An Efficient Localized RBF-FD Method to Simulate the Heston–Hull–White PDE in Finance

Abstract

The Heston–Hull–White three-dimensional time-dependent partial differential equation (PDE) is one of the important models in mathematical finance, at which not only the volatility is modeled based on a stochastic process but also the rate of interest is assumed to follow a stochastic dynamic. Hence, an efficient method is derived in this paper based on the methodology of the localized radial basis function generated finite difference (RBF-FD) scheme. The proposed solver uses the RBF-FD approximations on graded meshes along all three spatial variables and a high order time-stepping scheme. Stability is also studied in detail to show under what conditions the proposed method is stable. Computational simulations are given to support the theoretical discussions.

On the Stochastic Volatility in the Generalized Black-Scholes-Merton Model

“…Among more recent papers, let us mention those where combined models are considered. The Heston-Hull-White models are studied by Grzelak and Oosterlee (2011), Levendis and Maré (2022) and Liu et al (2023). The Heston-Cox-Ingersoll-Ross model is discussed in Cao et al (2016) and Mao et al (2022).…”