Modeling operational losses: a conditional Generalized Pareto regression based on a single-index assumption

In this paper, we consider a regression model in which the tail of the conditional distribution of the response can be approximated
by a Generalized Pareto distribution. Our model is based on a semiparametric single-index assumption on the conditional tail index while no further assumption on the conditional scale parameter is made. The underlying dimension reduction assumption allows the procedure to be of prime interest in the case where the dimension of the covariates is high, in which case the purely nonparametric techniques fail while the purely parametric one are too rough to correctly fit to the data. We propose an iterative algorithm in order to perform their practical implementation. Our results are supported by some simulations. To illustrate the proposed approach, the method is applied to a novel database of operational losses from the bank UniCredit