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Random orthogonal matrix simulation

journal contribution
posted on 2023-06-08, 12:23 authored by Walter Ledermann, Carol AlexanderCarol Alexander, Daniel Ledermann
This paper introduces a method for simulating multivariate samples that have exact means, covariances, skewness and kurtosis. We introduce a new class of rectangular orthogonal matrix which is fundamental to the methodology and we call these matrices L matrices. They may be deterministic, parametric or data specific in nature. The target moments determine the 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. This methodology is thus termed “ROM simulation”. Considering certain elementary types of random orthogonal matrices we demonstrate that they generate samples with different characteristics. ROM simulation has applications to many problems that are resolved using standard Monte Carlo methods. But no parametric assumptions are required (unless parametric L matrices are used) so 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.

History

Publication status

  • Published

Journal

Linear Algebra and its Applications

ISSN

0024-3795

Publisher

Elsevier

Issue

6

Volume

434

Page range

1444-1467

Department affiliated with

  • Business and Management Publications

Notes

Simulation; Orthogonal matrix; Random matrix; Ledermann matrix; L matrices; Multivariate moments; Volatility clustering; Value-at-risk

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-09-11

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