×

On the effectiveness of natural hedging for insurance companies and pension plans. (English) Zbl 1314.91142

Summary: Natural hedging is one possible method to reduce longevity risk exposure for an annuity provider or a pension plan. In this paper, we provide an assessment of the effectiveness of natural hedging between annuity and life products, using the correlated Poisson Lee-Carter model, Poisson common factor model, product-ratio model, and historical simulation. Our analysis is based on the mortality experience of UK assured lives, pensioners, and annuitants, and the national population of England and Wales. We consider a range of different scenarios, and find that the level of risk reduction is significant in general, with an average of around 60%. These results have important implications for those insurers, reinsurers, and pension plan sponsors who are seeking ways to hedge their unwanted risk exposures.

MSC:

91B30 Risk theory, insurance (MSC2010)
91G70 Statistical methods; risk measures
PDF BibTeX XML Cite
Full Text: DOI Link

References:

[1] Barbarin, J., Heath-jarrow-morton modelling of longevity bonds and the risk minimization of life insurance portfolios, Insurance Math. Econom., 43, 41-55, (2008) · Zbl 1140.91377
[2] Bayraktar, E.; Young, V. R., Hedging life insurance with pure endowments, Insurance Math. Econom., 40, 435-444, (2007) · Zbl 1183.91067
[3] Box, G. E.P.; Jenkins, G. M., Time series analysis: forecasting and control, (1976), Holden-Day Press San Francisco · Zbl 0109.37303
[4] Brouhns, N.; Denuit, M.; Vermunt, J. K., A Poisson log-bilinear regression approach to the construction of projected lifetables, Insurance Math. Econom., 31, 373-393, (2002) · Zbl 1074.62524
[5] Cairns, A. J.G.; Blake, D.; Dowd, K., Modelling and management of mortality risk: a review, Scand. Actuar. J., 2008, 2-3, 79-113, (2008) · Zbl 1224.91048
[6] Cairns, A. J.G.; Blake, D.; Dowd, K.; Coughlan, G. D.; Khalaf-Allah, M., Bayesian stochastic mortality modelling for two populations, ASTIN Bull., 41, 1, 29-59, (2011)
[7] Carter, L. R.; Lee, R. D., Modeling and forecasting US sex differentials in mortality, Int. J. Forecast., 8, 393-411, (1992)
[8] Chan, W. S.; Li, J. S.H.; Li, J., The CBD mortality indexes: modeling and applications, N. Am. Actuar. J., 18, 1, 38-58, (2014) · Zbl 1412.91037
[9] Continuous Mortality Investigation (CMI), 2012. Institute and Faculty of Actuaries, UK.
[10] Coughlan, G., Epstein, D., Ong, A., Sinha, A., Hevia-Portocarrero, J., Gingrich, E., Khalaf-Allah, M., Joseph, P., 2007a. LifeMetrics: a toolkit for measuring and managing longevity and mortality risks. Technical Document. Pension Advisory Group, JPMorgan.
[11] Coughlan, G., Epstein, D., Sinha, A., Honig, P., 2007b. q-forwards: derivatives for transferring longevity and mortality risk. Pension Advisory Group, JPMorgan.
[12] Coughlan, G. D.; Khalaf-Allah, M.; Ye, Y.; Kumar, S.; Cairns, A. J.G.; Blake, D.; Dowd, K., Longevity hedging 101: a framework for longevity basis risk analysis and hedge effectiveness, N. Am. Actuar. J., 15, 2, 150-176, (2011)
[13] Cowley, A.; Cummins, J. D., Securitization of life insurance assets and liabilities, J. Risk Insurance, 72, 2, 193-226, (2005)
[14] Cox, S. H.; Lin, Y., Natural hedging of life and annuity mortality risks, N. Am. Actuar. J., 11, 3, 1-15, (2007)
[15] Cox, S. H.; Lin, Y.; Tian, R.; Zuluaga, L. F., Mortality portfolio risk management, J. Risk Insurance, 80, 4, 853-890, (2013)
