Tri-Diagonal Preconditioner for Pricing Options

Journal of Computational and Applied Mathematics, 236: 4365-4374, 2012

17 Pages Posted: 28 Jan 2014

See all articles by Hong-Kui Pang

Hong-Kui Pang

Xuzhou Normal University

Ying-Ying Zhang

Chongqing University

Xiao-Qing Jin

University of Macau

Date Written: January 1, 2012

Abstract

The value of a contingent claim under a jump-diffusion process satisfies a partial integro-differential equation (PIDE). We localize and discretize this PIDE in space by the central difference formula and in time by the second order backward differentiation formula. The resulting system Tnx = b in general is a nonsymmetric Toeplitz system. We then solve this system by the normalized preconditioned conjugate gradient method. A tri-diagonal preconditioner Ln is considered. We prove that under certain conditions all the eigenvalues of the normalized preconditioned matrix (Ln(-1)Tn) (Ln(-1)Tn) are clustered around one, which implies a superlinear convergence rate. Numerical results exemplify our theoretical analysis.

Keywords: European call option, partial integro-differential equation, nonsymmetric Toeplitz system, normalized preconditioned system, tri-diagonal preconditioner, family of generating functions

Suggested Citation

Pang, Hong-Kui and Zhang, Ying-Ying and Jin, Xiao-Qing, Tri-Diagonal Preconditioner for Pricing Options (January 1, 2012). Journal of Computational and Applied Mathematics, 236: 4365-4374, 2012, Available at SSRN: https://ssrn.com/abstract=2386405

Hong-Kui Pang (Contact Author)

Xuzhou Normal University ( email )

Xuzhou, Jiangsu
China

Ying-Ying Zhang

Chongqing University ( email )

Shazheng Str 174, Shapingba District
Shazheng street, Shapingba district
Chongqing 400044, Chongqing 400030
China

HOME PAGE: http://user.qzone.qq.com/93347989/blog/1308306747

Xiao-Qing Jin

University of Macau ( email )

P.O. Box 3001
Macau
Macau

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