Smart expansion and fast calibration for jump diffusion

Eric Benhamou (), Emmanuel Gobet and Mohammed Miri
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Emmanuel Gobet: LJK
Mohammed Miri: LJK

Papers from arXiv.org

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.

Date: 2007-12, Revised 2008-09
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http://arxiv.org/pdf/0712.3485 Latest version (application/pdf)

Related works:
Journal Article: Smart expansion and fast calibration for jump diffusions (2009)
Working Paper: Smart expansion and fast calibration for jump diffusion (2009)
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:0712.3485

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