A contour integral method for the Black-Scholes and Heston equations
Date
2011
Authors
In't Hout K.J.
Weideman J.A.C.
Journal Title
Journal ISSN
Volume Title
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Abstract
A contour integral method recently proposed by W eideman [IMA J. Numer. Anal., 30 (2010), pp. 334-350] 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 Black-Scholes 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. © 2011 Society for Industrial and Applied Mathematics.
Description
Keywords
Black-scholes equation, Financial option pricing, Heston equation, Krylov methods, Laplace transform, Matrix exponential, Numerical contour integration, Parallelism, Black Scholes equations, Financial option pricing, Heston equation, Krylov method, Matrix exponential, Numerical contour integration, Parallelism, Economics, Laplace transforms, Linear systems, Mathematical operators
Citation
SIAM Journal on Scientific Computing
33
2
http://www.scopus.com/inward/record.url?eid=2-s2.0-79957621114&partnerID=40&md5=cd211a425ebf204ee1a7f33e6b98cb9c
33
2
http://www.scopus.com/inward/record.url?eid=2-s2.0-79957621114&partnerID=40&md5=cd211a425ebf204ee1a7f33e6b98cb9c