On Stochastic Partial Differential Equations and their applications to Derivative Pricing through a conditional Feynman-Kac formula
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866918328945082368 |
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| author | Das, Kaustav Guo, Ivan Loeper, Grégoire |
| author_facet | Das, Kaustav Guo, Ivan Loeper, Grégoire |
| contents | The price of a financial derivative can be expressed as an iterated conditional expectation, where the inner term conditions on the future of an auxiliary process. We show that this inner conditional expectation solves an SPDE (a 'conditional Feynman-Kac formula'). The problem requires conditioning on a backward filtration generated by the noise of the auxiliary process and enlarged by its terminal value, leading us to search for a backward Brownian motion here. This adds a source of irregularity to the SPDE which we tackle with new techniques. Lastly, we establish a new class of mixed Monte-Carlo PDE numerical methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_14870 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On Stochastic Partial Differential Equations and their applications to Derivative Pricing through a conditional Feynman-Kac formula Das, Kaustav Guo, Ivan Loeper, Grégoire Mathematical Finance Probability 60H15, 60H30, 91G20, 91G60 G.3 The price of a financial derivative can be expressed as an iterated conditional expectation, where the inner term conditions on the future of an auxiliary process. We show that this inner conditional expectation solves an SPDE (a 'conditional Feynman-Kac formula'). The problem requires conditioning on a backward filtration generated by the noise of the auxiliary process and enlarged by its terminal value, leading us to search for a backward Brownian motion here. This adds a source of irregularity to the SPDE which we tackle with new techniques. Lastly, we establish a new class of mixed Monte-Carlo PDE numerical methods. |
| title | On Stochastic Partial Differential Equations and their applications to Derivative Pricing through a conditional Feynman-Kac formula |
| topic | Mathematical Finance Probability 60H15, 60H30, 91G20, 91G60 G.3 |
| url | https://arxiv.org/abs/2106.14870 |