Article2005

On the discretization schemes for the CIR (and Bessel squared) processes

246 citations0/0 files storedMonte Carlo Methods and Applications

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Stochastic processes and financial applications Numerical methods for differential equations Mathematical Approximation and Integration

Abstract

In this paper, we focus on the simulation of the Cox-Ingersoll-Ross processes and present several discretization schemes of both the implicit and explicit types. We study their strong and weak convergence. We also examine numerically their behaviour and compare them to the schemes already proposed by Deelstra and Delbaen and Diop. Finally, we gather all the results obtained and recommend, in the standard case, the use of one of our explicit schemes.

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References

1993A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options 1985A Theory of the Term Structure of Interest Rates 2007Brownian Motion and Stochastic Calculus 1996The law of the Euler scheme for stochastic differential equations

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2009High order discretization schemes for the CIR process: Application to affine term structure and Heston models 2016THE 4/2 STOCHASTIC VOLATILITY MODEL: A UNIFIED APPROACH FOR THE HESTON AND THE 3/2 MODEL 2010Time Dependent Heston Model 2011An Euler-type method for the strong approximation of the Cox–Ingersoll–Ross process 2014First order strong approximations of scalar SDEs defined in a domain 2007Euler scheme for SDEs with non-Lipschitz diffusion coefficient: strong convergence 2011A note on Euler approximations for SDEs with Hölder continuous diffusion coefficients 2010Numerical simulation of a strongly nonlinear Ait-Sahalia-type interest rate model

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