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Disaster Probability and Options-Pricing with Disaster Risk. Robert Barro, April 2019, Paper, "We derive a new option-pricing formula from recursive preference and estimate disaster probability from option prices. 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 Epstein-Zin utility. The formula conforms with data on put-options prices for the U.S. S&P index from 1983 to 2018 and for analogous indices for other countries starting in the mid-1990s. The estimated disaster probability, inferred from monthly fixed effects, is highly correlated across countries and peaks during the financial crisis of 2008-09. The estimated disaster probability forecasts downside risk in the economy. Using quantile regressions, we find that the disaster probability forecasts growth vulnerabilities, defined GDP and Industrial Production growth at the lowest decile." Link