A Markov-switching Generalized additive model for compound Poisson processes, with applications to operational losses models

This paper is concerned with modeling the behavior of random sums over time. Such
models are particularly useful to describe the dynamics of operational losses, and
to correctly estimate tail-related risk indicators. However, time-varying dependence
structures make it a difficult task. To tackle these issues, we formulate a new Markov-
switching generalized additive compound process combining Poisson and generalized
Pareto distributions. This flexible model takes into account two important features:
on the one hand, we allow all parameters of the compound loss distribution to depend
on economic covariates in a flexible way. On the other hand, we allow this depen-
dence to vary over time, via a hidden state process. A simulation study indicates that,
even in the case of a short time series, this model is easily and well estimated with
a standard maximum likelihood procedure. Relying on this approach, we analyze a
novel dataset of 819 losses resulting from frauds at the Italian bank UniCredit. We
show that our model improves the estimation of the total loss distribution over time,
compared to standard alternatives. In particular, this model provides estimations of
the 99.9% quantile that are never exceeded by the historical total losses, a feature
particularly desirable for banking regulators.