Volatility in Equilibrium: Asymmetries and Dynamic Dependencies

47 Pages Posted: 7 Oct 2010

See all articles by Tim Bollerslev

Tim Bollerslev

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

George Tauchen

Duke University - Economics Group

Natalia Sizova

Rice University

Multiple version iconThere are 3 versions of this paper

Date Written: August 1, 2009

Abstract

Stock market volatility clusters in time, appears fractionally integrated, carries a risk premium, and exhibits asymmetric leverage effects relative to returns. At the same time, the volatility risk premium, defined by the difference between the risk-neutral and objective expectations of the volatility, is distinctly less persistent and appears short-memory. This paper develops the first internally consistent equilibrium based explanation for all of these empirical facts. The model is cast in continuous-time and entirely self-contained, involving non-separable recursive preferences. Our empirical investigations are made possible through the use of newly available high-frequency intra-day data for the VIX volatility index, along with corresponding high-frequency data for the S&P 500 aggregate market portfolio. We show that the qualitative implications from the new theoretical model match remarkably well with the distinct shapes and patterns in the sample autocorrelations and dynamic cross-correlations in the returns and volatilities observed in the data.

Keywords: Equilibrium asset pricing, stochastic volatility, leverage effect, volatility feedback, option implied volatility, realized volatility, variance risk premium

JEL Classification: C22, C51, C52, G12, G13, G14

Suggested Citation

Bollerslev, Tim and Tauchen, George E. and Sizova, Natalia, Volatility in Equilibrium: Asymmetries and Dynamic Dependencies (August 1, 2009). Economic Research Initiatives at Duke (ERID) Working Paper No. 73. Available at SSRN: https://ssrn.com/abstract=1687985 or http://dx.doi.org/10.2139/ssrn.1687985

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)

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George E. Tauchen

Duke University - Economics Group ( email )

Box 90097
221 Social Sciences
Durham, NC 27708-0097
United States
919-660-1812 (Phone)
919-684-8974 (Fax)

Natalia Sizova

Rice University ( email )

6100 South Main Street
Houston, TX 77005-1892
United States

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