Malliavin calculus for Levy markets and new sensitivities
D. Bayazit, C. A. Nolder
We present a method to apply the Malliavin calculus to calculate sensitivities for exponential Levy models built from the Variance Gamma and Normal Inverse Gaussian processes. We also present new sensitivities for these processes. The calculation of the sensitivities is based on a finite dimensional Malliavin calculus and we compare the results with finite dierence calculations. This is done using Monte Carlo methods. For European call and digital options we compare the simulation results with exact calculation of sensitivities using Fourier transform methods. The Malliavin method outperforms the finite dierence method especially when payoff has serious discontinuities.