The calculation of Solvency Capital Requirement using Copulas

Pellecchia, Marco and Perciaccante, Giovambattista (2019): The calculation of Solvency Capital Requirement using Copulas.

Abstract

Our aim is to present an alternative methodology to the standard formula imposed to the insurance regulation (the European directive knows as Solvency II) for the calculus of the capital requirements. We want to demonstrate how this formula is now obsolete and how is possible to obtain lower capital requirement through the theory of the copulas, function that are gaining increasing importance in various economic areas. A lower capital requirement involves the advantage for the various insurance companies not to have unproductive capital that can therefore be used for the production of further profits. Indeed the standard formula is adequate only with some particular assumptions, otherwise it can overestimate the capital requirements that are actually needed as the standard formula underestimates the effect of diversification.

• Item Type: MPRA Paper
• Language: English
• Keywords: Solvency II, Solvency Capital Requirement, Standard Formula, Value-at-Risk, Copula.
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C15 - Statistical Simulation Methods: General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C18 - Methodological Issues: General; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis

References

Artzner P, Delbarn F, Eber J, Heath D 1998. Coherent measures of risk. Mathematical Finance, 9(3) (July), pp. 223-228.

Campagne C 1961. Minimum Standards of Solvency for Insurance Firms. OECD, Paris.

Casella G, Berger R 2002. Statistical Inference. Second edition. International Series on Actuarial Science, University of Florida and University of North Carolina.

Ceiops 2010. CEIOPS’ Advice for Level 2 Implementing Measures on Solvency II.

Dickson D, Hardy M, Waters H 2009. Actuarial Mathematics for Life Contingent Risks. International Series on Actuarial Science, Cambridge.

Fitzpatrick J, Lédeczi Á 2013. Computer Programming with Matlab. Gumroad LLC, University of Vanderbilt of Nashville.

Frees E, Carriere J, Valdez E 1996. Annuity valuation with dependent mortality. The Journal of Risk and Insurance, 63(2) (June), pp. 229-261.

Jaworski P, Durante F, Härdle W, Rychkil T 2009. Copula Theory and Its Applications. Springer, Varsavia, Linz and Torun.

Maity R 2018. Statistical Methods in Hydrology and Hydroclimatology. Springer Transactions in Civil and Environmental Engineering.

McNeil A, Frey R, Embrechts P 2005. Quantitative Risk Management: Concepts, Techniques and Tools. Princeton Series in Finance, Princeton and Oxford.

Nelsen R 2006. An Introduction to copulas. Second edition, Springer Series in Statistic, Portland OR.

Nguyen T, Molinari R 2011. Risk Aggregation by Using Copulas in Internal Models. Journal of Mathematical Finance, 50-57, Graduate School of Business and Economics, Lahr.

Wang S 1998. Aggregation of Correlated Risk Portfolios: Models and Algorithms. Proceedings of the Casualty Actuarial Society, 85, pp.848- 939.

Youn H, Shemyakin A, Herman E 2002. A Re-Examination of the Joint Mortality Functions. North American Actuarial Journal, 6(1) (January), pp.166-170