Modified Method of Moments for Generalized Laplace Distributions

In this note, we consider the performance of the classic method of moments for parameter estimation of symmetric variance-gamma (generalized Laplace) distributions. Through both theoretical analysis (multivariate delta method) and a comprehensive simulation study, we demonstrate that caution must be used in applying the method of moments for generalized asymmetric Laplace distributions and related models, as performance is often unsatisfactory. In addition, we modify the method of moments by taking absolute moments to improve efficiency; in particular, our simulation studies demonstrate that our modified estimators have significantly improved performance for parameter values typically encountered in financial modelling.