Parameterizing correlations: a geometric interpretation |
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| Authors: | Rapisarda Francesco; Brigo Damiano; Mercurio Fabio |
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| Institution: |
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
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| Abstract: | ** Email: francesco.rapisarda{at}ubs.com
In this paper, we present a new interpretation of the parameterizationof a correlation matrix proposed earlier by some authors (Jäckel& Rebonato, 1999). This interpretation is based on viewingany correlation matrix as the result of the scalar productsof 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 approachin order to obtain more efficient optimization schemes whencalibrating a reduced-form model to a desired correlation structure. |
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| Keywords: | correlation matrix risk management rank reduction Libor Market Model |
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