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Localized Proxy Simulation Schemes for Generic and Robust Monte-Carlo Greeks

15 Pages Posted: 8 May 2007  

Christian P. Fries

Ludwig Maximilian University of Munich - Department of Mathematics; DZ Bank AG

Date Written: May 6, 2007

Abstract

For the numerical calculation of partial derivatives (aka.~sensitivites or greeks) from a Monte-Carlo simulation there are essentially two possible approaches: The pathwise method and the likelihood ratio method. Both methods have their shortcomings: While the pathwise method works very well for smooth payouts it fails for discontinuous payouts. On the other hand, the likelihood ratio gives much better results on discontinuous payouts, but falls short of the pathwise method if smooth payouts are considered.

In this paper, we present a modification to the (partial) proxy simulation scheme framework, resulting in a per-path selection of either the pathwise method or the likelihood ratio method. This allows us to chose the optimal simulation method on a path-by-path basis.

Since the method is implemented as a proxy simulation scheme as well, the sensitivities can be calculated from simple finite differences applied to the pricing engine.

Keywords: Monte-Carlo Sensitivities, Likelihood Ratio, Importance Sampling, Greeks, Proxy Simulation Scheme, Digital Option, Binary Option, Trigger Product, Target Redemption Note

JEL Classification: C15, G13

Suggested Citation

Fries, Christian P., Localized Proxy Simulation Schemes for Generic and Robust Monte-Carlo Greeks (May 6, 2007). Available at SSRN: https://ssrn.com/abstract=984744 or http://dx.doi.org/10.2139/ssrn.984744

Christian P. Fries (Contact Author)

Ludwig Maximilian University of Munich - Department of Mathematics ( email )

Theresienstrasse 39
Munich
Germany

DZ Bank AG ( email )

60265 Frankfurt am Main
Germany

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