Estimating Greeks for Variance-Gamma

Assuming the underlying assets follow a Variance-Gamma (VG) process, we consider the problem of estimating sensitivities such as the Greeks on a basket of stocks when Monte Carlo simulation is employed. We focus on a class of derivatives called mountain range options, comparing indirect methods (finite difference techniques such as forward differences) and two direct methods: infinitesimal perturbation analysis (IPA) and the likelihood ratio (LR) method, where the latter is also implemented via a recently proposed numerical technique developed by Glasserman and Liu (2007) using the characteristic function. We carry out numerical simulation experiments to evaluate the efficiency of the different estimators and discuss the strengths and weakness of each method.