[16] Cox, S. H.; Lin, Y.; Wang, S., Multivariate exponential tilting and pricing implications for mortality securitization, J. Risk Insurance, 73, 4, 719-736, (2006)
[17] Creighton, A.; Jin, H. H.; Piggott, J.; Valdez, E. A., Longevity insurance: a missing market, Singap. Econ. Rev., 50, 417-435, (2005)
[18] Cummins, J. D.; Venard, B., Handbook of international insurance: between global dynamics and local contingencies, (2007), Springer USA
[19] Dahl, M.; Glar, S.; Møller, T., Mixed dynamic and static risk-minimization with an application to survivor swaps, Eur. Actuar. J., 1, 2 Supplement, 233-260, (2011)
[20] Dahl, M.; Melchior, M.; Møller, T., On systematic mortality risk and risk-minimization with survivor swaps, Scand. Actuar. J., 2008, 2-3, 114-146, (2008) · Zbl 1224.91054
[21] D’Amato, V.; Haberman, S.; Piscopo, G.; Russolillo, M., Modelling dependent data for longevity projections, Insurance Math. Econom., 51, 694-701, (2012) · Zbl 1285.91054
[22] Debón, A.; Montes, F.; Martínez-Ruiz, F., Statistical methods to compare mortality for a group with non-divergent populations: an application to Spanish regions, Eur. Actuar. J., 1, 2, 291-308, (2011)
[23] Delwarde, A.; Denuit, M.; Guillén, M.; Vidiella-i-Anguera, A., Application of the Poisson log-bilinear projection model to the G5 mortality experience, Belg. Actuar. Bull., 6, 1, 54-68, (2006) · Zbl 1356.91056
[24] Dowd, K.; Blake, D.; Cairns, A. J.G.; Dawson, P., Survivor swaps, J. Risk Insurance, 73, 1, 1-17, (2006)
[25] Dowd, K.; Cairns, A. J.G.; Blake, D.; Coughlan, G. D.; Khalaf-Allah, M., A gravity model of mortality rates for two related populations, N. Am. Actuar. J., 15, 2, 334-356, (2011) · Zbl 1228.91032
[26] Ernst & Young, 2013. International GAAP 2013: Generally Accepted Accounting Practice under International Financial Reporting Standards. The International Financial Reporting Group of Ernst & Young.
[27] Gatzert, N.; Wesker, H., The impact of natural hedging on a life insurer’s risk situation, J. Risk Finance, 13, 5, 396-423, (2012)
[28] Gründl, H.; Post, T.; Schulze, R. N., To hedge or not to hedge: managing demographic risk in life insurance companies, J. Risk Insurance, 73, 1, 19-41, (2006)
[29] Hatzopoulos, P.; Haberman, S., Common mortality modeling and coherent forecasts. an empirical analysis of worldwide mortality data, Insurance Math. Econom., 52, 320-337, (2013) · Zbl 1284.91238
[30] Human Mortality Database (HMD) 2013. University of California, Berkeley (USA) and Max Planck Institute for Demographic Research (Germany). http://www.mortality.org.
[31] Hyndman, R. J.; Booth, H.; Yasmeen, F., Coherent mortality forecasting: the product-ratio method with functional time series models, Demography, 50, 1, 261-283, (2013)
[32] Jarner, S. F.; Kryger, E. M., Modelling adult mortality in small populations: the SAINT model, ASTIN Bull., 41, 2, 377-418, (2011) · Zbl 1239.91128
[33] Kogure, A.; Li, J.; Kamiya, S., A Bayesian multivariate risk-neutral method for pricing reverse mortgages, N. Am. Actuar. J., 18, 1, 242-257, (2014) · Zbl 1412.91047
[34] Lane Clark & Peacock LLP (LCP) 2012. LCP Pension Buy-Ins, Buy-Outs and Longevity Swaps 2012.
[35] Lee, R. D.; Carter, L. R., Modeling and forecasting US mortality, J. Amer. Statist. Assoc., 87, 419, 659-671, (1992) · Zbl 1351.62186
[36] Li, J., A Poisson common factor model for projecting mortality and life expectancy jointly for females and males, Popul. Stud., 67, 1, 111-126, (2013)
