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.
Cite this paper
Coppola, M. and D’Amato, V. (2014) Further Results about Calibration of Longevity Risk for the Insurance Business. Applied Mathematics
, 653-657. doi: 10.4236/am.2014.54061
 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
 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.
 Coppola, M. and D’Amato, V. (2012) Backtesting the Solvency Capital Requirement for Longevity Risk. The Journal of Risk Finance, 13, 309-319.
 IAIS (2008) International Association of Insurance Supervisors. Global Reinsurance Market Report.
 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
 CEIOPS (2010) QIS 5, Technical Specifications.
 Eiopa (2012) Technical Specifications for the Solvency II Valuation and Solvency Capital Requirements Calculations.
 Olivieri, A. and Pitacco, E. (2008) Solvency Requirements for Life Annuity: Some Comparisons. Giornale dell’Istituto Italiano degli Attuari LXXI, 1-2, 59-82.
 Schobel, R. and Zhu, J.W. (1998) Stochastic Volatility with an Ornstein-Uhlenbeck Process: An Extension. European Finance Review, 3, 46.
 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
 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
 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
 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
 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
 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
 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
 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.