Tails, Fears and Risk Premia

CREATES Research Paper No. 2009-26

46 Pages Posted: 14 Jun 2009

See all articles by Tim Bollerslev

Tim Bollerslev

Duke University - Finance; Duke University - Department of Economics; National Bureau of Economic Research (NBER)

Viktor Todorov

Northwestern University

Date Written: June 12, 2009

Abstract

We show that the compensation for rare events accounts for a large fraction of the equity and variance risk premia in the S&P 500 market index. The probability of rare events vary significantly over time, increasing in periods of high market volatility, but the risk premium for tail events cannot solely be explained by the level of the volatility. Our empirical investigations are essentially model-free. We estimate the expected values of the tails under the statistical probability measure from "medium" size jumps in high-frequency intraday prices and an extreme value theory approximation for the corresponding jump tail density. Our estimates for the risk-neutral expectations are based on short maturity out-of-the money options and new model-free option implied variation measures explicitly designed to separate the tail probabilities. At a general level, our results suggest that any satisfactory equilibrium based asset pricing model must be able to generate large and time-varying compensations for fears of disasters.

Keywords: rare events, jumps, high-frequency data, options, fears, extreme value theory, equity risk premium, variance risk premium

JEL Classification: C13, C14, G10, G12

Suggested Citation

Bollerslev, Tim and Todorov, Viktor, Tails, Fears and Risk Premia (June 12, 2009). CREATES Research Paper No. 2009-26. Available at SSRN: https://ssrn.com/abstract=1418488 or http://dx.doi.org/10.2139/ssrn.1418488

Tim Bollerslev (Contact Author)

Duke University - Finance ( email )

Durham, NC 27708-0120
United States
919-660-1846 (Phone)
919-684-8974 (Fax)

Duke University - Department of Economics

213 Social Sciences Building
Box 90097
Durham, NC 27708-0204
United States

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Viktor Todorov

Northwestern University ( email )

2001 Sheridan Road
Evanston, IL 60208
United States

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