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Approximating Correlation Matrices Using Stochastic Lie Group Methods

Author

Listed:
  • Michelle Muniz

    (Chair of Applied Mathematics and Numerical Analysis, University of Wuppertal, 42119 Wuppertal, Germany
    These authors contributed equally to this work.)

  • Matthias Ehrhardt

    (Chair of Applied Mathematics and Numerical Analysis, University of Wuppertal, 42119 Wuppertal, Germany
    These authors contributed equally to this work.)

  • Michael Günther

    (Chair of Applied Mathematics and Numerical Analysis, University of Wuppertal, 42119 Wuppertal, Germany
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Michelle Muniz & Matthias Ehrhardt & Michael Günther, 2021. "Approximating Correlation Matrices Using Stochastic Lie Group Methods," Mathematics, MDPI, vol. 9(1), pages 1-10, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:1:p:94-:d:474633
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    References listed on IDEAS

    as
    1. Vineer Bhansali & Mark B. Wise, 2001. "Forecasting Portfolio Risk in Normal and Stressed Markets," Papers nlin/0108022, arXiv.org, revised Sep 2001.
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    Cited by:

    1. Melike Bildirici & Yasemen Ucan & Sérgio Lousada, 2022. "Interest Rate Based on The Lie Group SO(3) in the Evidence of Chaos," Mathematics, MDPI, vol. 10(21), pages 1-9, October.

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