We combine the unbiased estimators in Rhee and Glynn (Operations Research: 63(5), 1026-1043, 2015) and the Heston model with stochastic interest rates. Specifically, we first develop a semi-exact log-Euler scheme for the Heston model with stochastic interest rates. Then, under mild assumptions, we show that the convergence rate in the $L^2$ norm is $O(h)$, where $h$ is the step size. The result applies to a large class of models, such as the Heston-Hull-While model, the Heston-CIR model and the Heston-Black-Karasinski model. Numerical experiments support our theoretical convergence rate.

翻译：我们结合了Rhee与Glynn（《运筹学》63(5), 1026-1043, 2015）中的无偏估计量，以及带随机利率的赫斯顿模型。具体而言，我们首先为带随机利率的赫斯顿模型提出了一种半精确对数欧拉格式。随后，在温和假设下，我们证明了该格式在$L^2$范数下的收敛速率为$O(h)$，其中$h$为步长。该结果适用于一大类模型，例如赫斯顿-赫尔-怀特模型、赫斯顿-CIR模型以及赫斯顿-布莱克-卡拉辛斯基模型。数值实验验证了我们的理论收敛速率。