Smart expansion and fast calibration for jump diffusion

Eric Benhamou (1) , Emmanuel Gobet (1) , Mohammed Miri (1)

1 LJK - Laboratoire Jean Kuntzmann

Using Malliavin calculus techniques, we derive an analytical formula for the price of European options, for any model including local volatility and jump Poisson process. We show that the accuracy of the formula depends on the smoothness of the payoff. Our approach relies on an asymptotic expansion related to small diffusion and small jump frequency. As a consequence, the calibration of such model becomes very fast.

Mots clés: asymptotic expansion; Malliavin calculus; volatility skew and smile; small diffusion process; small jump frequency

Domaines: Probabilités [math.PR]; Economies et finances

Eric Benhamou, Emmanuel Gobet, Mohammed Miri. Smart expansion and fast calibration for jump diffusion. 2007. ⟨hal-00200395v1⟩