Research

R. Barro and G. Liao: Rare Disaster Probability and Options Pricing

January 1, 2020

We derive an option-pricing formula from recursive preferences and estimate rare disaster probability. The new options-pricing formula applies to far-out-of-the money put options on the stock market when disaster risk dominates, the size distribution of disasters follows a power law, and the economy has a representative agent with a constant-relative-risk-aversion utility function. The formula conforms with options data on the S&P 500 index from 1983-2018 and for analogous indices for other countries.