The computation of Greeks with Multilevel Monte Carlo
We study the use of the multilevel Monte Carlo technique [2, 3] 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 weaknessesof these alternatives in different multilevel Monte Carlo settings.
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