Exact Moment Simulation using Random Orthogonal Matrices

Carol Alexander, Walter Ledermann and Daniel Ledermann
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Walter Ledermann: Emeritus Professor, University of Sussex

ICMA Centre Discussion Papers in Finance from Henley Business School, 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.

Keywords: simulation; L-matrices; multivariate moments; value-at-risk (search for similar items in EconPapers)
JEL-codes: C14 C15 C63 (search for similar items in EconPapers)
Pages: 31 pages
Date: 2009-09
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