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Article Dans Une Revue Stochastic Processes and their Applications Année : 2013

A Mean-Reverting SDE on Correlation matrices

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Résumé

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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Dates et versions

hal-00617111 , version 1 (26-08-2011)
hal-00617111 , version 2 (13-02-2012)

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Abdelkoddousse Ahdida, Aurélien Alfonsi. A Mean-Reverting SDE on Correlation matrices. Stochastic Processes and their Applications, 2013, 123 (4), pp.1472-1520. ⟨10.1016/j.spa.2012.12.008⟩. ⟨hal-00617111v2⟩
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