Malliavin Greeks without Malliavin calculus
AbstractWe derive and analyze Monte Carlo estimators of price sensitivities ("Greeks") for contingent claims priced in a diffusion model. There have traditionally been two categories of methods for estimating sensitivities: methods that differentiate paths and methods that differentiate densities. A more recent line of work derives estimators through Malliavin calculus. The purpose of this article is to investigate connections between Malliavin estimators and the more traditional and elementary pathwise method and likelihood ratio method. Malliavin estimators have been derived directly for diffusion processes, but implementation typically requires simulation of a discrete-time approximation. This raises the question of whether one should discretize first and then differentiate, or differentiate first and then discretize. We show that in several important cases the first route leads to the same estimators as are found through Malliavin calculus, but using only elementary techniques. Time-averaging of multiple estimators emerges as a key feature in achieving convergence to the continuous-time limit.
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Bibliographic InfoArticle provided by Elsevier in its journal Stochastic Processes and their Applications.
Volume (Year): 117 (2007)
Issue (Month): 11 (November)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description
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- Eric Benhamou, 2003. "Optimal Malliavin Weighting Function for the Computation of the Greeks," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 13(1), pages 37-53.
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- Eric FourniÃ© & Jean-Michel Lasry & Pierre-Louis Lions & JÃ©rÃ´me Lebuchoux, 2001. "Applications of Malliavin calculus to Monte-Carlo methods in finance. II," Finance and Stochastics, Springer, vol. 5(2), pages 201-236.
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