Modified Method of Moments for Generalized Laplace Distribution

TL;DR

This paper evaluates the classic method of moments for symmetric variance-gamma distributions, revealing its limitations, and introduces a modified approach using absolute moments that improves efficiency and competitiveness with maximum likelihood estimation.

Contribution

The paper proposes a modified method of moments using absolute moments, enhancing parameter estimation accuracy for symmetric variance-gamma distributions.

Findings

Original method often performs poorly in simulations.

Modified method with absolute moments shows significant improvement.

Modified estimators are competitive with maximum likelihood methods.

Abstract

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.