Efficient Monte Carlo Simulation of the Delta Vector of a Bermudian Swaption in the LIBOR Market Model

Abstract

We consider various methods for an efficient numerical computation of the Delta vector of a Bermudan swaption in a LIBOR market model setting. All methods are based on the least-squares Montel Carlo method of Longstaff & Schwartz (2001). Among them, we present three new approaches: a new version of the adjoint method introduced by Leclerc et al. (2009), a path-wise method based on the use of the forward drift, and a likelihood ratio approach. The new version of the adjoint method shows superior performance compared with the other methods.