Generating unfavourable VaR scenarios under Solvency II with patchwork copulas

Author:

Pfeifer Dietmar1,Ragulina Olena2

Affiliation:

1. Carl von Ossietzky Universität Oldenburg , Germany

2. Taras Shevchenko National University of Kyiv , Ukraine

Abstract

Abstract The central idea of the paper is to present a general simple patchwork construction principle for multivariate copulas that create unfavourable VaR (i.e. Value at Risk) scenarios while maintaining given marginal distributions. This is of particular interest for the construction of Internal Models in the insurance industry under Solvency II in the European Union. Besides this, the Delegated Regulation by the European Commission requires all insurance companies under supervision to consider different risk scenarios in their risk management system for the company’s own risk assessment. Since it is unreasonable to assume that the potential worst case scenario will materialize in the company, we think that a modelling of various unfavourable scenarios as described in this paper is likewise appropriate. Our explicit copula approach can be considered as a special case of ordinal sums, which in two dimensions even leads to the technically worst VaR scenario.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Modeling and Simulation,Statistics and Probability

Reference32 articles.

1. [1] Arbenz, P., C. Hummel, and G. Mainik (2012). Copula based hierarchical risk aggregation through sample reordering. Insurance Math. Econ. 51(1), 122–133.

2. [2] Basilevsky, A. (1983). Applied Matrix Algebra in the Statistical Sciences. North-Holland, New York.

3. [3] Boonen, T. J. (2017). Solvency II solvency capital requirement for life insurance companies based on expected shortfall. Eur. Actuar. J. 7, 405–434.

4. [4] Cadoni, P. (Ed.) (2014). Internal Models and Solvency II: From Regulation to Implementation. RISK Books, London.

5. [5] Cottin, C. and D. Pfeifer (2014). From Bernstein polynomials to Bernstein copulas. J. Appl. Funct. Anal. 9(3-4), 277–288.

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