2011/08/26 by Abdelkoddousse Ahdida, Ahdida, Abdelkoddousse, Aurélien Alfonsi +1
Economics, Econometrics and Finance · Mathematics · #Complex Systems and Time Series Analysis #Computational Finance (q-fin.CP) #FOS: Economics and business #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #q-fin.CP
paper · pdf · doi:10.48550/arxiv.1108.5264
openalex publication_date 2011/08/26 · arxiv created 2012/02/13 · arxiv updated 2012/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.