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THE PRICING OF MORTALITY-LINKED CONTINGENT CLAIMS: AN EQUILIBRIUM APPROACH

Published online by Cambridge University Press:  18 June 2013

Jeffrey T. Tsai  and
Larry Y. Tzeng
Jeffrey T. Tsai*
Affiliation:
Department of Quantitative Finance, National Tsing Hua University, 101, Sec. 2, Kuang-Fu Rd., Hsinchu, Taiwan30013, and Risk and Insurance Research Center, National Chengchi University, Taipei 116, Taiwan, Republic of China
Larry Y. Tzeng
Affiliation:
Department of Finance, National Taiwan University, Taipei 106, Taiwan, and Risk and Insurance Research Center, National Chengchi University, Taipei 116, Taiwan, Republic of China E-Mail: [email protected]
*
E-Mail: [email protected]
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Abstract

This study introduces an equilibrium approach to price mortality-linked securities in a discrete time economy, assuming that the mortality rate has a transformed normal distribution. This pricing method complements current studies on the valuation of mortality-linked securities, which only have discrete trading opportunities and insufficient market trading data. Like the Wang transform, the valuation relationship is still risk-neutral (preference-free) and the mortality-linked security is priced as the expected value of its terminal payoff, discounted by the risk-free rate. This study provides an example of pricing the Swiss Re mortality bond issued in 2003 and obtains an approximated closed-form solution.

Keywords

Longevity riskmortality-linked security valuationtransform normal distribution
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 43 , Issue 2 , May 2013 , pp. 97 - 121
Copyright
Copyright © ASTIN Bulletin 2013 

