## 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.

### MSC:

 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
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### References:

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