Working Paper

Tractable Rare Disaster Probability and Options-Pricing

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;

https://doi.org/10.17016/FEDS.2019.073

Bibliographic Information

Provider: Board of Governors of the Federal Reserve System (U.S.)

Part of Series: Finance and Economics Discussion Series

Publication Date: 2019-09-27

Number: 2019-073

Pages: 55 pages