Unbiased estimators for the Heston model with stochastic interest rates

01/28/2023

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by   Chao Zheng, et al.

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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.