Options-pricing formula with disaster risk - Robert J. Barro; Gordon Liao (American Enterprise Institute (AEI), 2017)
A 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 elasticity of the put-options price is one with respect to maturity and above one with respect to exercise price. An additional term reflects the volatility of disaster probability. The formula conforms with data on put-options prices for the U.S. S&P index from 1983 to 2017 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 U.S. peak is more dramatic in the stock-market crash of October 1987. The estimated U.S. disaster probability is highly positively correlated with the VIX indicator.
Keywords: A; 330; Economic growth; Stock market; economic risk; Gross Domestic Product (GDP)