Options-Pricing Formula with Disaster Risk
罗伯特·巴罗 Robert J. Barro
哈佛大学Paul M. Warburg经济学讲席教授
Robert J. Barro is Paul M. Warburg Professor of Economics at Harvard University, a senior fellow of the Hoover Institution of Stanford University, Makin Visiting Scholar at American Enterprise Institute, and a research associate of the National Bureau of Economic Research. He has a Ph.D. in economics from Harvard University and a B.S. in physics from Caltech. Barro is co-editor of Harvard’s Quarterly Journal of Economics and was recently President of the Western Economic Association and Vice President of the American Economic Association. He was a viewpoint columnist for Business Week from 1998 to 2006 and a contributing editor of The Wall Street Journal from 1991 to 1998. Noteworthy research includes empirical determinants of economic growth, economic effects of public debt and budget deficits, and the economics of religion. Current research focuses on the impact of rare disasters on asset markets and macroeconomic activity, with recent applications to environmental protection, quantities of safe assets, and pricing of stock options. Books include Macroeconomics: A Modern Approach, Economic Growth (2nd edition, with Xavier Sala-i-Martin), Nothing Is Sacred: Economic Ideas for the New Millennium, Determinants of Economic Growth, Getting It Right: Markets and Choices in a Free Society, and Education and Modernization Worldwide, from the 19th to the 21st Century (with Jong-Wha Lee).
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 U.S. S&P indices from 1983 to 2017 and for analogous indices for other countries over periods 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. For the United States, the peak is more dramatic in the stock-market crash of October 1987.