Schwarz Modulus Based Matrix Splittings with Minimal Polynomial Extrapolation Acceleration for linear complementarity problems arising from American option pricing
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918516369653760 |
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| author | Gande, Martin J. Liao, Si-Wei Lu, Liu-Di |
| author_facet | Gande, Martin J. Liao, Si-Wei Lu, Liu-Di |
| contents | Pricing American options is more complicated than pricing European options, because they can be exercised at any time, and one thus needs to solve a linear complementarity problem instead of simply doing time stepping for computing European options. We introduce a new Schwarz modulus-based splitting method for solving such linear complementarity problems, and further accelerate them using Modified Polynomial Extrapolation, a non-linear vector sequence acceleration technique, which is very much related to Krylov methods in the linear case. Numerical experiments on a model problem show that our new solver can have close to an order of magnitude lower iteration counts than the classically used modulus-based matrix splitting technique. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_22315 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Schwarz Modulus Based Matrix Splittings with Minimal Polynomial Extrapolation Acceleration for linear complementarity problems arising from American option pricing Gande, Martin J. Liao, Si-Wei Lu, Liu-Di Numerical Analysis Pricing American options is more complicated than pricing European options, because they can be exercised at any time, and one thus needs to solve a linear complementarity problem instead of simply doing time stepping for computing European options. We introduce a new Schwarz modulus-based splitting method for solving such linear complementarity problems, and further accelerate them using Modified Polynomial Extrapolation, a non-linear vector sequence acceleration technique, which is very much related to Krylov methods in the linear case. Numerical experiments on a model problem show that our new solver can have close to an order of magnitude lower iteration counts than the classically used modulus-based matrix splitting technique. |
| title | Schwarz Modulus Based Matrix Splittings with Minimal Polynomial Extrapolation Acceleration for linear complementarity problems arising from American option pricing |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2605.22315 |