Fast greeks by simulation in forward LIBOR models

Abstract

This paper develops methods for fast estimation of option price sensitivities in Monte Carlo simulation of term structure models. The models considered are based on discretely compounded forward rates with proportional volatilities. The ef®cient estimation of option deltas, gammas, and vegas are investigated in this setting. Various general methods are available in the Monte Carlo literature for computing such estimates; these methods are tailored to the term structure models and approximations speci®c to this setting are developed in order either to accelerate the methods or to expand their applicability. The authors provide some theoretical support for the application of the basic methods and evaluate the approximations through numerical experiments. The results indicate that the proposed algorithms can substantially improve on standard ®nite difference estimates of sensitivities.