A Mean-Reverting SDE on Correlation matrices
Probability
2012-02-14 v2 Computational Finance
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.
Keywords
Cite
@article{arxiv.1108.5264,
title = {A Mean-Reverting SDE on Correlation matrices},
author = {Abdelkoddousse Ahdida and Aurélien Alfonsi},
journal= {arXiv preprint arXiv:1108.5264},
year = {2012}
}