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Published in:
2009 | OriginalPaper | Chapter
Vibrato Monte Carlo Sensitivities
Author : Michael B. Giles
Published in: Monte Carlo and Quasi-Monte Carlo Methods 2008
Publisher: Springer Berlin Heidelberg
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We show how the benefits of the pathwise sensitivity approach to computing Monte Carlo Greeks can be extended to discontinuous payoff functions through a combination of the pathwise approach and the Likelihood Ratio Method. With a variance reduction modification, this results in an estimator which for timestep
h
has a variance which is
O
(
h
−1/2
) for discontinuous payoffs and
O
(1) for continuous payoffs. Numerical results confirm the variance is much lower than the
O
(
h
−1
) variance of the Likelihood Ratio Method, and the approach is also compatible with the use of adjoints to obtain multiple first order sensitivities at a fixed cost.