Volatility in Equilibrium: Asymmetries and Dynamic Dependencies

52 Pages Posted: 14 Apr 2010 Last revised: 6 May 2010

See all articles by Tim Bollerslev

Tim Bollerslev

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

Natalia Sizova

Rice University

George Tauchen

Duke University - Economics Group

Multiple version iconThere are 3 versions of this paper

Date Written: March 19, 2010


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 auto-correlations 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 Sizova, Natalia and Tauchen, George E., Volatility in Equilibrium: Asymmetries and Dynamic Dependencies (March 19, 2010). Economic Research Initiatives at Duke (ERID) Working Paper No. 35. Available at SSRN: https://ssrn.com/abstract=1589742 or http://dx.doi.org/10.2139/ssrn.1589742

Tim Bollerslev (Contact Author)

Duke University - Finance ( email )

Durham, NC 27708-0120
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Duke University - Department of Economics

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National Bureau of Economic Research (NBER)

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Natalia Sizova

Rice University ( email )

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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)

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