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In this note, we consider the performance of the classic method of momentsfor parameter estimation of symmetric variance-gamma (generalized Laplace)distributions. We do this through both theoretical analysis (multivariate deltamethod) and a comprehensive simulation study with comparison to maximumlikelihood estimation, finding performance is often unsatisfactory. Inaddition, we modify the method of moments by taking absolute moments to improveefficiency; in particular, our simulation studies demonstrate that our modifiedestimators have significantly improved performance for parameter valuestypically encountered in financial modelling, and is also competitive withmaximum likelihood estimation.

Modified Method of Moments for Generalized Laplace Distribution