TEST FOR CHANGES IN THE MODELED SOLVENCY CAPITAL REQUIREMENT OF AN INTERNAL RISK MODEL

ABSTRACT In the context of the Solvency II directive, the operation of an internal risk model is a possible way for risk assessment and for the determination of the solvency capital requirement of an insurance company in the European Union. A Monte Carlo procedure is customary to generate a model output. To be compliant with the directive, validation of the internal risk model is conducted on the basis of the model output. For this purpose, we suggest a new test for checking whether there is a significant change in the modeled solvency capital requirement. Asymptotic properties of the test statistic are investigated and a bootstrap approximation is justified. A simulation study investigates the performance of the test in the finite sample case and confirms the theoretical results. The internal risk model and the application of the test is illustrated in a simplified example. The method has more general usage for inference of a broad class of law-invariant and coherent risk measures on the basis of a paired sample.

Fire Risk Sub-Module Assessment under Solvency II. Calculating the Highest Risk Exposure

The European Directive 2009/138 of Solvency II requires adopting a new approach based on risk, applying a standard formula as a market proxy in which the risk profile of insurers is fundamental. This study focuses on the fire risk sub-module, framed within the man-made catastrophe risk module, for which the regulations require the calculation of the highest concentration of risks that make up the portfolio of an insurance company within a radius of 200 m. However, the regulations do not indicate a specific methodology. This study proposes a procedure consisting of calculating the cluster with the highest risk and identifying this on a map. The results can be applied immediately by any insurance company, covered under the Solvency II regulations, to determine their maximum exposure to the catastrophic man-made risk of fire, instantly providing them with the necessary input for calibration of the solvency capital requirement.

SCR en el riesgo de suscripción del seguro de vida: mortalidad, longevidad y reaseguro

The aim of this work is to propose an internal model based on the Monte Carlo’s simulation method, for the calculation of the solvency capital requirement of the subscription of life’s risk, of an insurances company that presents two risks, the survival and mortality ones. Unlike the standard model, the aggregation of these two risks will carry out without knowing the correlation matrixes. Afterwards, the effect that the different modalities of reinsurance have in the solvency capital requirement will be analyzed. The modalities of reinsurance object of analysis are the quota share, the surplus and the stop-loss.

Una herramienta de cálculo para la predicción de los Requerimientos de Capital en seguros de vida

Solvencia II (Directiva parlamentaria europea 2009/138/EC) establece los criterios y normas de carácter cuantitativo y cualitativo que las entidades aseguradoras que operan en la Unión Europea deben acometer para garantizar su solvencia y estabilidad financiera. Solvencia II está estructurada en tres pilares y abarca, a través de un esquema modular, los distintos riesgos a los que está expuesta una entidad aseguradora. Este trabajo se centra en algunos de los submódulos del negocio de vida y estudia el Solvency Capital Requirement (SCR) para tres tipos de seguros: seguro de capital diferido, seguro de vida entera y seguro de renta inmediata. En concreto, analiza dentro del modelo estándar el cálculo del requerimiento de capital en los submódulos del riesgo de mortalidad y de longevidad y presenta una herramienta de cálculo muy sencilla para, prefijada la tabla de mortalidad, simplificar al máximo el cálculo del SCR de cualquier cartera de asegurados de estos submódulos. Se muestra cómo agrupando el total de pólizas de una cartera por edad del asegurado y/o temporalidad puede predecirse el capital requerido de solvencia para una cartera y un riesgo determinado a través de una función lineal. Al contrario de lo que cabría esperar por la ley de los grandes números, los requerimientos relativos de capital no decrecen con el tamaño de la cartera.