Insurance Regulation in the European Union pp 245-260 | Cite as

# Risk Factor Contributions and Capital Allocation in Life Insurance in the Solvency II Framework

## Abstract

Quantification of capital requirements is a critical issue for any insurer. Solvency is assessed through the regulatory capital, but, in practice, insurance companies usually hold higher levels of economic capital assessed using risk-based models that allow for any type of risk the institution deals with. Once the economic capital of a company is determined, it should be allocated down to lower levels, such as business units, lines and products for a number of purposes and this allocation of capital has crucial importance. This chapter deals with some key aspects related to risk quantification and capital allocation in life insurance. Portfolios composed by different insurance contracts, with both life and death benefits, are investigated. The numerical results obtained explain that the features and benefits of a contract influence not only the assessment of the total risk but also its allocation to single factors, showing that such a risk measurement methodology could be a useful tool for new products improvement and management, in adherence to the principles stated by the Solvency II directive, specifically with respect to the own risk and solvency assessment (ORSA) and the implementation of internal models.

## Keywords

Allocation Risk factor contributions Life insurance Risk management## References

- Bruno, M., Camerini, E., & Tomassetti, A. (2000). Financial and demographic risks of a portfolio of life insurance policies with stochastic interest rates. Evaluation methods and applications.
*North American Actuarial Journal, 4*, 44–55.CrossRefGoogle Scholar - Cairns, A. J. G., Blake, D., & Dowd, K. (2006). A two-factor model for stochastic mortality with parameter uncertainty: Theory and calibration.
*Journal of Risk and Insurance, 73*, 687–718.CrossRefGoogle Scholar - Cox, J. C., Ingersoll, J. E., & Ross, S. A. (1985). A theory of the term structure of interest rates.
*Econometrica, 54*, 385–407.CrossRefGoogle Scholar - Denault, M. (2001). Coherent allocation of risk capital.
*Journal of Risk, 4*(1), 1–34.CrossRefGoogle Scholar - Dhaene, J., Tsanakas, A., Valdez, E. A., & Vanduffel, S. (2012). Optimal capital allocation principles.
*Journal of Risk and Insurance, 79*, 1–28.CrossRefGoogle Scholar - European Parliament and Council of the European Union. (2009). The taking-up and pursuit of the business of Insurance and Reinsurance (Solvency II), Directive 2009/138/EC.Google Scholar
- Gatzert, N., & Wesker, H. (2012). The impact of natural hedging on a life insurer’s risk situation.
*Journal of Risk Finance, 13*(5), 396–423.CrossRefGoogle Scholar - Gourieroux, C., Laurent, J., & Scaillet, O. (2000). Sensitivity analysis of values at risk.
*Journal of Empirical Finance, 7*, 225–245.CrossRefGoogle Scholar - Karabey, U. (2012).
*Risk capital allocation and risk quantification in insurance companies*. Doctoral thesis, Mathematical and Computer Sciences, Heriot-Watt University.Google Scholar - Karabey, U., Kleinow, T., & Cairns, A. J. G. (2014). Factor risk quantification in annuity models.
*Insurance: Mathematics and Economics, 58*, 34–45.Google Scholar - McNeil, A., Frey, R., & Embrechts, P. (2005).
*Quantitative risk management*. Princeton: Princeton University Press.Google Scholar - Pagan, A., & Ullah, A. (1999).
*Nonparametric econometrics*. New York: Cambridge University Press.CrossRefGoogle Scholar - Parker, G. (1997). Stochastic analysis of the interaction between investment and insurance risks.
*NAAJ, 1–2*, 55–84.Google Scholar - Rosen, D., & Saunders, D. (2010). Risk factor contributions in portfolio credit risk models.
*Journal of Banking & Finance, 34*, 336–349.CrossRefGoogle Scholar - Sherris, M. (2006). Solvency, capital allocation, and fair rate of return in insurance.
*Journal of Risk and Insurance, 73*, 71–96.CrossRefGoogle Scholar - Tasche, D. (1999). Risk contributions and performance measurement.
*Working Paper*, Technische Universität München.Google Scholar - Tasche, D. (2006). Measuring sectoral diversification in an asymptotic multi-factor framework.
*Journal of Credit Risk, 2*, 33–55.CrossRefGoogle Scholar - Tasche, D. (2008). Capital allocation to business units and sub-portfolios: The Euler principle. In A. Resti (Ed.),
*Pillar II in the new Basel accord: The challenge of economic capital*. London: Risk Books.Google Scholar - Tasche, D. (2009). Capital allocation for credit portfolios with kernel estimators.
*Quantitative Finance, 9*(5), 581–595.CrossRefGoogle Scholar - van der Vaart, A. (1998).
*Asymptotic statistics*. Cambridge: Cambridge University Press.CrossRefGoogle Scholar