Weak approximation of stochastic differential equations and application to derivative pricing
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2006
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| _version_ | 1866908337885413376 |
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| author | Ninomiya, Syoiti Victoir, Nicolas |
| author_facet | Ninomiya, Syoiti Victoir, Nicolas |
| contents | The authors present a new simple algorithm to approximate weakly stochastic differential equations in the spirit of [1] and [2]. They apply it to the problem of pricing Asian options under the Heston stochastic volatility model, and compare it with other known methods. It is shown that the combination of the suggested algorithm and quasi-Monte Carlo methods makes computations extremely fast.
[1] Shigeo Kusuoka, ``Approximation of Expectation of Diffusion Process and Mathematical Finance,'' Advanced Studies in Pure Mathematics, Proceedings of Final Taniguchi Symposium, Nara 1998 (T. Sunada, ed.), vol. 31 2001, pp. 147--165. [2] Terry Lyons and Nicolas Victoir, ``Cubature on Wiener Space,'' Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 460 (2004), pp. 169--198. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_math_0605361 |
| institution | arXiv |
| publishDate | 2006 |
| record_format | arxiv |
| spellingShingle | Weak approximation of stochastic differential equations and application to derivative pricing Ninomiya, Syoiti Victoir, Nicolas Probability Numerical Analysis 65C30, 65C05 The authors present a new simple algorithm to approximate weakly stochastic differential equations in the spirit of [1] and [2]. They apply it to the problem of pricing Asian options under the Heston stochastic volatility model, and compare it with other known methods. It is shown that the combination of the suggested algorithm and quasi-Monte Carlo methods makes computations extremely fast. [1] Shigeo Kusuoka, ``Approximation of Expectation of Diffusion Process and Mathematical Finance,'' Advanced Studies in Pure Mathematics, Proceedings of Final Taniguchi Symposium, Nara 1998 (T. Sunada, ed.), vol. 31 2001, pp. 147--165. [2] Terry Lyons and Nicolas Victoir, ``Cubature on Wiener Space,'' Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 460 (2004), pp. 169--198. |
| title | Weak approximation of stochastic differential equations and application to derivative pricing |
| topic | Probability Numerical Analysis 65C30, 65C05 |
| url | https://arxiv.org/abs/math/0605361 |