An Euler-type method for the strong approximation of the Cox–Ingersoll–Ross process
2011; Royal Society; Volume: 468; Issue: 2140 Linguagem: Inglês
10.1098/rspa.2011.0505
ISSN1471-2946
AutoresSteffen Dereich, Andreas Neuenkirch, Łukasz Szpruch,
Tópico(s)Fluid Dynamics and Turbulent Flows
ResumoWe analyse the strong approximation of the Cox–Ingersoll–Ross (CIR) process in the regime where the process does not hit zero by a positivity preserving drift-implicit Euler-type method. As an error criterion, we use the p th mean of the maximum distance between the CIR process and its approximation on a finite time interval. We show that under mild assumptions on the parameters of the CIR process, the proposed method attains, up to a logarithmic term, the convergence of order 1/2. This agrees with the standard rate of the strong convergence for global approximations of stochastic differential equations with Lipschitz coefficients, despite the fact that the CIR process has a non-Lipschitz diffusion coefficient.
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