Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-22T23:31:29.975Z Has data issue: false hasContentIssue false
  • English
  • Français

A CORRELATION SENSITIVITY ANALYSIS OF NON-LIFE UNDERWRITING RISK IN SOLVENCY CAPITAL REQUIREMENT ESTIMATION

Published online by Cambridge University Press:  29 April 2013

Lluís Bermúdez ,
Antoni Ferri  and
Montserrat Guillén
Lluís Bermúdez*
Affiliation:
Departament de Matemàtica Econòmica, Financera i Actuarial, Riskcenter-IREA, University of Barcelona, Diagonal 690, 08034 Barcelona, Spain
Antoni Ferri
Affiliation:
Departament d'Econometria, Estadistíca i Economia Espanyola, Riskcenter-IREA, University of Barcelona, Diagonal 690, 08034 Barcelona, Spain
Montserrat Guillén
Affiliation:
Departament d'Econometria, Estadistíca i Economia Espanyola, Riskcenter-IREA, University of Barcelona, Diagonal 690, 08034 Barcelona, Spain
*
Departament de Matemàtica Econòmica, Financera i Actuarial, Riskcenter-IREA, University of Barcelona, Diagonal 690, 08034 Barcelona, Spain, Tel.: +34-93-4037043; Fax: +34-93-4021821 E-Mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper analyses the impact of using different correlation assumptions between lines of business when estimating the risk-based capital reserve, the solvency capital requirement (SCR), under Solvency II regulations. A case study is presented and the SCR is calculated according to the standard model approach. Alternatively, the requirement is then calculated using an internal model based on a Monte Carlo simulation of the net underwriting result at a one-year horizon, with copulas being used to model the dependence between lines of business. To address the impact of these model assumptions on the SCR, we conduct a sensitivity analysis. We examine changes in the correlation matrix between lines of business and address the choice of copulas. Drawing on aggregate historical data from the Spanish non-life insurance market between 2000 and 2009, we conclude that modifications of the correlation and dependence assumptions have a significant impact on SCR estimation.

Keywords

Solvency IIsolvency capital requirementstandard modelinternal modelMonte Carlo simulationcopulas
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 43 , Issue 1 , January 2013 , pp. 21 - 37
Copyright
Copyright © ASTIN Bulletin 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bühlmann, H. and Gisler, A. (2005) A Course in Credibility Theory and Its Applications. Berlin: Springer.Google Scholar
CEIOPS (2010) Fifth Quantitative Impact Study – Technical Specifications. Available under https://eiopa.europa.eu/consultations/qis/index.htmlGoogle Scholar
Demarta, S. and McNeil, A.J. (2005) The t copula and related copulas. International Statistical Review, 73 (1), 111–129.CrossRefGoogle Scholar
Embrechts, P., McNeil, A.J. and Frey, R. (2005) Quantitative Risk Management, Concepts, Techniques and Tools. Princeton, NJ: Princeton University Press.Google Scholar
Englund, M., Guillén, M., Gustafsson, J., Nielsen, L.H. and Nielsen, P.J. (2008) Multivariate latent risk: A credibility approach. ASTIN Bulletin, 38 (1), 137–146.CrossRefGoogle Scholar
Ferri, A. and Bermúdez, L. (2012) Bayesian estimation of the correlation matrix between lines of business for non-life underwriting risk module SCR. In Proceedings of the Actuarial and Financial Mathematics Conference. Vanmaele, Michèle, Deelstra, Griselda, De Schepper, Ann, Dhaene, Jan, Schoutens, Wim, Vanduffel, Steven & Vyncke, David (Eds.), Universa Press, Belgium, pages 79–82.Google Scholar
Filipović, D. (2009) Multilevel risk aggregation. ASTIN Bulletin, 39 (2), 565–575.CrossRefGoogle Scholar
Gisler, A. (2009) The insurance risk in the SST and in Solvency II: Modeling and parameter estimation. Conference Paper, ASTIN Colloquium, Helsinki.CrossRefGoogle Scholar
Joe, H. (1997) Multivariate Models and Dependence Concepts. London: Chapman & Hall.Google Scholar
Nelsen, R.B. (1999) An Introduction to Copulas. Berlin: Springer.CrossRefGoogle Scholar
Pfeifer, D. and Straussburger, D. (2008) Stability problems with the SCR aggregation formula. Scandinavian Actuarial Journal, 1, 61–77.CrossRefGoogle Scholar
Sandström, A. (2007) Calibration for skewness. Scandinavian Actuarial Journal, 2, 126–134.CrossRefGoogle Scholar
Savelli, N. and Clemente, G.P. (2009) Modeling aggregate non-life underwriting risk: Standard formula vs internal model. Giornale dell' Instituto degli Attuari, 72, 295–333.Google Scholar
Savelli, N. and Clemente, G.P. (2011) Hierarchical structures in the aggregation of premium risk for insurance underwriting. Scandinavian Actuarial Journal, 3, 193–213.CrossRefGoogle Scholar
Sklar, A. (1959) Fonctions de répartition à n dimensions et leurs marges. Publications de l'Institute de Stadistique de l'Université de Paris, 8, 229–231.Google Scholar