  In this note, we consider the performance of the classic method of moments
for parameter estimation of symmetric variance-gamma (generalized Laplace)
distributions. We do this through both theoretical analysis (multivariate delta
method) and a comprehensive simulation study with comparison to maximum
likelihood estimation, finding 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, and is also competitive with
maximum likelihood estimation.
