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Alternating direction implicit finite difference schemes for the Heston-Hull-White partial differential equation

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  • Tinne Haentjens and Karel J. In 't Hout

Abstract

ABSTRACT 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 timedependent 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 parameters perform very well in all situations, in terms of stability, accuracy and efficiency.

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Handle: RePEc:rsk:journ0:2197357
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