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IMA Journal of Management Mathematics Advance Access published online on September 20, 2006
IMA Journal of Management Mathematics, doi:10.1093/imaman/dpl010
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© The authors 2006. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
Received January 28, 2005
Accepted June 26, 2006

Article

Parameterizing correlations: a geometric interpretation

Francesco Rapisarda 1 *, Damiano Brigo 2, and Fabio Mercurio 2

1 UBS Investment Bank, 1 Finsbury Avenue, London EC2M 2PP, UK
2 Product and Business Development Group, Banca IMI, Corso Matteotti, 4, I-20121 Milan, Italy

* To whom correspondence should be addressed.
Francesco Rapisarda, E-mail: francesco.rapisarda{at}ubs.com


  Abstract

In this paper, we present a new interpretation of the parameterization of a correlation matrix proposed earlier by some authors (Jäckel & Rebonato, 1999). This interpretation is based on viewing any correlation matrix as the result of the scalar products of a suitable set of unit vectors in a multidimensional space, each rotated from all the others by generalized Euler angles. It is possible to exploit the intuitive nature of this approach in order to obtain more efficient optimization schemes when calibrating a reduced-form model to a desired correlation structure.

Keywords: correlation matrix; risk management; rank reduction; Libor Market Model.
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