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Journal of Financial Econometrics Advance Access published online on July 27, 2009
Journal of Financial Econometrics, doi:10.1093/jjfinec/nbp009
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© The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oupjournals.org

Comparison of Volatility Measures: a Risk Management Perspective

Christian T. Brownlees
     Stern School of Business, New York University

Giampiero M. Gallo
     Dipartimento di Statistica "G. Parenti", Università di Firenze

Address correspondence to Giampiero M. Gallo, Dipartimento di Statistica "G. Parenti," Viale G. B. Morgagni 59, I-50134 Firenze, Italy, or e-mail: gallog{at}ds.unifi.it.

JEL Classification: C22, C51, C52, C53


  Abstract

In this paper we address the issue of forecasting Value–at–Risk (VaR) using different volatility measures: realized volatility, bipower realized volatility, two-scales realized volatility, realized kernel, as well as the daily range. We propose a dynamic model with a flexible trend specification bonded with a penalized maximum likelihood estimation strategy: the P-spline multiplicative error model. Exploiting ultra-high-frequency data (UHFD) volatility measures, VaR predictive ability is considerably improved upon relative to a baseline GARCH but not so relative to the range; there are gains from modeling volatility trends and from using realized kernels that are robust to dependent microstructure noise.

KEYWORDS: GARCH, MEM, P-splines, VaR, volatility measures

We would like to thank René Garcia, the associate editor, and an anonymous referee for comments that led to a substantial improvement in the focus and in the presentation. We would also like to thank Federico Bandi, Riccardo Colacito, Frank Diebold, Francesca Di Iorio, Rob Engle, Farhang Farazmand, Clifford Hurvich, Eric Ghysels, Silvia Gonçalves, Bryan Kelly, Axel Kind, Christian Macaro, Marc Paolella, Gonzalo Rangel, Neil Shephard, Marina Vannucci, David Veredas, Norman White, Michael Wolf, as well as participants in seminars at New York University, Rice University, Université Libre de Bruxelles, and University of Zürich, in the Conference on "Volatility and High Frequency Data," Chicago, April 2007, and in the SoFiE Inaugural Conference, New York, June 2008. Financial support by Italian Miur PRIN under grant no. PRIN 2006131140_004 is gratefully acknowledged. Computations were performed on the grid at the NYU Stern Center for Research Computing (SCRC). All mistakes are ours.

Received February 1, 2008; revised April 22, 2009; accepted June 2, 2009


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