A Mean-Reverting SDE on Correlation matrices
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 of creation:||2013|
|Date of revision:|
|Publication status:||Published in Stochastic Processes and their Applications, Elsevier, 2013, 123 (4), pp.1472-1520. <10.1016/j.spa.2012.12.008>|
|Note:||View the original document on HAL open archive server: https://hal-enpc.archives-ouvertes.fr/hal-00617111v2|
|Contact details of provider:|| Web page: https://hal.archives-ouvertes.fr/|
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