Tractable Rare Disaster Probability and Options-Pricing
56 Pages Posted: 22 Oct 2019
Date Written: 2019-09-27
We derive an option-pricing formula from recursive preference 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 Epstein-Zin utility. 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 equity index returns and growth vulnerabilities in the economy.
Keywords: Disaster Probability, Option Prices, Rare Disaster, Tail Risk, Uncertainty, Volatility
JEL Classification: E44, G13, G12
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