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

26 Pages Posted: 3 Oct 2006  

Christian P. Fries

LMU Munich, Department of Mathematics; DZ Bank AG

Mark S. Joshi

University of Melbourne - Centre for Actuarial Studies

Date Written: September 30, 2006

Abstract

We consider a generic framework which allows to calculate robust Monte-Carlo sensitivities seamlessly through simple finite difference approximation. The method proposed is a generalization and improvement of the proxy simulation scheme method (Fries and Kampen, 2005).

As a benchmark we apply the method to the pricing of digital caplets and target redemption notes using LIBOR and CMS indices under a LIBOR Market Model. We calculate stable deltas, gammas and vegas by applying direct finite difference to the proxy simulation scheme pricing.

The framework is generic in the sense that it is model and almost product independent. The only product dependent part is the specification of the proxy constraint. This allows for an elegant implementation, where new products may be included at small additional costs.

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. and Joshi, Mark S., Partial Proxy Simulation Schemes for Generic and Robust Monte-Carlo Greeks (September 30, 2006). Available at SSRN: https://ssrn.com/abstract=934012 or http://dx.doi.org/10.2139/ssrn.934012

Christian P. Fries (Contact Author)

LMU Munich, Department of Mathematics ( email )

Theresienstrasse 39
Munich
Germany

DZ Bank AG ( email )

60265 Frankfurt am Main
Germany

Mark Joshi

University of Melbourne - Centre for Actuarial Studies ( email )

Melbourne, 3010
Australia

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