Gestione del rischio operativo : stima e simulazione frattale della distribuzione delle perdite operative

The main aim of this thesis consists of introducing an alternative method for estimating the distribution of operational losses and to show how one can avoid the Loss Distribution Approach (LDA) and Extreme Value Theory (EVT) problems using an alternative estimation technique based on fractal analysis. The Loss Distribution Approach (LDA) is the classical method used in this context and it involves actuarial mathematics models; the literature has shown as few data on the operational loss events can lead to distortions in the estimation of the effective distribution. This work describes a new quantitative analysis for operational risk measurement based on fractal estimations and simulations of data series. The fractal distribution function estimator has been studied by Iacus and La Torre, where they showed, through a Monte Carlo analysis, that this estimator works better than the empirical distribution function estimator when small samples are considered. We apply this technique to the loss distribution function estimation using an Italian banking group database and we compare it with the LDA methodology