  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.
