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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2013-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2013/651573 |
| 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. |
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| ISSN: | 0972-6802 1758-4965 |