Smart expansion and fast calibration for jump diffusion

Details Smart expansion and fast calibration for jump diffusion Smart expansion and fast calibration for jump diffusion

2007-12-20

arxiv.org/abs/0712.3485v2

Economy

Quantitative Finance

Pricing of Securities

in Finance and Stochastics (2009) a paraitre

Scientific paper

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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