Sharp L1-approximation of the log-Heston stochastic differential equation by Euler-type methods

We study the L-1-approximation of the log-Heston stochastic differential equation at equidistant time points by Euler-type methods. We establish the convergence order 1/2 is an element of for is an element of > 0 arbitrarily small if the Feller index nu of the underlying Cox-Ingersoll-Ross process satisfies nu > 1. Thus, we recover the standard convergence order of the Euler scheme for stochastic differential equations with globally Lipschitz coefficients. Moreover, we discuss the nu <= 1 case and illustrate our findings with several numerical examples.