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A Mean-Reverting SDE on Correlation matrices

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  • Abdelkoddousse Ahdida

    (CERMICS)

  • Aur\'elien Alfonsi

    (CERMICS)

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    Abstract

    We introduce a mean-reverting SDE whose solution is naturally defined on the space of correlation matrices. This SDE can be seen as an extension of the well-known Wright-Fisher diffusion. We provide conditions that ensure weak and strong uniqueness of the SDE, and describe its ergodic limit. We also shed light on a useful connection with Wishart processes that makes understand how we get the full SDE. Then, we focus on the simulation of this diffusion and present discretization schemes that achieve a second-order weak convergence. Last, we explain how these correlation processes could be used to model the dependence between financial assets.

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    File URL: http://arxiv.org/pdf/1108.5264
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    Paper provided by arXiv.org in its series Papers with number 1108.5264.

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    Date of creation: Aug 2011
    Date of revision: Feb 2012
    Handle: RePEc:arx:papers:1108.5264

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    Web page: http://arxiv.org/

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    1. Gourieroux, Christian & Jasiak, Joann, 2006. "Multivariate Jacobi process with application to smooth transitions," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 475-505.
    2. Robert Fernholz & Ioannis Karatzas, 2005. "Relative arbitrage in volatility-stabilized markets," Annals of Finance, Springer, vol. 1(2), pages 149-177, November.
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