Further Results about Calibration of Longevity Risk for the Insurance Business

Mariarosaria Coppola, Valeria D’Amato

Department of Political Sciences, Federico II University, Naples, Italy.
Department of Statistics and Economics, Campus di Fisciano, University of Salerno, Salerno, Italy.

DOI: 10.4236/am.2014.54061                

Abstract

In life insurance business, longevity risk, i.e. the risk that the insured population lives longer than the expected, represents the heart of the risk assessment, having significant impact in terms of solvency capital requirements (SCRs) needed to front the firm obligations. The credit crisis has shown that systemic risk as longevity risk is relevant and that for many insurers it is actually the dominant risk. With the adoption of the Solvency II directive, a new area for insurance in terms of solvency regulation has been opened up. The international guidelines prescribe a market consistent valuation of balance sheets, where the solvency capital requirements to be set aside are calculated according to a modular structure. By mapping the main risk affecting the insurance portfolio, the capital amount able to cover the liabilities corresponds to each measured risk. In Solvency II, the longevity risk is included into underwriting risk module. In particular, the rules propose that companies use a standard model for measuring the SCRs. Nevertheless, the legislation under consideration allows designing tailor-made internal models. As regards the longevity risk assessment, the regulatory standard model leads to noteworthy inconsistencies. In this paper, we propose a stochastic volatility model combined with a so-called coherent risk measure as the expected shortfall for measuring the SCRs according to more realistic assumptions on future evolution of longevity trend. Finally empirical evidence is provided.

Keywords

Solvency II; Solvency Capital Requirement; Longevity Risk; Longevity Shocks; Expected Shortfall

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Borger M. (2010) Deterministic Shock vs. Stochastic Value-At-Risk—An Analysis of the Solvency II Standard Model Approach to Longevity Risk. Blatter der DGVFM, 31, 225-259. http://dx.doi.org/10.1007/s11857-010-0125-z
[2]	Coppola, M. and D’Amato, V. (2013) The Solvency Capital Requirement Management for an Insurance Company. ASMDA 2013 Conference, Matarò (Barcelona), 25-28 June 2013.
[3]	Coppola, M. and D’Amato, V. (2012) Backtesting the Solvency Capital Requirement for Longevity Risk. The Journal of Risk Finance, 13, 309-319.
[4]	IAIS (2008) International Association of Insurance Supervisors. Global Reinsurance Market Report.
[5]	Hari, N., De Waegenaere, A., Melenberg, B. and Nijman, T.E. (2008) Longevity Risk in Portfolios of Pension Annuities. Insurance Mathematics and Economics, 42, 505-518. http://dx.doi.org/10.1016/j.insmatheco.2007.01.012
[6]	CEIOPS (2010) QIS 5, Technical Specifications. https://eiopa.europa.eu/consultations/qis/quantitative-impact-study-5/technical-specifications/index.html
[7]	Eiopa (2012) Technical Specifications for the Solvency II Valuation and Solvency Capital Requirements Calculations.
[8]	Olivieri, A. and Pitacco, E. (2008) Solvency Requirements for Life Annuity: Some Comparisons. Giornale dell’Istituto Italiano degli Attuari LXXI, 1-2, 59-82.
[9]	Schobel, R. and Zhu, J.W. (1998) Stochastic Volatility with an Ornstein-Uhlenbeck Process: An Extension. European Finance Review, 3, 46.
[10]	Stein, J. and Stein, E. (1991) Stock Price Distributions with Stochastic Volatility: An Analytic Approach. Review of Financial Studies, 4, 727-752. http://dx.doi.org/10.1093/rfs/4.4.727
[11]	Cox, J.C., Ingersoll, J.E. and Ross, S. (1985) A Theory of the Term Structure of Interest Rates. Econometrica, 53, 385-407. http://dx.doi.org/10.2307/1911242
[12]	Acerbi, C. and Tasche, D. (2002) Expected Shortfall: A Natural Coherent Alternative to Value at Risk. Economic Notes, 31, 379-388. http://dx.doi.org/10.1111/1468-0300.00091
[13]	Artzner, P., Delbaen, F., Eber, J.-M. and Heath, D. (1999) Coherent Measures of Risk. Mathematical Finance, 9, 203228. http://dx.doi.org/10.1111/1467-9965.00068
[14]	CEA (2006) Working Paper on the Risk Measures VaR and TailVaR. http://ec.europa.eu/internal_market/insurance/docs/2006-markt-docs/2534-06-annex-cea_en.pdf
[15]	Dowd, K. and Blake, D. (2006) After VaR: The Theory, Estimation, and Insurance Applications of Quantile-Based Risk Measures. Journal of Risk and Insurance, 73, 193-229. http://dx.doi.org/10.1111/j.1539-6975.2006.00171.x
[16]	Huisman, R., Koedijk, K.G., Kool, C.J.M. and Palm, F. (2001) Tail-Index Estimates in Small Samples. Journal of Business & Economic Statistics, 19, 208-216. http://dx.doi.org/10.1198/073500101316970421
[17]	Butt, Z. and Haberman, S. (2009) Ilc: A Collection of R Functions for Fitting a Class of Lee-Carter Mortality Models Using Iterative Fitting Algorithms. Actuarial Research Paper, No. 190.