions reveal that increases in p*t lead to economic downturns. Second, disaster risk is priced in the cross section of U.S. equity returns. A zero-cost equity portfolio with exposure to disasters earns risk-adjusted returns of 7.6% per year. Finally, a calibrated version of the model reasonably matches the: (i) sensitivity of the aggregate stock market to changes in the likelihood of a disaster and (ii) loss rates of disaster risky stocks during the 2008 financial crisis.

Keywords: disaster risk, rare events, option pricing, pricing of disaster risk