A pure dual approach for hedging Bermudan options
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909352241135616 |
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| author | Alfonsi, Aurélien Kebaier, Ahmed Lelong, Jérôme |
| author_facet | Alfonsi, Aurélien Kebaier, Ahmed Lelong, Jérôme |
| contents | This paper develops a new dual approach to compute the hedging portfolio of a Bermudan option and its initial value. It gives a "purely dual" algorithm following the spirit of Rogers (2010) in the sense that it only relies on the dual pricing formula. The key is to rewrite the dual formula as an excess reward representation and to combine it with a strict convexification technique. The hedging strategy is then obtained by using a Monte Carlo method, solving backward a sequence of least square problems. We show convergence results for our algorithm and test it on many different Bermudan options. Beyond giving directly the hedging portfolio, the strength of the algorithm is to assess both the relevance of including financial instruments in the hedging portfolio and the effect of the rebalancing frequency. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_18761 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A pure dual approach for hedging Bermudan options Alfonsi, Aurélien Kebaier, Ahmed Lelong, Jérôme Mathematical Finance Probability Computational Finance 62L15, 60G40, 91G20, 65C05 This paper develops a new dual approach to compute the hedging portfolio of a Bermudan option and its initial value. It gives a "purely dual" algorithm following the spirit of Rogers (2010) in the sense that it only relies on the dual pricing formula. The key is to rewrite the dual formula as an excess reward representation and to combine it with a strict convexification technique. The hedging strategy is then obtained by using a Monte Carlo method, solving backward a sequence of least square problems. We show convergence results for our algorithm and test it on many different Bermudan options. Beyond giving directly the hedging portfolio, the strength of the algorithm is to assess both the relevance of including financial instruments in the hedging portfolio and the effect of the rebalancing frequency. |
| title | A pure dual approach for hedging Bermudan options |
| topic | Mathematical Finance Probability Computational Finance 62L15, 60G40, 91G20, 65C05 |
| url | https://arxiv.org/abs/2404.18761 |