Principal Component Value at Risk

21 Pages Posted: 22 Dec 2002

See all articles by Raymond G. M. Brummelhuis

Raymond G. M. Brummelhuis

University of London - Economics, Mathematics and Statistics

Antonio Cordoba

Universidad Autónoma de Madrid - Department of Mathematics

Maite Quintanilla

University of Toronto

Luis A. Seco

University of Toronto

Abstract

Value at risk (VaR) is an industrial standard for monitoring financial risk in an investment portfolio. It measures potential losses within a given confidence interval. The implementation, calculation, and interpretation of VaR contains a wealth of mathematical issues that are not fully understood. In this paper we present a methodology for an approximation to value at risk that is based on the principal components of a sensitivity-adjusted covariance matrix. The result is an explicit expression in terms of portfolio deltas, gammas, and the variance/covariance matrix. It can be viewed as a nonlinear extension of the linear model given by the delta-normal VaR or Risk Metrics (J.P. Morgan, 1996).

Suggested Citation

Brummelhuis, Raymond G. M. and Barba Cordoba, Antonio and Quintanilla, Maite and Seco, Luis A., Principal Component Value at Risk. Mathematical Finance, Vol. 12, pp. 23-43, 2002. Available at SSRN: https://ssrn.com/abstract=309293

Raymond G. M. Brummelhuis

University of London - Economics, Mathematics and Statistics ( email )

Malet Street
London, WC1E 7HX
United Kingdom

Antonio Barba Cordoba

Universidad Autónoma de Madrid - Department of Mathematics ( email )

Campus de Cantoblanco
Ctra. de Colmenar, km.15
28049 Madrid
Spain

Maite Quintanilla

University of Toronto

Department of Mathematics
Toronto, Ontario M5S 3E6
Canada

Luis A. Seco (Contact Author)

University of Toronto ( email )

Department of Mathematics
Toronto, Ontario M5S 3E6
Canada

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