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 .
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 .
R
jump Poisson
Poisson jump
A
function
R
. As a consequence, the calibration of such model becomes very fast
/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