The truncated Euler–Maruyama method for CIR model driven by fractional Brownian motion

Abstract

Recently, Hong et al. (2020) established the strong convergence rate of the backward Euler scheme for the Cox–Ingersoll–Ross (CIR) model driven by fractional Brownian motion with Hurst parameter H∈(1/2,1), which may effect the efficiency of computation. Taking advantage of being explicit and easily implementable, a positivity preserving explicit scheme is proposed in this paper. For overcoming the difficulties caused by the unbounded diffusion coefficient, an auxiliary equation with a constant diffusion coefficient obtained by proper Lamperti transformation is used. By means of Malliavin calculus, we show that the truncated Euler–Maruyama scheme applied to this auxiliary equation not only ensures the positivity of the numerical solution, but also has the H-order rate of the root mean square error over a finite time interval. Furthermore, by transforming back, an explicit scheme for the original CIR model is obtained and has the same convergence order. Finally, some numerical experiments are provided to illustrate the theoretical results.