A mean-reverting SDE on correlation matrices

Abdelkoddousse Ahdida and Aurélien Alfonsi

Stochastic Processes and their Applications, 2013, vol. 123, issue 4, 1472-1520

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 give a possible application of these processes in finance and argue that they could easily replace and improve the standard assumption of a constant correlation.

Keywords: Correlation; Wright–Fisher diffusions; Multi-allele Wright–Fisher model; Jacobi processes; Wishart processes; Discretization schemes; Multi-asset model (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (10)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:123:y:2013:i:4:p:1472-1520

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DOI: 10.1016/j.spa.2012.12.008

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