Alternative Models of Stock Prices Dynamics

38 Pages Posted: 31 Jan 2001

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: January 23, 2001

Abstract

The purpose of this paper is to shed further light on the tensions that exist between the empirical fit of stochastic volatility (SV) models and their linkage to option pricing. A number of recent papers have investigated several specifications of one-factor SV diffusion models associated with option pricing models. The empirical failure of one-factor affine, Constant Elasticity of Variance (CEV), and one-factor log-linear SV models leaves us with two strategies to explore: (1) add a jump component to better fit the tail behavior or (2) add an additional (continuous path) factor where one factor controls the persistence in volatility and the second determines the tail behavior. Both have been partially pursued and our paper embarks on a more comprehensive examination which yields some rather surprising results. Adding a jump component to the basic Heston affine model is known to be a successful strategy as demonstrated by Andersen et al. (1999), Eraker et al. (1999), Chernov et al. (1999), and Pan (1999). Unfortunately, the presence of a jump component introduces quite a few unpleasant econometric issues. In addition, several financial issues, like hedging and risk factors become more complex. In this paper we show that a two-factor log-linear SV diffusion model (without jumps) appears to yield a remarkably good empirical fit. We estimate the model via the EMM procedure of Gallant and Tauchen (1996) which allows us to compare the non-nested log-linear SV diffusion with the affine jump specification. Obviously, there is one drawback to the log-linear SV models when it comes to pricing derivatives since no closed-form solutions are available. Against this cost weights the advantage of avoiding all the complexities involved with jump processes.

Suggested Citation

Chernov, Mikhail and Gallant, A. Ronald and Ghysels, Eric and Tauchen, George E., Alternative Models of Stock Prices Dynamics (January 23, 2001). Available at SSRN: https://ssrn.com/abstract=257646 or http://dx.doi.org/10.2139/ssrn.257646

Mikhail Chernov

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 (Contact Author)

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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