[37] Li, J., Dacorogna, M., Tan, C.I., 2014. The impact of joint mortality modelling on hedging effectiveness of mortality derivatives. In: Tenth International Longevity Risk and Capital Markets Solutions Conference, Santiago, Chile.
[38] Li, J. S.H.; Hardy, M. R., Measuring basis risk in longevity hedges, N. Am. Actuar. J., 15, 2, 177-200, (2011) · Zbl 1228.91042
[39] Li, N.; Lee, R., Coherent mortality forecasts for a group of populations: an extension of the Lee-Carter method, Demography, 42, 3, 575-594, (2005)
[40] Li, J. S.H.; Ng, A. C.Y., Canonical valuation of mortality-linked securities, J. Risk Insurance, 78, 4, 853-884, (2011)
[41] Lin, T.; Tsai, C. C.L., On the mortality/longevity risk hedging with mortality immunization, Insurance Math. Econom., 53, 580-596, (2013) · Zbl 1290.91093
[42] Liu, X.; Braun, W. J., Investigating mortality uncertainty using the block bootstrap, J. Probab. Stat., (2010), Article ID 813583
[43] Milevsky, M. A.; Promislow, S. D., Mortality derivatives and the option to annuitise, Insurance Math. Econom., 29, 299-318, (2001) · Zbl 1074.62530
[44] Ngai, A.; Sherris, M., Longevity risk management for life and variable annuities: the effectiveness of static hedging using longevity bonds and derivatives, Insurance Math. Econom., 49, 100-114, (2011)
[45] Plat, R., Stochastic portfolio specific mortality and the quantification of mortality basis risk, Insurance Math. Econom., 45, 123-132, (2009) · Zbl 1231.91226
[46] Renshaw, A.; Haberman, S., Lee-Carter mortality forecasting: a parallel generalized linear modelling approach for england and wales mortality projections, Appl. Stat., 51, 119-137, (2003) · Zbl 1111.62359
[47] Russolillo, M.; Giordano, G.; Haberman, S., Extending the Lee-Carter model: a three-way decomposition, Scand. Actuar. J., 2011, 2, 96-117, (2011) · Zbl 1277.62260
[48] Tsai, C. C.L.; Chung, S. L., Actuarial applications of the linear hazard transform in mortality immunization, Insurance Math. Econom., 53, 48-63, (2013) · Zbl 1284.91272
[49] Tsai, J. T.; Wang, J. L.; Tzeng, L. Y., On the optimal product mix in life insurance companies using conditional value at risk, Insurance Math. Econom., 46, 235-241, (2010) · Zbl 1231.91244
[50] Villegas, A. M.; Haberman, S., On the modelling and forecasting of socio-economic mortality differentials: an application to deprivation and mortality in england, N. Am. Actuar. J., 18, 1, 168-193, (2014) · Zbl 1412.91057
[51] Wang, C. W.; Huang, H. C.; Hong, D. C., A feasible natural hedging strategy for insurance companies, Insurance Math. Econom., 52, 532-541, (2013) · Zbl 1284.91274
[52] Wang, J. L.; Huang, H. C.; Yang, S. S.; Tsai, J. T., An optimal product mix for hedging longevity risk in life insurance companies: the immunization theory approach, J. Risk Insurance, 77, 2, 473-497, (2010)
[53] Yang, S. S.; Wang, C. W., Pricing and securitization of multi-country longevity risk with mortality dependence, Insurance Math. Econom., 52, 157-169, (2013) · Zbl 1284.91556
[54] Zhou, R.; Li, J. S.H.; Tan, K. S., Pricing standardized mortality securitizations: a two-population model with transitory jump effects, J. Risk Insurance, 80, 3, 733-774, (2013)
[55] Zhou, R.; Wang, Y.; Kaufhold, K.; Li, J. S.H.; Tan, K. S., Modeling period effects in multi-population mortality models: applications to solvency II, N. Am. Actuar. J., 18, 1, (2014) · Zbl 1412.91060
[56] Zhu, N., Bauer, D., 2012. A cautious note on natural hedging of longevity risk. In: Eighth International Longevity Risk and Capital Markets Solutions Conference, Canada.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.