  We study the use of the multilevel Monte Carlo technique in the context of
the calculation of Greeks. The pathwise sensitivity analysis differentiates the
path evolution and reduces the payoff's smoothness. This leads to new
challenges: the inapplicability of pathwise sensitivities to non-Lipschitz
payoffs often makes the use of naive algorithms impossible. These challenges
can be addressed in three different ways: payoff smoothing using conditional
expectations of the payoff before maturity; approximating the previous
technique with path splitting for the final timestep; using of a hybrid
combination of pathwise sensitivity and the Likelihood Ratio Method. We
investigate the strengths and weaknesses of these alternatives in different
multilevel Monte Carlo settings.
