Parameterizing correlations: a geometric interpretation
Francesco Rapisarda, Damiano Brigo, Fabio Mercurio · IMA Journal of Management Mathematics · 2006
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.