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A Mean-Reverting SDE on Correlation matrices

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  • Abdelkoddousse Ahdida

    (CERMICS)

  • Aur'elien Alfonsi

    (CERMICS)

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.

Suggested Citation

  • Abdelkoddousse Ahdida & Aur'elien Alfonsi, 2011. "A Mean-Reverting SDE on Correlation matrices," Papers 1108.5264, arXiv.org, revised Feb 2012.
    • Handle: RePEc:arx:papers:1108.5264
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