Exact and high order discretization schemes for Wishart processes and their affine extensions

Abdelkoddousse Ahdida and Aurélien Alfonsi ()
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Abdelkoddousse Ahdida: CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École nationale des ponts et chaussées
Aurélien Alfonsi: 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, CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École nationale des ponts et chaussées

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Abstract: This work deals with the simulation of Wishart processes and affine diffusions on positive semidefinite matrices. To do so, we focus on the splitting of the infinitesimal generator, in order to use composition techniques as Ninomiya and Victoir or Alfonsi. Doing so, we have found a remarkable splitting for Wishart processes that enables us to sample exactly Wishart distributions, without any restriction on the parameters. It is related but extends existing exact simulation methods based on Bartlett's decomposition. Moreover, we can construct high-order discretization schemes for Wishart processes and second-order schemes for general affine diffusions. These schemes are in practice faster than the exact simulation to sample entire paths. Numerical results on their convergence are given.

Keywords: Wishart processes; affine processes; exact simulation; discretization schemes; weak error; Bartlett's decomposition.; Bartlett's decomposition (search for similar items in EconPapers)
Date: 2013
Note: View the original document on HAL open archive server: https://hal.science/hal-00491371v1
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Citations: View citations in EconPapers (8)

Published in The Annals of Applied Probability, 2013, 23 (3), pp.1025-1073. ⟨10.1214/12-AAP863⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00491371

DOI: 10.1214/12-AAP863

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