A Mean-Reverting SDE on Correlation matrices

Abdelkoddousse Ahdida (1) , Aurélien Alfonsi (1, 2)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
2 MATHRISK - Mathematical Risk handling

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.

Domaines: Probabilités [math.PR]; Finance quantitative [q-fin.CP]

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⟩