ADI finite difference schemes for the Heston-Hull-White PDE
This work provides a robust numerical method for pricing options under the Heston-Hull-White model, which is important for quantitative finance practitioners dealing with complex derivative pricing.
The paper demonstrates that Alternating Direction Implicit (ADI) time discretization schemes, when properly parameterized, provide stable, accurate, and efficient numerical solutions for the three-dimensional Heston-Hull-White PDE across various conditions, including arbitrary correlations, time-dependent parameters, and different option types.
In this paper we investigate the effectiveness of Alternating Direction Implicit (ADI) time discretization schemes in the numerical solution of the three-dimensional Heston-Hull-White partial differential equation, which is semidiscretized by applying finite difference schemes on nonuniform spatial grids. We consider the Heston-Hull-White model with arbitrary correlation factors, with time-dependent mean-reversion levels, with short and long maturities, for cases where the Feller condition is satisfied and for cases where it is not. In addition, both European-style call options and up-and-out call options are considered. It is shown through extensive tests that ADI schemes, with a proper choice of their parameters, perform very well in all situations - in terms of stability, accuracy and efficiency.