Partial proxy simulation schemes for generic and robust Monte Carlo Greeks

Christian P. Fries, Mark S. Joshi

Abstract

ABSTRACT

We consider a generic framework that allows us 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 (2007)). As a benchmark we apply the method to the pricing of digital caplets and target redemption notes using LIBOR and CMS indexes 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.