The impact of natural hedging on a life insurer's risk situation

Emerald - Tập 13 Số 5 - Trang 396-423 - 2012
NadineGatzert1, HannahWesker1
1Chair for Insurance Economics, Friedrich‐Alexander‐University of Erlangen‐Nürnberg, Nürnberg, Germany

Tóm tắt

PurposeSystematic mortality risk, i.e. the risk of unexpected changes in mortality and survival rates, can substantially impact a life insurers' risk and solvency situation. By using the “natural hedge” between life insurance and annuities, insurance companies have an effective tool for reducing their net‐exposure. The purpose of this paper is to analyze this risk management tool and to quantify its effectiveness in hedging against changes in mortality with respect to default risk measures.Design/methodology/approachTo achieve this goal, the paper models the insurance company as a whole and takes into account the interaction between assets and liabilities. Systematic mortality risk is considered in two ways. First, systematic mortality risk is modeled using scenario analyses and, second, empirically observed changes in mortality rates for the last 10‐15 years are used.FindingsThe paper demonstrates that the consideration of both the asset and liability side is vital to obtain deeper insight into the impact of natural hedging on an insurer's risk situation and shows how to reach a desired safety level while simultaneously immunizing the portfolio against changes in mortality rates.Originality/valueThe paper contributes to the literature by considering the insurance company as a whole in a multi‐period setting and taking into account both, assets and liabilities, as well as their interaction. Furthermore, the paper shows how to obtain a desired safety level while simultaneously immunizing a portfolio against changes in default risk.

Từ khóa


Tài liệu tham khảo

Antolin, P. (2007), “Longevity risk and private pensions”, OECD Working Papers on Insurance and Private Pensions No. 3, OECD Publishing, Paris.

Bacinello, A.R. (2003), “Fair valuation of a guaranteed life insurance participating contract embedding a surrender option”, Journal of Risk and Insurance, Vol. 70 No. 3, pp. 461‐87.

Bayraktar, E. and Young, V. (2007), “Hedging life insurance with pure endowments”, Insurance: Mathematics and Economics, Vol. 40 No. 3, pp. 435‐44.

Biffis, E., Denuit, M. and Devolder, P. (2010), “Stochastic mortality under measure changes”, Scandinavian Actuarial Journal, Vol. 4, pp. 284‐311.

Björk, T. (2009), Arbitrage Theory in Continuous Finance, 3rd ed., Oxford University Press, Oxford.

Blake, D. and Burrows, W. (2001), “Survivor bonds: helping to hedge mortality risk”, Journal of Risk and Insurance, Vol. 68 No. 2, pp. 339‐48.

Blake, D., Cairns, A. and Dowd, K. (2006), “Living with mortality: longevity bonds and other mortality‐linked securities”, British Actuarial Journal, Vol. 12 No. 1, pp. 153‐97.

Blake, D., de Waegenaere, A., MacMinn, R. and Nijman, T. (2009), “Longevity risk and capital markets: the 2008‐2009 update”, Insurance: Mathematics and Economics, Vol. 46 No. 1, pp. 135‐8.

Brillinger, D.R. (1986), “The natural variability of vital rates and associated statistics”, Biometrics, Vol. 42 No. 4, pp. 693‐734.

Brouhns, N., Denuit, M. and Vermunt, J.K. (2002a), “A Poisson log‐bilinear regression approach to the construction of projected lifetables”, Insurance: Mathematics and Economics, Vol. 31 No. 3, pp. 373‐93.

Brouhns, N., Denuit, M. and Vermunt, J.K. (2002b), “Measuring the longevity risk in mortality projections”, Bulletin of the Swiss Association of Actuaries, Vol. 2002 No. 2, pp. 105‐30.

Cairns, A., Blake, D. and Dowd, K. (2006b), “A two‐factor model for stochastic mortality with parameter uncertainty: theory and calibration”, Journal of Risk and Insurance, Vol. 73 No. 4, pp. 687‐718.

Cairns, A., Blake, D., Dowd, K., Coughlan, G.D., Epstein, D., Ong, A. and Balevich, I. (2009), “A quantitative comparison of stochastic mortality models using data from England and Wales and the United States”, North American Actuarial Journal, Vol. 13 No. 1, pp. 1‐35.

Carriere, J.F. (1999), “No‐arbitrage pricing for life insurance and annuities”, Economics Letters, Vol. 64 No. 3, pp. 339‐42.

Coppola, M., Di Lorenzo, E., Orlando, A. and Sibillo, M. (2011), “Solvency analysis and demographic risk measures”, The Journal of Risk Finance, Vol. 12 No. 4, pp. 252‐69.

Cowley, A.J. and Cummins, D. (2005), “Securitization of life insurance assets and liabilities”, Journal of Risk and Insurance, Vol. 72 No. 2, pp. 193‐226.

Cox, S.H. and Lin, Y. (2007), “Natural hedging of life and annuity mortality risk”, North American Actuarial Journal, Vol. 11 No. 3, pp. 1‐15.

