A Mean-Reverting SDE on Correlation matrices

Abdelkoddousse Ahdida and Aurélien Alfonsi ()
Additional contact information
Abdelkoddousse Ahdida: CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École nationale des ponts et chaussées
Aurélien Alfonsi: CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École nationale des ponts et chaussées, MATHRISK - Mathematical Risk handling - Inria Paris-Rocquencourt - Inria - Institut National de Recherche en Informatique et en Automatique - UPEM - Université Paris-Est Marne-la-Vallée - ENPC - École nationale des ponts et chaussées

Post-Print from HAL

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.

Date: 2013
Note: View the original document on HAL open archive server: https://enpc.hal.science/hal-00617111v2
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (10)

Published in Stochastic Processes and their Applications, 2013, 123 (4), pp.1472-1520. ⟨10.1016/j.spa.2012.12.008⟩

Downloads: (external link)
https://enpc.hal.science/hal-00617111v2/document (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00617111

DOI: 10.1016/j.spa.2012.12.008

Access Statistics for this paper

More papers in Post-Print from HAL
Bibliographic data for series maintained by CCSD ().