Title
Efficient and stable numerical solution of the Heston-Cox-Ingersoll-Ross partial differential equation by alternating direction implicit finite difference schemesEfficient and stable numerical solution of the Heston-Cox-Ingersoll-Ross partial differential equation by alternating direction implicit finite difference schemes
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Research group
Applied mathematics
Publication type
article
Publication
London,
Subject
Mathematics
Source (journal)
International journal of computer mathematics. - London
Volume/pages
90(2013):11, p. 2409-2430
ISSN
0020-7160
ISI
000327589500015
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
This paper concerns the numerical solution of the three-dimensional Heston-Cox-Ingersoll-Ross partial differential equation for the fair values of European-style financial options. We follow the method-of-lines approach and first semidiscretize on suitable nonuniform Cartesian spatial grids by applying finite difference schemes. The main aim of this paper is to investigate various prominent alternating direction implicit schemes for the effective time discretization of the obtained, very large, semidiscrete systems. For this purpose an extensive numerical study is performed, among others, for arbitrary correlation factors, for time-dependent mean-reversion levels, for short and long maturities, for cases where the Feller condition is satisfied and for cases where it is not. Also, the approximation of the hedging quantities Delta and Gamma is discussed and double barrier knock-out call options are considered.
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