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| HAL: hal-00200395, version 2 |
| arXiv: 0712.3485 |
| DOI: 10.1007/s00780-009-0102-3 |
| Detailed view |  Export this paper |
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| Finance and Stochastics 13, 4 (2009) 563-589 |
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| Available versions: | v1 (2007-12-20) | v2 (2008-09-30) |
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| Smart expansion and fast calibration for jump diffusion |
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| Eric Benhamou 1Emmanuel Gobet 2 |
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| (2009-09) |
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| Using Malliavin calculus techniques, we derive an analytical formula for the price of European options, for any model including local volatility and Poisson jump process. We show that the accuracy of the formula depends on the smoothness of the payoff function. Our approach relies on an asymptotic expansion related to small diffusion and small jump frequency/size. Our formula has excellent accuracy (the error on implied Black-Scholes volatilities for call option is smaller than 2 bp for various strikes and maturities). Additionally, model calibration becomes very rapid. |
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| 1: | Pricing Partners |
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Pricing Partners |
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| 2: | Laboratoire Jean Kuntzmann (LJK) |
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CNRS : UMR5224 – Université Joseph Fourier - Grenoble I – Université Pierre-Mendès-France - Grenoble II – Institut Polytechnique de Grenoble - Grenoble Institute of Technology |
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| Subject | : | Mathematics/Probability Humanities and Social Sciences/Economies and finances |
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| asymptotic expansion – Malliavin calculus – volatility skew and smile – small diffusion process – small jump frequency/size |
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| hal-00200395, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00200395 | |
| oai:hal.archives-ouvertes.fr:hal-00200395 | |
| From: Emmanuel Gobet | |
| Submitted on: Tuesday, 30 September 2008 17:15:42 | |
| Updated on: Friday, 18 January 2013 23:20:11 | |
