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Simulation of multi-asset option Greeks under a special Lévy model by Malliavin calculus. (English) Zbl 1373.60096

Summary: 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.

MSC:

60H07 Stochastic calculus of variations and the Malliavin calculus
60G51 Processes with independent increments; Lévy processes
65C05 Monte Carlo methods

Software:

TOMS659; sobol.cc
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Full Text: DOI

References:

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