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Exact Moment Simulation using Random Orthogonal Matrices

Author

Listed:
  • Carol Alexander

    (ICMA Centre, University of Reading)

  • Walter Ledermann

    (Emeritus Professor, University of Sussex)

  • Daniel Ledermann

    (ICMA Centre, University of Reading)

Abstract

This paper introduces a method for simulating multivariate samples that have exact means, covariances, skewness and kurtosis. A new class of rectangular orthogonal matrices is fundamental to the methodology, and these ``L-matrices'' can be deterministic, parametric or data specific in nature. The target moments determine an L-matrix, then infinitely many random samples with the same exact moments may be generated by multiplying the L-matrix by arbitrary random orthogonal matrices. The methodology is thus termed ``ROM simulation''. We discuss certain classes of random orthogonal matrices and show how each class produces samples with different characteristics. ROM simulation has applications to many problems that are resolved using standard Monte Carlo methods. But since no parametric assumptions are required there is no sampling error caused by the discrete approximation of a continuous distribution, which is a major source of error in standard Monte Carlo simulations. For illustration, we apply ROM simulation to determine the value-at-risk of a stock portfolio.

Suggested Citation

  • Carol Alexander & Walter Ledermann & Daniel Ledermann, 2009. "Exact Moment Simulation using Random Orthogonal Matrices," ICMA Centre Discussion Papers in Finance icma-dp2009-09, Henley Business School, University of Reading.
    • Handle: RePEc:rdg:icmadp:icma-dp2009-09
    as

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    File URL: http://www.icmacentre.ac.uk/files/icma/dp_200909_2.pdf
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    References listed on IDEAS

    as
    1. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-862, November.
    2. Pérignon, Christophe & Smith, Daniel R., 2010. "The level and quality of Value-at-Risk disclosure by commercial banks," Journal of Banking & Finance, Elsevier, vol. 34(2), pages 362-377, February.
    Full references (including those not matched with items on IDEAS)

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    Keywords

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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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