Modeling non-stationary operational risk: A smooth-transition distributional regression approach

The distribution of operational losses is particularly challenging to model, due to the high probability of extremes and the existence of time-varying structural dependencies. In particular, operational loss severity distribution is often concerned with changes in regulations, business cycles or financial crises that affect the dependence structure with potential predictors. To help accounting for this empirical feature, we introduce smooth-transition (ST) Generalized Pareto (GP). In this time-varying regression model, the parameters of the GP distribution are related to explanatory variables through a regression function, which depends itself on a time-varying predictor of structural changes. First, we discuss the computational challenges associated to this class of models. Then, we propose several estimation strategies and investigate their finite sample properties in a simulation study. Eventually, we use our findings to study the time-varying dependence structure of monthly operational risks with market volatility and past extreme events.