We study the $L^1$-approximation of the log-Heston SDE at equidistant time points by Euler-type methods. We establish the convergence order $ 1/2-\epsilon$ for $\epsilon >0$ arbitrarily small, if the Feller index $\nu$ of the underlying CIR process satisfies $\nu > 1$. Thus, we recover the standard convergence order of the Euler scheme for SDEs with globally Lipschitz coefficients. Moreover, we discuss the case $\nu \leq 1$ and illustrate our findings by several numerical examples.

翻译：本文研究利用Euler型方法在等距时间点上对对数-Heston SDE进行$L^1$-逼近。我们证明，若底层CIR过程的Feller指数$\nu$满足$\nu > 1$，则对任意小的$\epsilon > 0$，收敛阶为$1/2-\epsilon$。由此，我们恢复了具有全局Lipschitz系数的SDE的Euler格式的标准收敛阶。此外，我们讨论$\nu \leq 1$的情形，并通过若干数值例子验证我们的结论。