A Discrete-Time Model for Daily S&P 500 Returns and Realized Variations: Jumps and Leverage Effects

43 Pages Posted: 24 Aug 2005

See all articles by Tim Bollerslev

Tim Bollerslev

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

Uta Kretschmer

University of Bonn, Department of Economics

Christian Pigorsch

Ludwig Maximilian University of Munich (LMU) - Department of Statistics

George Tauchen

Duke University - Economics Group

Abstract

We develop an empirically highly accurate discrete-time daily stochastic volatility model that explicitly distinguishes between the jump and continuous-time components of price movements using nonparametric realized variation and Bipower variation measures constructed from high-frequency intraday data. The model setup allows us to directly assess the structural inter-dependencies among the shocks to returns and the two different volatility components. The model estimates suggest that the leverage effect, or asymmetry between returns and volatility, works primarily through the continuous volatility component. The excellent fit of the model makes it an ideal candidate for an easy-to-implement auxiliary model in the context of indirect estimation of empirically more realistic continuous-time jump diffusion and Levy-driven stochastic volatility models, effectively incorporating the relevant information in the high-frequency data.

Keywords: Stochastic volatility, Realized volatility, Bipower variation, Jumps, Leverage effect, Return distributions, Simultaneous equation model

JEL Classification: C10, C30, C50, G10

Suggested Citation

Bollerslev, Tim and Kretschmer, Uta and Pigorsch, Christian and Tauchen, George E., A Discrete-Time Model for Daily S&P 500 Returns and Realized Variations: Jumps and Leverage Effects. Available at SSRN: https://ssrn.com/abstract=782749 or http://dx.doi.org/10.2139/ssrn.782749

Tim Bollerslev

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

Uta Kretschmer

University of Bonn, Department of Economics ( email )

Postfach 2220
D-53113 Bonn
Germany

Christian Pigorsch

Ludwig Maximilian University of Munich (LMU) - Department of Statistics ( email )

Ludwigstr. 33
Munchen, D-80539
Germany

George E. Tauchen (Contact Author)

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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