Multivariate Stochastic Volatility Models with Correlated Errors

31 Pages Posted: 21 Jan 2006

See all articles by David X. Chan

David X. Chan

Cendant Corporation

Robert Kohn

University of New South Wales - School of Economics and School of Banking and Finance

Chris Kirby

UNC Charlotte - Belk College of Business

Date Written: December 30, 2005

Abstract

We develop a Bayesian approach for parsimoniously estimating the correlation structure of the errors in a multivariate stochastic volatility model. Since the number of parameters in the joint correlation matrix of the return and volatility errors is potentially very large, we impose a prior that allows the off-diagonal elements of the inverse of the correlation matrix to be identically zero. The model is estimated using a Markov chain simulation method that samples from the posterior distribution of the volatilities and parameters. We illustrate the approach using both simulated and real examples. In the real examples, the method is applied to equities at three levels of aggregation: returns for firms within the same industry, returns for different industries and returns aggregated at the index level. We find pronounced correlation effects only at the highest level of aggregation.

Keywords: Bayesian estimation, Correlation matrix, Leverage, Markov chain Monte Carlo, Model averaging

JEL Classification: C11, C15, C30

Suggested Citation

Chan, David X. and Kohn, Robert and Kirby, Chris, Multivariate Stochastic Volatility Models with Correlated Errors (December 30, 2005). Available at SSRN: https://ssrn.com/abstract=876348 or http://dx.doi.org/10.2139/ssrn.876348

David X. Chan

Cendant Corporation ( email )

1 Sylvan Way
Parsippany, NJ
United States

Robert Kohn (Contact Author)

University of New South Wales - School of Economics and School of Banking and Finance ( email )

Australian School of Business
Sydney NSW 2052, ACT 2600
Australia
+61 2 9385 2150 (Phone)

Chris Kirby

UNC Charlotte - Belk College of Business ( email )

9201 University City Boulevard
Charlotte, NC 28223
United States

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