We 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 Eulertype method. As an error criterion, we use the pth 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.
|Number of pages||11|
|Journal||Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences|
|Publication status||Published - 8 Apr 2012|