Vibrato Monte Carlo sensitivities
We show how the benefits of the pathwise sensitivity approach to computing Monte Carlo Greeks can be extended to discontinuous payoff functions through a combination of the pathwise approach and the Likelihood Ratio Method. With a variance reduction modification, this results in an estimator which f...
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| Μορφή: | Book section |
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Springer Verlag
2009
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| _version_ | 1826269629493805056 |
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| author | Giles, M |
| author_facet | Giles, M |
| author_sort | Giles, M |
| collection | OXFORD |
| description | We show how the benefits of the pathwise sensitivity approach to computing Monte Carlo Greeks can be extended to discontinuous payoff functions through a combination of the pathwise approach and the Likelihood Ratio Method. With a variance reduction modification, this results in an estimator which for timestep h has a variance which is O(h -1/2) for discontinuous payoffs and O(1) for continuous payoffs. Numerical results confirm the variance is much lower than the O(h -1) variance of the Likelihood Ratio Method, and the approach is also compatible with the use of adjoints to obtain multiple first order sensitivities at a fixed cost. © Springer-Verlag Berlin Heidelberg 2009. |
| first_indexed | 2024-03-06T21:28:04Z |
| format | Book section |
| id | oxford-uuid:43c276e7-c86b-495b-93cd-96bc432d862a |
| institution | University of Oxford |
| last_indexed | 2024-03-06T21:28:04Z |
| publishDate | 2009 |
| publisher | Springer Verlag |
| record_format | dspace |
| spelling | oxford-uuid:43c276e7-c86b-495b-93cd-96bc432d862a2022-03-26T14:57:21ZVibrato Monte Carlo sensitivitiesBook sectionhttp://purl.org/coar/resource_type/c_3248uuid:43c276e7-c86b-495b-93cd-96bc432d862aSymplectic Elements at OxfordSpringer Verlag2009Giles, MWe show how the benefits of the pathwise sensitivity approach to computing Monte Carlo Greeks can be extended to discontinuous payoff functions through a combination of the pathwise approach and the Likelihood Ratio Method. With a variance reduction modification, this results in an estimator which for timestep h has a variance which is O(h -1/2) for discontinuous payoffs and O(1) for continuous payoffs. Numerical results confirm the variance is much lower than the O(h -1) variance of the Likelihood Ratio Method, and the approach is also compatible with the use of adjoints to obtain multiple first order sensitivities at a fixed cost. © Springer-Verlag Berlin Heidelberg 2009. |
| spellingShingle | Giles, M Vibrato Monte Carlo sensitivities |
| title | Vibrato Monte Carlo sensitivities |
| title_full | Vibrato Monte Carlo sensitivities |
| title_fullStr | Vibrato Monte Carlo sensitivities |
| title_full_unstemmed | Vibrato Monte Carlo sensitivities |
| title_short | Vibrato Monte Carlo sensitivities |
| title_sort | vibrato monte carlo sensitivities |
| work_keys_str_mv | AT gilesm vibratomontecarlosensitivities |