Although the variance-gamma distribution is a flexible model for log-returns of financial assets, so far it has found rather limited applications in finance and risk management. One of the reasons is that maximum likelihood estimation of its parameters is not straightforward. We develop an EM-type algorithm that bypasses the evaluation of the full likelihood, which may be dicult because the density is not in closed form and is unbounded for small values of the shape parameter. Moreover, we study the relative eciency of our approach with respect to the maximum likelihood estimation procedures implemented in the VarianceGamma and ghyp R packages. Extensive simulation experiments and real-data analyses suggest that the multicycle ECM algorithm and the routines in the ghyp R package give the best results in terms of root-mean-squared-error, for both parameter and Value-at-Risk estimation.

Keywords: Multicycle EM algorithm; maximum likelihood; numerical optimization; risk estimation.