  In this paper we give easy-to-implement closed-form expressions for European
and Asian Greeks for general L2-payoff functions and underlying assets in an
exponential L\'evy process model with nonvanishing Brownian motion part. The
results are based on Hilbert space valued Malliavin Calculus and extend
previous results from the literature. Numerical experiments suggest, that in
the case of a continuous payoff function, a combination of Malliavin Monte
Carlo Greeks and the finite difference method has a better convergence
behavior, whereas in the case of discontinuous payoff functions, the Malliavin
Monte Carlo method clearly is the superior method compared to the finite
difference approach, for first- and second order Greeks. Reduction arguments
from the literature based on measure change imply that the expressions for the
Greeks in this paper also hold true for generalized Asian options in particular
for fixed and floating strike Asian options.
