In designing credit rating systems under the new Basel Accord, considerable effort has been devoted to rating assignment and quantification, while the choice of the optimal bucket structure has received less attention. To fill this gap, we propose two “bucketing” strategies based on constrained optimisation, paying attention to the implications of rating buckets for loan-pricing and adverse selection phenomena. We compare them with some more naïve approaches, based on a sample of about 100,000 European companies. We also analyse the persistence of our performance measures over time, as well as the effect of large exposures being associated with low-PD obligors.

We introduce a statistical model for operational losses based on heavy-tailed distributions and bipartite graphs, which captures the event type and business line structure of operational risk data. The model explicitly takes into account the Pareto tails of losses and the heterogeneous dependence structures between them. We then derive estimators and provide estimation methods for individual as well as aggregated tail risk, measured in terms of Value-at-Risk and Conditional-Tail-Expectation for very high confidence levels, and introduce also an asymptotically full capital allocation method for portfolio risk. Having access to real-world operational risk losses from the Italian banking system, we apply our model to these data, and carry out risk estimation in terms of the previously derived quantities. Simulation studies further reveal first that even with a small number of observations, the proposed estimation methods produce estimates that converge to the true asymptotic values, and second, that quantifying dependence by means of the empirical network has a big impact on estimates at both individual and aggregate level, as well as for capital allocations.

Operational risk data, when available, are usually scarce, heavy-tailed and possibly dependent. In this work, we introduce a model that captures such real-world characteristics and explicitly deals with heterogeneous pairwise and tail dependence of losses. By considering flexible families of copulas, we can easily move beyond modeling bivariate dependence among losses and estimate the total risk capital for the seven- and eight-dimensional distributions of event types and business lines. Using real-world data, we then evaluate the impact of realistic dependence modeling on estimating the total regulatory capital, which turns out to be up to 38% smaller than what the standard Basel approach would prescribe.

This paper explores the relationship between environmental, social and governance (ESG) information and systemic risk, an increasingly important issue for both regulators and investors. While ESG ratings are widely used to assess a company’s non-financial performance, the impact of these factors on financial stability and systemic risk is still under debate. By extending the Forecast Error Variance Decomposition (FEVD) method with a double regularization on both the underlying vector autoregressive (VAR) parameters and the covariance matrix of the VAR residuals, we are able to address the curse of dimensionality within each estimation. This allows us to examine how vulnerable a company is and how much systemic impact a company has given its specific ESG. Looking at a larger sample of European stocks over the period 2007-2022, we empirically show that both the best and worst ESG performers have the largest impact on the financial system in normal times. However, during a crisis, companies with the best ESG ratings generate significant spillovers throughout the system. These findings highlight the importance of incorporating ESG factors into systemic risk assessments and monitoring companies’ ESG performance to ensure financial stability. Policymakers can benefit from this research by supporting investment in high ESG companies to mitigate relevant spillovers during stressed market conditions, when such companies are more interconnected.

We introduce the Conditional Autoregressive Quantile–Located VaR (QL–CoCaViaR), which extends the Conditional Value–at–Risk (Adrian and Brunnermeier, 2016) by using an estimation process capturing the state in which the financial system and a conditioning company are jointly in distress. Furthermore, we include autoregressive components of conditional quantiles to explicitly model volatility clustering and heteroskedasticity. We support our model with a large empirical analysis, in which we use both classical and novel backtesting methods. Our results show that the quantile–located relationships lead to relevant improvements in terms of predictive accuracy during stressed periods, providing a valuable tool for regulators to assess systemic events.

We introduce a financial portfolio optimization framework that allows to automatically select the relevant assets and estimate their weights by relying on a sorted ℓ1-Norm penalization, henceforth SLOPE. To solve the optimization problem, we develop a new efficient algorithm, based on the Alternating Direction Method of Multipliers. SLOPE is able to group constituents with similar correlation properties, and with the same underlying risk factor exposures. Depending on the choice of the penalty sequence, our approach can span the entire set of optimal portfolios on the risk-diversification frontier, from minimum variance to the equally weighted. Our empirical analysis shows that SLOPE yields optimal portfolios with good out-of-sample risk and return performance properties, by reducing the overall turnover, through more stable asset weight estimates. Moreover, using the automatic grouping property of SLOPE, new portfolio strategies, such as sparse equally weighted portfolios, can be developed to exploit the data-driven detected similarities across assets.