Smart expansion and fast calibration for jump diffusion
AbstractUsing 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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Bibliographic InfoPaper provided by HAL in its series Post-Print with number hal-00200395.
Date of creation: Sep 2009
Date of revision:
Publication status: Published, Finance and Stochastics, 2009, 13, 4, 563-589
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asymptotic expansion; Malliavin calculus; volatility skew and smile; small diffusion process; small jump frequency/size;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-07-03 (All new papers)
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