Computing Greeks using multilevel path simulation

Abstract

We investigate the extension of the multilevel Monte Carlo method [2, 3] to the calculation of Greeks. The pathwise sensitivity analysis [5] differentiates the path evolution and effectively reduces the smoothness of the payoff. This leads to new challenges: the use of naive algorithms is often impossible because of the inapplicability of pathwise sensitivities to discontinuous payoffs.

These challenges can be addressed in three different ways: payoff smoothing using conditional expectations of the payoff before maturity [5]; an approximation of the above technique using path splitting for the final timestep [1]; the use of a hybrid combination of pathwise sensitivity and the Likelihood Ratio Method [4]. We discuss the strengths and weaknesses of these alternatives in different multilevel Monte Carlo settings.