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, and then, under mild assumptions, we show that the convergence rate in $L^2$ 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 confirm our theoretical convergence rate.

翻译：我们结合Rhee和Glynn (Operations Research: 63(5), 1026-1043, 2015)中的无偏估计量与带随机利率的Heston模型。具体而言，我们首先为带随机利率的Heston模型开发了一个半精确log-Euler格式，然后在温和假设下，证明了该格式在$L^2$范数下的收敛阶为$O(h)$，其中$h$为步长。该结果适用于一大类模型，例如Heston-Hull-White模型、Heston-CIR模型和Heston-Black-Karasinski模型。数值实验验证了我们的理论收敛阶。