Multivariate Stochastic Volatility Via Wishart Random Processes

57 Pages Posted: 25 Dec 2004

See all articles by Alexander Philipov

Alexander Philipov

George Mason University - Department of Finance

Mark E. Glickman

Harvard University - Department of Statistics

Date Written: December 14, 2004

Abstract

Financial models for asset and derivatives pricing, risk management, portfolio optimization, and asset allocation rely on volatility forecasts. Time-varying volatility models, such as GARCH and Stochastic Volatility (SVOL), have been successful in improving forecasts over constant volatility models. We develop a new multivariate SVOL framework for modeling financial data that assumes covariance matrices stochastically varying through a Wishart process. In our formulation, scalar variances naturally extend to covariance matrices rather than vectors of variances as in traditional SVOL models. Model fitting is performed using Markov chain Monte Carlo simulation from the posterior distribution. Due to the complexity of the model, an efficiently designed Gibbs sampler is described that produces inferences with a manageable amount of computation. Our approach is illustrated on a multivariate time series of monthly industry portfolio returns. In a test of the economic value of our model, minimum-variance portfolios based on our SVOL covariance forecasts outperform out-of-sample portfolios based on alternative covariance models such as Dynamic Conditional Correlations and factor-based covariances.

Keywords: Bayesian time series, Financial data, Stochastic covariance, Time-varying correlations

JEL Classification: G12, G10

Suggested Citation

Philipov, Alexander and Glickman, Mark E., Multivariate Stochastic Volatility Via Wishart Random Processes (December 14, 2004). Available at SSRN: https://ssrn.com/abstract=635123 or http://dx.doi.org/10.2139/ssrn.635123

Alexander Philipov (Contact Author)

George Mason University - Department of Finance ( email )

Fairfax, VA 22030
United States

HOME PAGE: http://mason.gmu.edu/~aphilipo

Mark E. Glickman

Harvard University - Department of Statistics

Science Center 7th floor
One Oxford Street
Cambridge, MA 02138-2901
United States

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