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The Solvency II regulatory framework requires European insurance companies to guarantee their solvability and stability by retaining enough Own Funds to cover future unexpected losses at a given confidence level. A Standard Formula approach is provided to estimate the capital requirement needed. Still, Solvency II allows internal methodologies to quantify the capital absorption arising from specific risk types or even to replace the Standard Formula with a full internal model. This work proposes a new internal model approach to measure the Catastrophe Recession Risk. The Recession Risk implies a mandatory capital absorption component for the insurance companies operating in the credit and suretyship business. The proposed model is based on the CreditRisk+ model and designed to behave countercyclically, aligning with the original intent of the European supervisory authority when first introducing this risk into the Solvency II risks' taxonomy. Additionally, the model is applied to define an index for monitoring future recession crises based on the time series of past default rates. [ABSTRACT FROM AUTHOR]

In credit insurance practice, insurers must address the lack of information that affects their knowledge of present and past underwritten risks. In this context, classical frequency estimators, although effectively employed in various financial and actuarial applications to measure absorbing events, are not suitable. Given that default frequency estimation is affected by the temporal distribution of the invoices issued by an insured seller during the credit insurance coverage period, this study proposes a behavioral model to describe the commercial relationships between insured sellers and their buyers. The model is parsimonious and easily calibrated based on historical data. A closed-form estimator for the number of default events is introduced by the model parameterization, allowing for a precise inference of the actual default frequency over a given period, which compensates for the bias caused by unobserved events. The proposed method is numerically tested against the simultaneous presence of multiple behavioral types, whose composition may change over time, but still enables a credit insurance company to accurately estimate claim and default probabilities. [ABSTRACT FROM AUTHOR]

The CreditRisk + model is one of the industry standards for the valuation of default risk in credit loans portfolios. The calibration of CreditRisk + requires, inter alia, the specification of the parameters describing the structure of dependence among default events. This work addresses the calibration of these parameters. In particular, we study the dependence of the calibration procedure on the sampling period of the default rate time series, that might be different from the time horizon onto which the model is used for forecasting, as it is often the case in real life applications. The case of autocorrelated time series and the role of the statistical error as a function of the time series period are also discussed. The findings of the proposed calibration technique are illustrated with the support of an application to real data. [ABSTRACT FROM AUTHOR]