A New Class of Stochastic Volatility Models with Jumps: Theory and Estimation

37 Pages Posted: 7 Nov 1999

See all articles by Mikhail Chernov

Mikhail Chernov

UCLA Anderson

A. Ronald Gallant

Duke University - Fuqua School of Business, Economics Group; New York University - Department of Economics

Eric Ghysels

University of North Carolina Kenan-Flagler Business School; University of North Carolina (UNC) at Chapel Hill - Department of Economics

George Tauchen

Duke University - Economics Group

Date Written: October 13, 1999

Abstract

The purpose of this paper is to propose a new class of jump diffusions which feature both stochastic volatility and random intensity jumps. Previous studies have focused primarily on pure jump processes with constant intensity and log-normal jumps or constant jump intensity combined with a one factor stochastic volatility model. We introduce several generalizations which can better accommodate several empirical features of returns data. In their most general form we introduce a class of processes which nests jump-diffusions previously considered in empirical work and includes the affine class of random intensity models studied by Bates (1998) and Duffie, Pan and Singleton (1998) but also allows for non-affine random intensity jump components. We attain the generality of our specification through a generic Levy process characterization of the jump component. The processes we introduce share the desirable feature with the affine class that they yield analytically tractable and explicit option pricing formula. The non-affine class of processes we study include specifications where the random intensity jump component depends on the size of the previous jump which represent an alternative to affine random intensity jump processes which feature correlation between the stochastic volatility and jump component. We also allow for and experiment with different empirical specifications of the jump size distributions. We use two types of data sets. One involves the S&P500 and the other comprises of 100 years of daily Dow Jones index. The former is a return series often used in the literature and allows us to compare our results with previous studies. The latter has the advantage to provide a long time series and enhances the possibility of estimating the jump component more precisely. The non-affine random intensity jump processes are more parsimonious than the affine class and appear to fit the data much better.

JEL Classification: G13, C14, C52, C53

Suggested Citation

Chernov, Mikhail and Gallant, A. Ronald and Ghysels, Eric and Tauchen, George E., A New Class of Stochastic Volatility Models with Jumps: Theory and Estimation (October 13, 1999). Available at SSRN: https://ssrn.com/abstract=189628 or http://dx.doi.org/10.2139/ssrn.189628

Mikhail Chernov (Contact Author)

UCLA Anderson ( email )

110 Westwood Plaza
Los Angeles, CA 90095-1481
United States

A. Ronald Gallant

Duke University - Fuqua School of Business, Economics Group ( email )

Box 90097
Durham, NC 27708-0097
United States

New York University - Department of Economics ( email )

269 Mercer Street, 7th Floor
New York, NY 10011
United States

Eric Ghysels

University of North Carolina Kenan-Flagler Business School ( email )

Kenan-Flagler Business School
Chapel Hill, NC 27599-3490
United States

University of North Carolina (UNC) at Chapel Hill - Department of Economics ( email )

Gardner Hall, CB 3305
Chapel Hill, NC 27599
United States
919-966-5325 (Phone)
919-966-4986 (Fax)

HOME PAGE: http://www.unc.edu/~eghysels/

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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