QuasiMonte CarloBased Conditional Malliavin Method for ContinuousTime Asian Option Greeks
Abstract
Although many methods for computing the Greeks of discretetime Asian options are proposed, few methods to calculate the Greeks of continuoustime Asian options are known. In this paper, we develop an integration by parts formula in the multidimensional Malliavin calculus, and apply it to obtain the Greeks formulae for continuoustime Asian options in the multiasset situation. We combine the Malliavin method with the quasiMonte Carlo method to calculate the Greeks in simulation. We discuss the asymptotic convergence of simulation estimates for the continuoustime Asian option Greeks obtained by Malliavin derivatives. We propose to use the conditional quasiMonte Carlo method to smooth Malliavin Greeks, and show that the calculation of conditional expectations analytically is viable for many types of Asian options. We prove that the new estimates for Greeks have good smoothness. For binary Asian options, Asian call options and upandout Asian call options, for instance, our estimates are infinitely times differentiable. We take the gradient principal component analysis method as a dimension reduction technique in simulation. Numerical experiments demonstrate the large efficiency improvement of the proposed method, especially for Asian options with discontinuous payoff functions.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 DOI:
 10.48550/arXiv.2109.05279
 arXiv:
 arXiv:2109.05279
 Bibcode:
 2021arXiv210905279Y
 Keywords:

 Mathematics  Numerical Analysis;
 Mathematics  Probability;
 Mathematics  Statistics Theory