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On the Calculation of the Solvency Capital Requirement Based on Nested Simulations*

Published online by Cambridge University Press:  09 August 2013

Daniel Bauer ,
Andreas Reuss  and
Daniela Singer
Daniel Bauer
Affiliation:
Department of Risk Management and Insurance, Georgia State University, 35 Broad Street. Atlanta, GA 30303. USA, Tel.: +1-404-413-7490, Fax: +1-404-413-7499, E-Mail: [email protected]
Andreas Reuss
Affiliation:
Institute for Finance and Actuarial Sciences (ifa), Helmholtzstrasse 22. 89081 Ulm.Germany, Tel.: +49-(731)-50-31251, Fax: +49-(731)-50-31239, E-Mail: [email protected]
Daniela Singer
Affiliation:
Institute for Finance and Actuarial Sciences (ifa), Helmholtzstrasse 22. 89081 Ulm.Germany, Tel.: +49-(731)-50-31259, Fax: +49-(731)-50-31239, E-Mail: [email protected]
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Abstract

Within the European Union, risk-based funding requirements for insurance companies are currently being revised as part of the Solvency II project. However, many life insurers struggle with the implementation, which to a large extent appears to be due to a lack of know-how regarding both, stochastic modeling and efficient techniques for the numerical implementation.

The current paper addresses these problems by providing a mathematical framework for the derivation of the required risk capital and by reviewing different alternatives for the numerical implementation based on nested simulations. In particular, we seek to provide guidance for practitioners by illustrating and comparing the different techniques based on numerical experiments.

Keywords

Solvency IIValue-at-Risknested simulationsscreening procedures
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 42 , Issue 2 , November 2012 , pp. 453 - 499
Copyright
Copyright © International Actuarial Association 2012

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Footnotes

*

Parts of this paper are taken from an earlier paper called “Solvency II and Nested Simulations — a Least-Squares Monte Carlo Approach” and from the third author's doctoral dissertation (cf. Bergmann (2011)). The authors are grateful for helpful comments from an anonymous referee and seminar participants at the 2009 ARIA meeting, the 2009 CMA Workshop on Insurance Mathematics and Longevity Risk, the 2010 International Congress of Actuaries, Georgia State University, Humboldt University of Berlin, Ulm University, and the University of Duisburg-Essen. All remaining errors are ours.

