In a recent post I discussed some of my work relating to modelling extreme values in various economic data-sets. The work that my colleagues and I have been undertaking focuses on the use of the Generalized Pareto distribution (GPD). The estimation of the parameters of this model facilitates estimates of Value at Risk (VaR) and Expected Shortfall (ES).
There are various ways of estimating the parameters of the GPD but, not surprisingly, maximum likelihood estimation (MLE) is a common choice. However, there are some real traps when it comes to estimating the GPD using MLE, and they're worth knowing about if you're into this sort of thing.