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Although many methods for computing the Greeks of discrete-time Asian optionsare proposed, few methods to calculate the Greeks of continuous-time Asianoptions are known. In this paper, we develop an integration by parts formula inthe multi-dimensional Malliavin calculus, and apply it to obtain the Greeksformulae for continuous-time Asian options in the multi-asset situation. Wecombine the Malliavin method with the quasi-Monte Carlo method to calculate theGreeks in simulation. We discuss the asymptotic convergence of simulationestimates for the continuous-time Asian option Greeks obtained by Malliavinderivatives. We propose to use the conditional quasi-Monte Carlo method tosmooth Malliavin Greeks, and show that the calculation of conditionalexpectations analytically is viable for many types of Asian options. We provethat the new estimates for Greeks have good smoothness. For binary Asianoptions, Asian call options and up-and-out Asian call options, for instance,our estimates are infinitely times differentiable. We take the gradientprincipal component analysis method as a dimension reduction technique insimulation. Numerical experiments demonstrate the large efficiency improvementof the proposed method, especially for Asian options with discontinuous payofffunctions.

Quasi-Monte Carlo-Based Conditional Malliavin Method for Continuous-Time Asian Option Greeks