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References

Bauer, D., Börger, M. and Russ, J. (2010) On the pricing of longevity-linked securities. Insurance: Mathematics and Economics, 46, 139–149.Google Scholar
Bayraktar, E., Milevsky, M.A., Promislow, S.D. and Young, V.R. (2009) Valuation of mortality risk via the instantaneous Sharpe ratio: Applications to life annuities. Journal of Economic Dynamics & Control, 33, 676–691.CrossRefGoogle Scholar
Bayraktar, E. and Young, V.R. (2007) Hedging life insurance with pure endowments. Insurance: Mathematics and Economics, 40 (3), 435–444.Google Scholar
Biffis, E. (2005) Affine processes for dynamic mortality and actuarial valuations. Insurance: Mathematics and Economics, 37, 443–468.Google Scholar
Biffis, E. and Millossovich, P. (2006) The fair value of guaranteed annuity options. Scandinavian Actuarial Journal, 1, 23–41.CrossRefGoogle Scholar
Black, F. and Scholes, M.S. (1973) The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637–659.CrossRefGoogle Scholar
Blake, D., Cairns, A.J. and Dowd, K. (2006a) Living with mortality: Longevity bonds and other mortality-linked securities. British Actuarial Journal, 12, 153–197.CrossRefGoogle Scholar
Blake, D., Cairns, A.J., Dowd, K. and MacMinn, R. (2006b) Longevity bonds: Financial engineering, valuation, and hedging. Journal of Risk and Insurance, 73, 647–672.CrossRefGoogle Scholar
Brennan, M.J. (1979) The pricing of contingent claims in discrete time models. Journal of Finance, 34, 53–68.CrossRefGoogle Scholar
Cairns, A.J., Blake, D. and Dowd, K. (2006a) Pricing death: Frameworks for the valuation and securitization of mortality risk. ASTIN Bulletin, 36, 79–120.CrossRefGoogle Scholar
Cairns, A.J., Blake, D. and Dowd, K. (2006b) A two-factor model for stochastic mortality with parameter uncertainty: Theory and calibration. Journal of Risk and Insurance, 73, 687–718.CrossRefGoogle Scholar
Camara, A. (2003) A generalization of the Brennan–Rubinstein approach for the pricing of derivatives. Journal of Finance, 58, 805–819.CrossRefGoogle Scholar
Chen, H. and Cox, S.H. (2009) Modeling mortality with jumps: Applications to mortality securitization. Journal of Risk and Insurance, 76, 727–751.CrossRefGoogle Scholar
Chen, B., Zhang, L. and Lin, Z. (2010) On the robustness of longevity risk pricing. Insurance: Mathematics and Economics, 47, 358–373.Google Scholar
Cox, S.H. and Lin, Y. (2007) Natural hedging of life and annuity mortality risks. North American Actuarial Journal, 11 (3), 1–15.CrossRefGoogle Scholar
Cox, S.H., Lin, Y. and Pedersen, H. (2010) Mortality risk modeling: Applications to insurance securitization. Insurance: Mathematics and Economics, 46 (1), 242–253.Google Scholar
Cox, S.H., Lin, Y. and Wang, S. (2006) Multivariate exponential tilting and pricing implications for mortality securitization. Journal of Risk and Insurance, 73, 719–736.CrossRefGoogle Scholar
Dahl, M. and Moller, T. (2006) Valuation and hedging of life insurance liabilities with systematic mortality risk. Insurance: Mathematics and Economics, 39, 193–217.Google Scholar
Denuit, M., Devolder, P. and Goderniaux, A. (2007) Securitization of longevity risk: Pricing survivor bonds with Wang transform in the Lee–Carter framework. Journal of Risk and Insurance, 74, 87–113.CrossRefGoogle Scholar
Dowd, K., Blake, D., Cairns, A.J. and Dawson, P. (2006) Survivor swaps. Journal of Risk and Insurance, 1, 1–17.CrossRefGoogle Scholar
Ingersoll, J.E. (1987) Theory of Financial Decision Making. Maryland: Rowman & Littlefield.Google Scholar
Johnson, N.L. (1949) Systems of frequency curves generated by methods of translation. Biometrika, 36, 149–176.CrossRefGoogle ScholarPubMed
Johnson, N.L., Kotz, S. and Balakrishnan, N. (1994) Continuous Univariate Distributions, Vol. 1. New York: Wiley.Google Scholar
Lin, Y. and Cox, S.H. (2005) Securitization of mortality risks in life annuities. Journal of Risk and Insurance, 72, 227–252.CrossRefGoogle Scholar
Lin, Y. and Cox, S.H. (2008) Securitization of catastrophe mortality risks. Insurance: Mathematics and Economics, 42, 628–637.Google Scholar
Milevsky, M.A. and Promislow, S.D. (2001) Mortality derivatives and the option to annuitize. Insurance: Mathematics and Economics, 29, 299–318.Google Scholar
Milevsky, M.A., Promislow, S.D. and Young, V.R. (2005) Financial valuation of mortality risk via the instantaneous Sharpe ratio: Applications to pricing pure endowments. Department of Mathematics, University of Michigan.Google Scholar
Rubinstein, M. (1976) The valuation of uncertain income streams and the pricing of options. Bell Journal of Economics and Management Science, 7, 407–425.CrossRefGoogle Scholar
Sherris, M. (2006) Solvency, capital allocation, and fair rate of return in insurance. The Journal of Risk and Insurance, 73 (1), 71–96.CrossRefGoogle Scholar
Slifker, J.F. and Shapiro, S.S. (1980) The Johnson system: Selection and parameter estimation. Tecgnometrics, 22, 239–246.CrossRefGoogle Scholar
Wang, S.S. (2000) A class of distortion operations for pricing financial and insurance risks. Journal of Risk and Insurance, 67, 15–36.CrossRefGoogle Scholar
Wang, S.S. (2002) A universal framework for pricing financial and insurance risks. ASTIN Bulletin, 32, 213–234.CrossRefGoogle Scholar
Young, V.R. (2008) Pricing life insurance under stochastic mortality via the instantaneous Sharpe ratio. Insurance: Mathematics and Economics, 42, 691–703.Google Scholar