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Journal of Financial Econometrics Advance Access originally published online on August 21, 2009
Journal of Financial Econometrics 2009 7(4):412-436; doi:10.1093/jjfinec/nbp011
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© The Author 2009. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

CHICAGO: A Fast and Accurate Method for Portfolio Risk Calculation

Simon A. Broda
     Department of Quantitative Economics, University of Amsterdam

Marc S. Paolella
     Swiss Banking Institute, University of Zurich and Swiss Finance Institute

Address correspondence to Simon A. Broda, Department of Quantitative Economics, Amsterdam School of Economics, University of Amsterdam, Roetersstraat 11, 1018 WB Amsterdam, The Netherlands, or e-mail: s.a.broda{at}uva.nl

JEL Classification: C13, C32, G11


  Abstract

This paper shows how independent component analysis can be used to estimate the generalized orthogonal GARCH model in a fraction of the time otherwise required. The proposed method is a two-step procedure, separating the estimation of the correlation structure from that of the univariate dynamics, thus facilitating the incorporation of non-Gaussian innovations distributions in a straightforward manner. The generalized hyperbolic distribution provides an excellent parametric description of financial returns data and is used for the univariate fits, but its convolutions, necessary for portfolio risk calculations, are intractable. This restriction is overcome by saddlepoint approximations for the Value at Risk and expected shortfall, which are computationally cheap and retain excellent accuracy far into the tails. It is further shown that the mean-expected shortfall portfolio optimization problem can be solved efficiently in the context of the model. A simulation study and an application to stock returns demonstrate the validity of the procedure.

KEYWORDS: expected shortfall, multivariate GARCH, portfolio optimization, saddlepoint approximation, Value at Risk

Part of this research has been carried out within the National Centre of Competence in Research "Financial Valuation and Risk Management" (NCCR FINRISK), which is a research program supported by the Swiss National Science Foundation. The paper was written while the first author was at the Swiss Banking Institute of the University of Zurich. The authors wish to thank the two anonymous referees for their valuable comments.

Received January 11, 2008; revised July 6, 2009; accepted July 6, 2009


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