Publication
Title
A contour integral method for the Black-Scholes and Heston equations
Author
Abstract
A contour integral method recently proposed by Weideman [IMA J. Numer. Anal., 30 (2010), pp. 334350] for integrating semidiscrete advection-diffusion PDEs is improved and extended for application to some of the important equations of mathematical finance. Using estimates for the numerical range of the spatial operator, optimal contour parameters are derived theoretically and tested numerically. An improvement on the existing method is the use of Krylov methods for the shifted linear systems, the solution of which represents the major computational cost of the algorithm. A parallel implementation is also considered. Test examples presented are the BlackScholes PDE in one space dimension and the Heston PDE in two dimensions, for both vanilla and barrier options. In the Heston case efficiency is compared to ADI splitting schemes, and experiments show that the contour integral method is superior for the range of medium to high accuracy requirements.
Language
English
Source (journal)
SIAM journal on scientific computing. - Philadelphia, Pa
Publication
Philadelphia, Pa : 2011
ISSN
1064-8275
Volume/pages
33:2(2011), p. 763-785
ISI
000289973500014
Full text (Publisher's DOI)
Full text (open access)
UAntwerpen
Faculty/Department
Research group
Publication type
Subject
Affiliation
Publications with a UAntwerp address
External links
Web of Science
E-info
Record
Identification
Creation 25.03.2011
Last edited 04.12.2017
To cite this reference