A Mean-Reverting SDE on Correlation matrices

Abdelkoddousse Ahdida and Aur\'elien Alfonsi
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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.

Date: 2011-08, Revised 2012-02
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1108.5264

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