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Tractable Rare Disaster Probability and Options-Pricing

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Abstract

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.

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  • Robert J. Barro & Gordon Y. Liao, 2019. "Tractable Rare Disaster Probability and Options-Pricing," Finance and Economics Discussion Series 2019-073, Board of Governors of the Federal Reserve System (U.S.).
    • Handle: RePEc:fip:fedgfe:2019-73
    DOI: 10.17016/FEDS.2019.073
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    More about this item

    Keywords

    Disaster Probability; Option Prices; Rare Disaster; Tail Risk; Uncertainty; Volatility;
    All these keywords.

    JEL classification:

    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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