Wykorzystanie kaskad kopuli w agregacji ryzyka w procesie wyznaczania kapitałowych wymogów wypłacalności w Solvency II
The use of vine copula constructions in the process of determining solvency capital requirements in Solvency II

Author(s): Krystian Szczęsny
Subject(s): Politics, Economy, Supranational / Global Economy, Business Economy / Management, Micro-Economics, EU-Accession / EU-DEvelopment, Marketing / Advertising, Business Ethics, Socio-Economic Research, EU-Legislation
Published by: Wydawnictwo Uniwersytetu Ekonomicznego w Poznaniu
Keywords: dyrektywa Solvency II;kapitałowy wymóg wypłacalności;agregacja ryzyka;ubezpieczyciele;kaskady kopuli;
Summary/Abstract: One of the basic aspects of the Solvency II Directive introduced in 2016 is the protection of the insured against the insolvency of insurance companies. For this purpose, by aggregating the solvency capital requirements for the specific types of risk to which the insurer is exposed, the solvency capital requirement (SCR) and the diversification effect (ED) are determined. Insurers are able to calculate the SCR using the Standard Formula given by the authors of the Directive or internal models developed by their insurance companies. The Standard Formula is based on the variance-covariance method, which assumes a constant correlation matrix that defines the relationships between aggregated risks to which the insurer is exposed. The aim of the research is to use, in internal models, pair-copula constructions in order to model the relationship between aggregated risk modules. The structure of the relationship between the aggregated risks is modeled with the use of C-vine and D-vine copula, while the range of possible SCRs resulting from various dependency modeling methods is determined using the ARA (Adaptive Rearrangement Algorithm). In the study, the author arbitrarily assumes loss distributions for the insurer’s five major risk modules, i.e. market, counterparty default, life, health, and non-life modules. The author compares the ED obtained by the variance-covariance method,the ED obtained with the use of copula and the ED corresponding to the upper limit of the SCR determined by the ARA algorithm. The conducted research shows how important in the SCR and ED determination process is the role played by the correct identification of the structure of the relationship between aggregated risks and presents the possibilities of using pair-copula constructions for this purpose.

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