Markov Chain Monte Carlo Methods for Generalized Stochastic Volatility Models

Posted: 28 Dec 2000

See all articles by Siddhartha Chib

Siddhartha Chib

Washington University in St. Louis - John M. Olin Business School

Neil Shephard

Harvard University

Federico Nardari

University of Melbourne - Department of Finance

Date Written: October 2000

Abstract

This paper is concerned with simulation based inference in generalized models of stochastic volatility defined by heavy-tailed student-t distributions (with unknown degrees of freedom) and covariate effects in the observation and volatility equations and a jump component in the observation equation. By building on the work of Kim, Shephard and Chib (1998), we develop efficient Markov chain Monte Carlo algorithms for estimating these models. The paper also discusses how the likelihood function of these models can be computed by appropriate particle filter methods. Computation of the marginal likelihood by the method of Chib (1995) is also considered. The methodology is extensively tested and validated on simulated data and then applied in detail to daily returns data on the S&P 500 index where several stochastic volatility models are formally compared under various priors on the parameters.

Keywords: Bayes factor, Markov chain monte carlo, marginal likelihood, mixture models, particle filters, simulation based inference, stochastic volatility

JEL Classification: C1, C15, C22

Suggested Citation

Chib, Siddhartha and Shephard, Neil and Nardari, Federico, Markov Chain Monte Carlo Methods for Generalized Stochastic Volatility Models (October 2000). Available at SSRN: https://ssrn.com/abstract=249409

Siddhartha Chib (Contact Author)

Washington University in St. Louis - John M. Olin Business School ( email )

One Brookings Drive
Campus Box 1133
St. Louis, MO 63130-4899
United States
314-935-4657 (Phone)
314-935-6359 (Fax)

Neil Shephard

Harvard University ( email )

1875 Cambridge Street
Cambridge, MA 02138
United States

Federico Nardari

University of Melbourne - Department of Finance ( email )

Faculty of Economics and Commerce
Parkville, Victoria 3010 3010
Australia

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