Approximating Correlation Matrices Using Stochastic Lie Group Methods

Michelle Muniz, Matthias Ehrhardt and Michael Günther
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Michelle Muniz: Chair of Applied Mathematics and Numerical Analysis, University of Wuppertal, 42119 Wuppertal, Germany
Matthias Ehrhardt: Chair of Applied Mathematics and Numerical Analysis, University of Wuppertal, 42119 Wuppertal, Germany
Michael Günther: Chair of Applied Mathematics and Numerical Analysis, University of Wuppertal, 42119 Wuppertal, Germany

Mathematics, 2021, vol. 9, issue 1, 1-10

Abstract: Specifying time-dependent correlation matrices is a problem that occurs in several important areas of finance and risk management. The goal of this work is to tackle this problem by applying techniques of geometric integration in financial mathematics, i.e., to combine two fields of numerical mathematics that have not been studied yet jointly. Based on isospectral flows we create valid time-dependent correlation matrices, so called correlation flows, by solving a stochastic differential equation (SDE) that evolves in the special orthogonal group. Since the geometric structure of the special orthogonal group needs to be preserved we use stochastic Lie group integrators to solve this SDE. An application example is presented to illustrate this novel methodology.

Keywords: stochastic Lie group methods; isospectral flow; time-dependent correlation matrix; geometric integration; risk management (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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