The computation of Greeks with multilevel Monte Carlo
AbstractWe study the use of the multilevel Monte Carlo technique in the context of the calculation of Greeks. The pathwise sensitivity analysis differentiates the path evolution and reduces the payoff's smoothness. This leads to new challenges: the inapplicability of pathwise sensitivities to non-Lipschitz payoffs often makes the use of naive algorithms impossible. These challenges can be addressed in three different ways: payoff smoothing using conditional expectations of the payoff before maturity; approximating the previous technique with path splitting for the final timestep; using of a hybrid combination of pathwise sensitivity and the Likelihood Ratio Method. We investigate the strengths and weaknesses of these alternatives in different multilevel Monte Carlo settings.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1102.1348.
Date of creation: Feb 2011
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-02-19 (All new papers)
- NEP-CIS-2011-02-19 (Confederation of Independent States)
- NEP-CMP-2011-02-19 (Computational Economics)
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