Partial Proxy Simulation Schemes for Generic and Robust Monte-Carlo Greeks
26 Pages Posted: 3 Oct 2006
Date Written: September 30, 2006
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: Suggested Citation