Download this Paper Open PDF in Browser

Bayesian Analysis of a Stochastic Volatility Model with Leverage Effect and Fat Tails

Boston College Finance Dept. Working Paper

31 Pages Posted: 16 Jul 2001  

Eric Jacquier

Boston University School of Management; HEC Montreal - Department of Finance

Peter E. Rossi

University of California, Los Angeles (UCLA) - Anderson School of Management

Nick Polson

University of Chicago - Booth School of Business

Date Written: May 2001

Abstract

The basic univariate stochastic volatility model specifies that conditional volatility follows a log-normal auto-regressive model with innovations assumed to be independent of the innovations in the conditional mean equation. Since the introduction of practical methods for inference in the basic volatility model (JPR-(1994)), it has been observed that the basic model is too restrictive for many financial series. We extend the basic SVOL to allow for a so-called "Leverage effect" via correlation between the volatility and mean innovations, and for fat-tails in the mean equation innovation. A Bayesian Markov Chain Monte Carlo algorithm is developed for the extended volatility model. Thus far, likelihood-based inference for the correlated SVOL model has not appeared in the literature. We develop Bayes Factors to assess the importance of the leverage and fat-tail extensions. Sampling experiments reveal little loss in precision from adding the model extensions but a large loss from using the basic model in the presence of mis-specification. For both equity and exchange rate data, there is overwhelming evidence in favor of models with fat-tailed volatility innovations, and for a leverage effect in the case of equity indices. We also find that volatility estimates from the extended model are markedly different from those produced by the basic SVOL.

Keywords: ARCH, Bayes factor, Fat-tails, Gibbs Leverage effect, Metropolis, MCMC, Stochastic volatility

JEL Classification: C1, C11, C15, G1

Suggested Citation

Jacquier, Eric and Rossi , Peter E. and Polson, Nick, Bayesian Analysis of a Stochastic Volatility Model with Leverage Effect and Fat Tails (May 2001). Boston College Finance Dept. Working Paper. Available at SSRN: https://ssrn.com/abstract=275500 or http://dx.doi.org/10.2139/ssrn.275500

Eric Jacquier (Contact Author)

Boston University School of Management ( email )

595 Commonwealth Avenue
Boston, MA 02215
United States

HEC Montreal - Department of Finance ( email )

3000 Chemin de la Cote-Sainte-Catherine
Montreal, QC H3T 2A7
Canada

Peter E. Rossi

University of California, Los Angeles (UCLA) - Anderson School of Management ( email )

110 Westwood Plaza
Los Angeles, CA 90095-1481
United States
773-294-8616 (Phone)

Nick Polson

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States
773-702-7513 (Phone)
773-702-0458 (Fax)

Paper statistics

Downloads
965
Rank
18,344
Abstract Views
3,755