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In this paper, we investigate the optimal strong convergence rate ofnumerical approximations for the Cox--Ingersoll--Ross model driven byfractional Brownian motion with Hurst parameter $H\in(1/2,1)$. To deal with thedifficulties caused by the unbounded diffusion coefficient, we study anauxiliary equation based on Lamperti transformation. By means of Malliavincalculus, we prove that the backward Euler scheme applied to this auxiliaryequation ensures the positivity of the numerical solution, and is of strongorder one. Furthermore, a numerical approximation for the original model isobtained and converges with the same order.

Optimal Strong Convergence Rate of a Backward Euler Type Scheme for the Cox--Ingersoll--Ross Model Driven by Fractional Brownian Motion