Title: A self-calibrating method for heavy-tailed data modeling: Applications in finance and insurance
Authors: Marie Kratz - ESSEC Business School, CREAR (France) [presenting]
Abstract: A new self-calibrating method for heavy-tailed modeling is proposed. One of the main issues in the statistical literature of extremes concerns the tail index estimation, closely linked to the determination of a threshold above which a Generalized Pareto Distribution (GPD) can be fitted. Approaches to this estimation may be classified into two classes, one using threshold methods, in which the threshold to estimate the tail is chosen graphically according to the problem, the other suggesting self-calibrating methods, where the threshold is algorithmically determined. Our approach belongs to this second class proposing a hybrid distribution for heavy tailed data modeling, which links a normal (or lognormal) distribution to a GPD via an exponential distribution that bridges the gap between mean and asymptotic behaviors. A new unsupervised algorithm is then developed for estimating the parameters of this model. The effectiveness of the method is studied in terms of goodness-of-fit on simulated data, and compared with other more standard EVT approaches. One advantage of the method is that it provides a good fit of the entire distribution rather than simply the tail, allowing for a full pricing of the risk when considering applications in risk management. We provide examples of applications in finance, insurance and neuroscience.