High order discretization schemes for the CIR process: application to affine term structure and heston models. (English) Zbl 1198.60030

Summary: This paper presents weak second and third order schemes for the Cox-Ingersoll-Ross (CIR) process, without any restriction on its parameters. At the same time, it gives a general recursive construction method for getting weak second order schemes that extend the one introduced by S. Ninomiya and N. Victoir [Appl. Math. Finance 15, No. 2, 107–121 (2008; Zbl 1134.91524)]. Combine both these results, this allows us to propose a second order scheme for more general affine diffusions. Simulation examples are given to illustrate the convergence of these schemes on CIR and Heston models.


60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
65C30 Numerical solutions to stochastic differential and integral equations
91B70 Stochastic models in economics


Zbl 1134.91524
Full Text: DOI


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