A Finite Difference Scheme for Pricing American Put Options under Kou's Jump-Diffusion Model
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 und...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2013/651573 |
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| _version_ | 1832565213705011200 |
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| author | Jian Huang Zhongdi Cen Anbo Le |
| author_facet | Jian Huang Zhongdi Cen Anbo Le |
| author_sort | Jian Huang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-135aea790bdc4e12a3aa5fbfeff36aba |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-135aea790bdc4e12a3aa5fbfeff36aba2025-02-03T01:08:49ZengWileyJournal of Function Spaces and Applications0972-68021758-49652013-01-01201310.1155/2013/651573651573A Finite Difference Scheme for Pricing American Put Options under Kou's Jump-Diffusion ModelJian Huang0Zhongdi Cen1Anbo Le2Institute of Mathematics, Zhejiang Wanli University, Ningbo, Zhejiang 315100, ChinaInstitute of Mathematics, Zhejiang Wanli University, Ningbo, Zhejiang 315100, ChinaInstitute of Mathematics, Zhejiang Wanli University, Ningbo, Zhejiang 315100, ChinaWe 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.http://dx.doi.org/10.1155/2013/651573 |
| spellingShingle | Jian Huang Zhongdi Cen Anbo Le A Finite Difference Scheme for Pricing American Put Options under Kou's Jump-Diffusion Model Journal of Function Spaces and Applications |
| title | A Finite Difference Scheme for Pricing American Put Options under Kou's Jump-Diffusion Model |
| title_full | A Finite Difference Scheme for Pricing American Put Options under Kou's Jump-Diffusion Model |
| title_fullStr | A Finite Difference Scheme for Pricing American Put Options under Kou's Jump-Diffusion Model |
| title_full_unstemmed | A Finite Difference Scheme for Pricing American Put Options under Kou's Jump-Diffusion Model |
| title_short | A Finite Difference Scheme for Pricing American Put Options under Kou's Jump-Diffusion Model |
| title_sort | finite difference scheme for pricing american put options under kou s jump diffusion model |
| url | http://dx.doi.org/10.1155/2013/651573 |
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