References

CEIOPS Internal Model Expert Group (2009) Stock-taking report on the use of Internal Models in Insurance. http://www.gcactuaries.org/documents/ceiops_stocktaking_IM_120109.pdf.Google Scholar
CFO Forum (2009) Market Consistent Embedded Value Principles. http://www.cfoforum.n1/downloads/MCEV_Principles_and_Guidance_October_2009.pdf.Google Scholar
CRO Forum (2009) Internal models benchmarking study — Summary results. http://www.croforum.org/assets/files/publications/crofintmodelbms30jan09.pdf.Google Scholar
Babbel, D.F., Gold, J. and Merrill, C.B. (2002) Fair Value of Liabilities: The Financial Economics Perspective. North American Actuarial Journal 6, 12–27.CrossRefGoogle Scholar
Bauer, D., Bergmann, D. and Kiesel, R. (2010) On the Risk-Neutral Valuation of Life Insurance Contracts with Numerical Methods in View. ASTIN Bulletin 40, 31–61.Google Scholar
Bauer, D., Kiesel, R., Kling, A. and Russ, J. (2006) Risk-neutral valuation of participating life insurance contracts. Insurance: Mathematics and Economics 39, 171–183.Google Scholar
Bergmann, D. (2011) Nested Simulations in Life Insurance. Dissertation. ifa Verlag, Ulm. Google Scholar
Bingham, N. and Kiesel, R. (2004) Risk-Neutral Valuation (Second Edition). Springer, Berlin.CrossRefGoogle Scholar
Broadie, M., Du, Y. and Moallemi, C.C. (2011) Efficient Risk Estimation via Nested Sequential Simulation. Management Science 57, 1172–1194.CrossRefGoogle Scholar
Embrechts, P., Klüppelberg, C. and Mikosch, T. (1997) Modelling Extremal Events for Insurance and Finance. Springer, Berlin.Google Scholar
European Commission (2010) QIS5 Technical Specifications. http://ec.europa.eu/internal_market/insurance/docs/solvency/qis5/201007/technical_specifications_en.pdf.Google Scholar
Federal Office of Private Insurance (2006) Technical document on the Swiss Solvency Test. http://www.bvp.admin.ch/themen/00506/00552/index.html?lang=en.Google Scholar
Girard, L. (2002) An Approach to Fair Valuation of Insurance Liabilities using the Firm's Cost of Capital. North American Actuarial Journal 6, 18–41.Google Scholar
Glasserman, P. (2004) Monte Carlo Methods in Financial Engineering. Springer, New York.Google Scholar
Gordy, M.B. and Juneja, D. (2010) Nested simulations in portfolio risk measurement. Management Science 56, 1833–1848.Google Scholar
Gray, R.M. (2009) Probability, Random Processes, and Ergodic Properties. Springer, 2nd edition, New York.CrossRefGoogle Scholar
Kling, A., Richter, A. and Russ., J. (2007) The interaction of guarantees, surplus distribution, and asset allocation in with-profit life insurance policies. Insurance: Mathematics and Economics 40, 164–178.Google Scholar
Klumpes, P.J.M. and Morgan, K. (2008) Solvency II versus IFRS: Cost of Capital Implications for Insurance Firms. Proceedings of the 2008 ASTIN Colloquium.Google Scholar
Lan, H., Nelson, B.L. and Staum, J. (2007a) Two-level simulation for risk management. Proceedings of the 2007 INFORMS Simulation Society Research Workshop.Google Scholar
Lan, H., Nelson, B.L. and Staum, J. (2007b) A confidence interval for tail conditional expectation via two-level simulation. In: Henderson, S.G., Biller, B., Hsieh, M.-H., Shortle, J., Tew, J.D., Barton, R.R. (Eds.), Proceedings of the 2007 Winter Simulation Conference, IEEE Press, pp. 949–957.Google Scholar
Lan, H., Nelson, B.L. and Staum, J. (2010) A confidence interval procedure for expected shortfall risk measurement via two-level simulation. Operations Research 58, 1481–1490.Google Scholar
Liebwein, P. (2006) Risk Models for Capital Adequacy: Applications in the Context of Solvency II and Beyond. The Geneva Papers on Risk and Insurance: Issues and Practice 31, 528–550.Google Scholar
Liu, M., Nelson, B.L., Staum, J. (2010) An Efficient Simulation Procedure for Point Estimation of Expected Shortfall. In: Johansson, B., Jain, S., Montoya-Torres, J., Hugan, J., Yücesan, E. (Eds.), Proceedings of the 2010 Winter Simulation Conference, IEEE Press, pp. 2821–2831.Google Scholar
Miller, R.G. (1974) The jackknife — a review. Biometrica 61, 1–15.Google Scholar
Pfeifer, D. and Strassburger, D. (2008) Solvency II: stability problems with the SCR aggregation formula. Scandinavian Actuarial Journal 2008(1), 61–77.Google Scholar
Ronkainen, V., Koskinen, L. and Bergland, R. (2007) Topical modelling issues in Solvency II. Scandinavian Actuarial Journal 2007(2), 135–146.Google Scholar
Sandström, A. (2007) Solvency II: Calibration for skewness. Scandinavian Actuarial Journal 2007(2), 126–134.Google Scholar
Society of Actuaries (SOA) (2008) Economic Capital for Life Insurance Companies. http://www.soa.org/files/pdf/research-ec-report.pdf.Google Scholar
Zaglauer, K. and Bauer, D. (2008) Risk-neutral valuation of participating life insurance contracts in a stochastic interest rate environment. Insurance: Mathematics and Economics 43, 29–40.Google Scholar
Zhu, N. and Bauer, D. (2011) Applications of Forward Mortality Factor Models in Life Insurance Practice. Geneva Papers on Risk and Insurance: Issues and Practice 36, 567–594.Google Scholar