Estimating Value-at-Risk for the g-and-h distribution: an indirect inference approach

peer reviewedThe g-and-h distribution is a flexible model with desirable theoretical properties. Especially, it is able to handle well the complex behavior of loss data. However, parameter estimation is difficult, because the density cannot be written in closed form. In this paper we develop an indirect inference method using the skewed-t distribution as instrumental model. We show that the skewed-t is a well suited auxiliary model and study the numerical issues related to its implementation. A Monte Carlo analysis and an application to operational losses suggest that the indirect inference estimators of the parameters and of the VaR outperform the quantile-based estimators