Calibration of the Pareto and related distributions -a reference-intrinsic approach

Abstract: We study two Bayesian (Reference Intrinsic and Jeffreys prior) and two frequentist (MLE and PWM) approaches to calibrating the Pareto and related distributions. Three of these approaches are compared in a simulation study and all four to investigate how much equity risk capital banks subject to Basel II banking regulations must hold. The Reference Intrinsic approach, which is invariant under one-to-one transformations of the data and parameter, performs better when fitting a generalised Pareto distribution to data simulated from a Pareto distribution and is competitive in the case study on equity capital requirements