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SIMULATION OF MULTI-ASSET OPTION GREEKS UNDER A SPECIAL LÉVY MODEL BY MALLIAVIN CALCULUS

Part of: Stochastic processes Stochastic analysis Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  17 February 2016

YONGZENG LAI  and
HAIXIANG YAO
YONGZENG LAI
Affiliation:
Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, N2L 3C5, Canada email ylai@wlu.ca
HAIXIANG YAO*
Affiliation:
School of Finance, Guangdong University of Foreign Studies, Guangzhou 510006, China email yaohaixiang@gdufs.edu.cn
*
✉yaohaixiang@gdufs.edu.cn
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Abstract

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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.

Keywords

subordinated Brownian motionsmulti-asset optionsoption sensitivities or GreeksMalliavin calculusquasi-Monte Carlo methods

MSC classification

Primary: 60H07: Stochastic calculus of variations and the Malliavin calculus
Secondary: 60G51: Processes with independent increments; L'evy processes 65C05: Monte Carlo methods
Type
Research Article
Information
The ANZIAM Journal , Volume 57 , Issue 3 , January 2016 , pp. 280 - 298
Copyright
© 2016 Australian Mathematical Society 

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