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

Abstract

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

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References in corpus (5)

• Rate of convergence and asymptotic error distribution of Euler approximation schemes for fractional diffusions
• A Milstein-type scheme without Levy area terms for SDEs driven by fractional Brownian motion
• Fractional Cox--Ingersoll--Ross process with non-zero <<mean>>
• Strong convergence rate of Runge--Kutta methods and simplified step-$N$ Euler schemes for SDEs driven by fractional Brownian motions
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• Stochastic differential equations driven by fractional Brownian motion with locally Lipschitiz drift and their Euler approximation