A finite difference scheme for pricing American put options under Kou's jump-diffusion model
type: Item
instance of: scholarly article
title: A finite difference scheme for pricing American put options under Kou's jump-diffusion model
zbMATH Open document ID: 1264.91138
DOI: 10.1155/2013/651573
author: Jian Huang
author: Zhongdi Cen
author: Anbo Le
published in: Journal of Function Spaces and Applications
publication date: 2013-05-29T00:00:00Z
review text: Summary: We present a stable finite difference scheme on a piecewise uniform mesh along with a penalty method for pricing American put options under Kou's jump-diffusion model. By adding a penalty term, the partial integrodifferential complementarity problem arising from pricing American put options under Kou's jump-diffusion model is transformed into a nonlinear parabolic integro-differential equation. Then a finite difference scheme is proposed to solve the penalized integrodifferential equation, which combines a central difference scheme on a piecewise uniform mesh with respect to the spatial variable with an implicit-explicit time stepping technique. This leads to the solution of problems with a tridiagonal M-matrix. It is proved that the difference scheme satisfies the early exercise constraint. Furthermore, it is proved that the scheme is oscillation-free and is second-order convergent with respect to the spatial variable. The numerical results support the theoretical results.
Mathematics Subject Classification ID: 91G60
Mathematics Subject Classification ID: 91G20
Mathematics Subject Classification ID: 65N06
zbMATH DE Number: 6167911
Wikidata QID: Q59014581
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/651573
OpenAlex ID: W2050532895
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description: scientific article; zbMATH DE number 6167911