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Principal Component Value at Risk

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  • R. BRUMMELHUIS
  • A. CÓRDOBA
  • M. QUINTANILLA
  • L. SECO

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 RiskMetrics (J.P. Morgan, 1996).

Suggested Citation

  • R. Brummelhuis & A. Córdoba & M. Quintanilla & L. Seco, 2002. "Principal Component Value at Risk," Mathematical Finance, Wiley Blackwell, vol. 12(1), pages 23-43, January.
    • Handle: RePEc:bla:mathfi:v:12:y:2002:i:1:p:23-43
    DOI: 10.1111/1467-9965.00002
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    Cited by:

    1. Jules Sadefo Kamdem, 2005. "Value-At-Risk And Expected Shortfall For Linear Portfolios With Elliptically Distributed Risk Factors," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(05), pages 537-551.
    2. Sadefo Kamdem, J. & Genz, A., 2008. "Approximation of multiple integrals over hyperboloids with application to a quadratic portfolio with options," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3389-3407, March.
    3. Brummelhuis, Raymond & Luo, Zhongmin, 2017. "CDS Rate Construction Methods by Machine Learning Techniques," MPRA Paper 79194, University Library of Munich, Germany.
    4. Roberta Fiori & Simonetta Iannotti, 2006. "Scenario Based Principal Component Value-at-Risk: an Application to Italian Banks' Interest Rate Risk Exposure," Temi di discussione (Economic working papers) 602, Bank of Italy, Economic Research and International Relations Area.
    5. Charles Lee & Kristy Tran, 2010. "Adaptive algorithms for maximizing overall stock return," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 33(2), pages 81-95, November.

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