Approximating Correlation Matrices Using Stochastic Lie Group Methods

Mathematics

Michael Günther¹  Michelle Muniz¹  Matthias Ehrhardt¹ 

[1] Chair of Applied Mathematics and Numerical Analysis, University of Wuppertal, 42119 Wuppertal, Germany;

关键词: stochastic Lie group methods;    isospectral flow;    time-dependent correlation matrix;    geometric integration;    risk management;   

DOI  :  10.3390/math9010094

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown