julien Hambuckers

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

This paper is concerned with modelling the behaviour 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 dependence 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 analyse a novel data-set 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.

Understanding the Economic Determinants of the Severity of Operational Losses: A regularized Generalized Pareto Regression Approach,

We investigate a novel database of 10,217 extreme operational losses from the Italian bank UniCredit, covering a period of 10 years and 7 different event types. Our goal is to shed light on the dependence between the severity distribution of these losses and a set of macroeconomic, financial and firm-specific factors. To do so, we use Generalized Pareto regression techniques, where both the scale and shape parameters are assumed to be functions of these explanatory variables. In this complex distributional regression framework, we perform the selection of the relevant covariates with a state-of-the-art penalized-likelihood estimation procedure relying on L1-penalty terms. A simulation study indicates that this approach efficiently selects covariates of interest and tackles spurious regression issues encountered when dealing with integrated time series. The results of our empirical analysis have important implications in terms of risk management and regulatory policy. In particular, we found that high Italian unemployment rate and low GDP growth rate in the European Union are associated with smaller probabilities of extreme severities, whereas high values of the VIX and high growth rates of housing prices are associated with more extreme losses. Looking at firm-specific factors, low leverage ratio and high deposit growth rate are associated with a higher likelihood of extreme losses. Lastly, we illustrate the impact of different economic scenarios on the requested capital for operational risk. We find important discrepancies across event types and scenarios.

A robust statistical approach to select adequate error distributions for financial returns

ABSTRACT In this article, we propose a robust statistical approach to select an appropriate error distribution, in a classical multiplicative heteroscedastic model. In a first step, unlike to the traditional approach, we do not use any GARCH-type estimation of the conditional variance. Instead, we propose to use a recently developed nonparametric procedure [31]: the local adaptive volatility estimation. The motivation for using this method is to avoid a possible model misspecification for the conditional variance. In a second step, we suggest a set of estimation and model selection procedures (Berk–Jones tests, kernel density-based selection, censored likelihood score, and coverage probability) based on the so-obtained residuals. These methods enable to assess the global fit of a set of distributions as well as to focus on their behaviour in the tails, giving us the capacity to map the strengths and weaknesses of the candidate distributions. A bootstrap procedure is provided to compute the rejection regions in this semiparametric context. Finally, we illustrate our methodology throughout a small simulation study and an application on three time series of daily returns (UBS stock returns, BOVESPA returns and EUR/USD exchange rates).