Option Sensitivity Simulation by Malliavin Calculus and Quasi-Monte Carlo Methods

This paper discusses simulation of the sensitivities or Greek letters of options by Malliavin calculus (MV) combined with Monte Carlo (MC) and quasi-Monte Carlo (QMC) methods. Formulas for Greek letters are derived for options with one underlying asset in both path independent and path dependent cases. Numerical results show that the MV method is much more efficient than the finite difference (FD) method for options with non-smooth payoff functions. The superiority of the first over the second is more significant when combined with QMC methods.