Smart expansion and fast calibration for jump diffusion

Eric Benhamou (), Emmanuel Gobet () and Mohammed Miri ()
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Emmanuel Gobet: MATHFI - Mathématiques financières - LJK - Laboratoire Jean Kuntzmann - UPMF - Université Pierre Mendès France - Grenoble 2 - UJF - Université Joseph Fourier - Grenoble 1 - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - CNRS - Centre National de la Recherche Scientifique
Mohammed Miri: Pricing Partners - Pricing Partners, MATHFI - Mathématiques financières - LJK - Laboratoire Jean Kuntzmann - UPMF - Université Pierre Mendès France - Grenoble 2 - UJF - Université Joseph Fourier - Grenoble 1 - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - CNRS - Centre National de la Recherche Scientifique

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Abstract: 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.

Keywords: asymptotic expansion; Malliavin calculus; volatility skew and smile; small diffusion process; small jump frequency/size (search for similar items in EconPapers)
Date: 2009-09
Note: View the original document on HAL open archive server: https://hal.science/hal-00200395v2
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Citations: View citations in EconPapers (21)

Published in Finance and Stochastics, 2009, 13 (4), pp.563-589. ⟨10.1007/s00780-009-0102-3⟩

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Related works:
Journal Article: Smart expansion and fast calibration for jump diffusions (2009)
Working Paper: Smart expansion and fast calibration for jump diffusion (2008)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00200395

DOI: 10.1007/s00780-009-0102-3

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