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June 2013 Exact and high-order discretization schemes for Wishart processes and their affine extensions
Abdelkoddousse Ahdida, Aurélien Alfonsi
Ann. Appl. Probab. 23(3): 1025-1073 (June 2013). DOI: 10.1214/12-AAP863

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 did Ninomiya and Victoir [Appl. Math. Finance 15 (2008) 107–121] or Alfonsi [Math. Comp. 79 (2010) 209–237]. 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.

Citation

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Abdelkoddousse Ahdida. Aurélien Alfonsi. "Exact and high-order discretization schemes for Wishart processes and their affine extensions." Ann. Appl. Probab. 23 (3) 1025 - 1073, June 2013. https://doi.org/10.1214/12-AAP863

Information

Published: June 2013
First available in Project Euclid: 7 March 2013

zbMATH: 1269.65003
MathSciNet: MR3076677
Digital Object Identifier: 10.1214/12-AAP863

Subjects:
Primary: 60H35 , 65C30 , 91B70

Keywords: Affine processes , Bartlett’s decomposition , discretization schemes , exact simulation , weak error , Wishart processes

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.23 • No. 3 • June 2013
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