Vibrato Monte Carlo Sensitivities

Michael B. Giles ()
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Michael B. Giles: Oxford University Mathematical Institute, Oxford-Man Institute of Quantitative Finance

A chapter in Monte Carlo and Quasi-Monte Carlo Methods 2008, 2009, pp 369-382 from Springer

Abstract: Abstract 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.

Keywords: Conditional Expectation; Path Simulation; Order Sensitivity; Adjoint Approach; Likelihood Ratio Method (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-04107-5_23

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DOI: 10.1007/978-3-642-04107-5_23

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