Simulation of multi-asset option Greeks under a special Lévy model by Malliavin calculus

Yongzeng Lai, Haixiang Yao


We discuss simulation of sensitivities or Greeks of multi-asset European style options under a special Lévy process model: that is, the subordinated Brownian motion model. The Malliavin calculus method combined with Monte Carlo and quasi-Monte Carlo methods is used in the simulations. Greeks are expressed in terms of the expectations of the option payoff functions multiplied by the weights involving Malliavin derivatives for multi-asset options. Numerical results show that the Malliavin calculus method is usually more efficient than the finite difference method for options with nonsmooth payoffs. The superiority of the former method over the latter is even more significant when both are combined with quasi-Monte Carlo methods.



subordinated Brownian motions; multi-asset options; option sensitivities or Greeks; Malliavin calculus; quasi-Monte Carlo methods


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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.