Tractable Rare Disaster Probability and Options-Pricing

56 Pages Posted: 22 Oct 2019

See all articles by Robert J. Barro

Robert J. Barro

Harvard University

Gordon Liao

Board of Governors of the Federal Reserve System

Date Written: 2019-09-27

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.

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

JEL Classification: E44, G13, G12

Suggested Citation

Barro, Robert J. and Liao, Gordon, Tractable Rare Disaster Probability and Options-Pricing (2019-09-27). FEDS Working Paper No. 2019-073. Available at SSRN: https://ssrn.com/abstract=3473059 or http://dx.doi.org/10.17016/FEDS.2019.073

Robert J. Barro (Contact Author)

Harvard University

1875 Cambridge Street
Cambridge, MA 02138
United States

Gordon Liao

Board of Governors of the Federal Reserve System ( email )

20th Street and Constitution Avenue NW
Washington, DC 20551
United States

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