A Mean-Reverting SDE on Correlation matrices
AbstractWe 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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Date of creation: 2013
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Publication status: Published, Stochastic Processes and their Applications, 2013, 123, 4, 1472-1520
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This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-12-15 (All new papers)
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