September 2019 (Revised March 2020)

Rare Disaster Probability and Options-Pricing

Robert J. Barro and Gordon Y. Liao


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. The disaster probability, inferred from monthly fixed effects, is highly correlated across countries, peaks during the 2008-2009 financial crisis, and forecasts rates of economic growth.
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Original paper: PDF

Keywords: Disaster Probability, Option Prices, Rare Disaster, Tail Risk, Uncertainty, Volatility


PDF: Full Paper

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Last Update: March 27, 2020