Dahl, M. (2004), “Stochastic mortality in life insurance: market reserves and mortality‐linked insurance contracts”, Insurance: Mathematics and Economics, Vol. 35 No. 1, pp. 113‐36.

Evans, J. and Sherris, M. (2009), “Longevity management issues for Australia's future tax system”, Commissioned Paper for Australia's Future Tax System Review Panel, Department of the Treasury (Australia), Canberra.

Gatzert, N. and Kling, A. (2007), “Analysis of participating life insurance contracts: a unification approach”, Journal of Risk and Insurance, Vol. 74 No. 3, pp. 547‐70.

Gatzert, N. and Wesker, H. (2011), “Mortality risk and its effect on shortfall and risk management”, Journal of Risk and Insurance, Vol. 70 No. 3, pp. 461‐87.

Gatzert, N., Hoermann, G. and Schmeiser, H. (2009), “The impact of the secondary market on life insurers surrender profits”, Journal of Risk and Insurance, Vol. 76 No. 4, pp. 887‐908.

Gerrard, R., Haberman, S. and Vigna, E. (2004), “Optimal investment choices post‐retirement in a defined contribution pension scheme”, Insurance: Mathematics and Economics, Vol. 35 No. 2, pp. 321‐42.

Gerstner, T., Griebel, M., Holtz, M. and Haep, M. (2008), “A general asset‐liability management model for the efficient simulation of portfolios of life insurance policies”, Insurance: Mathematics and Economics, Vol. 42 No. 2, pp. 704‐16.

Glasserman, P. (2008), Monte Carlo Methods in Financial Engineering, Springer, New York, NY (reprint).

Grosen, A. and Jørgensen, P.L. (2000), “Fair valuation of life insurance liabilities: the impact of interest rate guarantees, surrender options and bonus policies”, Insurance: Mathematics and Economics, Vol. 26 No. 1, pp. 37‐57.

Grosen, A. and Jørgensen, P.L. (2002), “Life insurance liabilities at market value: an analysis of insolvency risk, bonus policy, and regulatory intervention rules in a barrier option framework”, Journal of Risk and Insurance, Vol. 69 No. 1, pp. 63‐91.

Gründl, H., Post, T. and Schulze, R. (2006), “To hedge or not to hedge: managing demographic risk in life insurance companies”, Journal of Risk and Insurance, Vol. 73 No. 1, pp. 19‐41.

Hanewald, K. (2010), “Mortality modeling: Lee‐Carter, the macroeconomy, and cause‐specific mortality”, working paper, Humboldt‐Universität zu Berlin, Berlin.

Hanewald, K., Piggott, J. and Sherris, M. (2011), “Individual post‐retirement longevity risk management under systematic mortality risk”, working paper, University of New South Wales, Kensington.

Lee, R.D. and Carter, L.R. (1992), “Modeling and forecasting US mortality”, Journal of the American Statistical Association, Vol. 87 No. 419, pp. 659‐71.

Lin, Y. and Cox, S.H. (2008), “Securitization of Catastrophe mortality risks”, Insurance: Mathematics and Economics, Vol. 42 No. 2, pp. 628‐37.

Luciano, E., Regis, L. and Vigna, E. (2011a), “Delta and gamma hedging of mortality and interest rate risk”, Working Paper No. 01/2011, International Centre for Economic Research, Torino.

Luciano, E., Regis, L. and Vigna, E. (2011b), “Natural delta and gamma hedging of mortality and interest rate risk”, Working Paper No. 21/2011, International Centre for Economic Research, Torino.

Ribeiro, R. and di Pietro, V. (2009), “Longevity risk and portfolio allocation”, Investment Strategies No. 57, J.P. Morgan, London.

Wang, J.L., Huang, H.C., Yang, S.S. and Tsai, J.T. (2010), “An optimal product mix for hedging longevity risk in life insurance companies: the immunization theory approach”, Journal of Risk and Insurance, Vol. 77 No. 2, pp. 473‐97.

Wetzel, C. and Zwiesler, H.‐J. (2008), “Das Vorhersagerisiko der Sterblichkeitsentwicklung – Kann es durch eine geeignete Portfoliozusammensetzung minimiert werden?”, Blätter der DGVFM, Vol. 29 No. 1, pp. 73‐107.

Wills, S. and Sherris, M. (2010), “Securitization, structuring and pricing of longevity risk”, Insurance: Mathematics and Economics, Vol. 46 No. 1, pp. 173‐85.

Cairns, A., Blake, D. and Dowd, K. (2006a), “Pricing death: frameworks for the valuation and securitization of mortality risk”, ASTIN Bulletin, Vol. 36, pp. 79‐120.

Milevsky, M.M. and Promislow, D. (2003), “Can life insurance be used to hedge payout annuities? Part 1: modeling longevity risk”, working paper, York University, Toronto.

Olivieri, A. (2001), “Uncertainty in mortality projections: an actuarial perspective”, Insurance: Mathematics and Economics, Vol. 29 No. 2, pp. 231‐45.

Thông tin
Thông tin xuất bản

Emerald

Tập 13 Số 5

396-423

Thông tin tác giả