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DYNAMIC HEDGING OF LONGEVITY RISK: THE EFFECT OF TRADING FREQUENCY

Published online by Cambridge University Press:  31 August 2017

Hong Li
Hong Li*
Affiliation:
School of Finance, Nankai University, Tongyan Road 38, 300350, Tianjin, P.R.China
*
E-Mail: [email protected]
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Abstract

This paper investigates dynamic hedging strategies for pension and annuity liabilities that are exposed to longevity risk. In particular, we consider a hedger who wishes to minimize the variance of her hedging error using index-based longevity-linked derivatives. To cope with the fact that liquidity of longevity-linked derivatives is still limited, we consider a liquidity constrained case where the hedger can only trade longevity-linked derivatives at a frequency lower than other assets. Time-consistent, closed-form solutions of optimal hedging strategies are obtained under a forward mortality framework. In the numerical illustration, we show that lowering the trading of the longevity-linked derivatives to a 2-year frequency only leads to a slight loss of the hedging performance. Moreover, even when the longevity-linked derivatives are traded at a very low (5-year) frequency, dynamic hedging strategies still significantly outperform the static one.

Keywords

Dynamic hedginglongevity riskminimum varianceforward mortality model
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 48 , Issue 1 , January 2018 , pp. 197 - 232
Copyright
Copyright © Astin Bulletin 2017 

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References

Ang, A., Papanikolaou, D. and Westerfield, M.M. (2014) Portfolio choice with illiquid assets. Management Science, 60 (11), 2737–2761.Google Scholar
Basak, S. and Chabakauri, G. (2010) Dynamic mean-variance asset allocation. Review of Financial Studies, 23 (8), 2970–3016.Google Scholar
Basak, S. and Chabakauri, G. (2012) Dynamic hedging in incomplete markets: A simple solution. Review of financial studies, 25 (6), 1845–1896.Google Scholar
Bauer, D., Benth, F.E. and Kiesel, R. (2012) Modeling the forward surface of mortality. SIAM Journal on Financial Mathematics, 3 (1), 639–666.Google Scholar
Bauer, D., Börger, M. and Ruß, J. (2010) On the pricing of longevity-linked securities. Insurance: Mathematics and Economics, 46 (1), 139–149.Google Scholar
Bauer, D., Börger, M., Ruß, J. and Zwiesler, H.-J. (2008) The volatility of mortality. Asia-Pacific Journal of Risk and Insurance, 3 (1), 172–199.CrossRefGoogle Scholar
Bauer, D. and Ruß, J. (2006) Pricing longevity bonds using implied survival probabilities. In 2006 meeting of the American Risk and Insurance Association (ARIA).Google Scholar
Bayraktar, E., Milevsky, M.A., David Promislow, S. and Young, V.R. (2009) Valuation of mortality risk via the instantaneous sharpe ratio: Applications to life annuities. Journal of Economic Dynamics and Control, 33 (3), 676–691.Google Scholar
Biffis, E. (2005) Affine processes for dynamic mortality and actuarial valuations. Insurance: Mathematics and Economics, 37 (3), 443–468.Google Scholar
Biffis, E., Denuit, M. and Devolder, P. (2010) Stochastic mortality under measure changes. Scandinavian Actuarial Journal, 2010 (4), 284–311.CrossRefGoogle Scholar
Biffs, B., and Blake, D. (2014) Keeping some skin in the game: How to start a capital market in longevity risk transfers. North American Actuarial Journal, 18 (1), 14–21.Google Scholar
Blackburn, C. and Sherris, M. (2013) Consistent dynamic affine mortality models for longevity risk applications. Insurance: Mathematics and Economics, 53 (1), 64–73.Google Scholar
Blackburn, C. and Sherris, M. (2014) Forward mortality modelling of multiple populations. Working paper.Google Scholar
Blake, D., Cairns, A.J.G. and Dowd, K. (2006) Living with mortality: Longevity bonds and other mortality-linked securities. British Actuarial Journal, 12 (01), 153–197.Google Scholar
Cairns, A.J.G. (2011) Modelling and management of longevity risk: Approximations to survivor functions and dynamic hedging. Insurance: Mathematics and Economics, 49 (3), 438–453.Google Scholar
Cairns, A.J.G. (2013) Robust hedging of longevity risk. Journal of Risk and Insurance, 80 (3), 621–648.Google Scholar
Cairns, A.J.G., Blake, D., Dawson, P. and Dowd, K. (2005) Pricing the risk on longevity bonds. Life and Pensions, 1 (2), 41–44.Google Scholar
Cairns, A.J.G., Dowd, K., Blake, D. and Coughlan, G.D. (2014) Longevity hedge effectiveness: A decomposition. Quantitative Finance, 14 (2), 217–235.Google Scholar
Caplin, A. and Leahy, J. (2006) The recursive approach to time inconsistency. Journal of Economic Theory, 131 (1), 134–156.Google Scholar
CRO Forum (2010) Longevity risk. CRO Briefing Emerging Risks Initiative Position Paper, http://www.thecroforum.org/longevity-risk/.Google Scholar
Dahl, M., Glar, S. and Møller, T. (2011) Mixed dynamic and static risk-minimization with an application to survivor swaps. European Actuarial Journal, 1 (2), 233–260.CrossRefGoogle Scholar
Dahl, M., Melchior, M. and Møller, T. (2008) On systematic mortality risk and risk-minimization with survivor swaps. Scandinavian Actuarial Journal, 2008 (2–3), 114–146.Google Scholar
Dawson, P., Dowd, K., Cairns, A.J.G. and Blake, D. (2010) Survivor derivatives: A consistent pricing framework. Journal of Risk and Insurance, 77 (3), 579–596.Google Scholar
De Jong, F. and Santa-Clara, P. (1999) The dynamics of the forward interest rate curve: A formulation with state variables. Journal of Financial and Quantitative Analysis, 34 (01), 131–157.Google Scholar
De Rosa, C., Luciano, E. and Regis, L. (2017) Basis risk in static versus dynamic longevity-risk hedging. Scandinavian Actuarial Journal, 2017 (4), 343–365.Google Scholar
Driessen, J., Klaassen, P. and Melenberg, B. (2003) The performance of multi-factor term structure models for pricing and hedging caps and swaptions. Journal of Financial and Quantitative Analysis, 38 (03), 635–672.Google Scholar
Heath, D., Jarrow, R. and Morton, A. (1992) Bond pricing and the term structure of interest rates: A new methodology for contingent claims valuation. Econometrica: Journal of the Econometric Society, 60, 77–105.Google Scholar
Inui, K. and Kijima, M. (1998) A markovian framework in multi-factor heath-jarrow-morton models. Journal of Financial and Quantitative Analysis, 33 (03), 423–440.Google Scholar
Jeanblanc, M., Yor, M. and Chesney, M. (2009) Mathematical Methods for Financial Markets. New York: Springer.Google Scholar
Kallsen, J. (2002) Utility-based derivative pricing in incomplete markets. In Mathematical Finance Bachelier Congress 2000 (eds. Geman, H., Madan, D., Pliska, S.R., and Vorst, T.), pp. 313–338. New York: Springer.Google Scholar
Karatzas, I. (1991) Brownian Motion and Stochastic Calculus, Volume 113. New York: Springer.Google Scholar
Lee, R.D. and Carter, L.R. (1992) Modeling and forecasting us mortality. Journal of the American Statistical Association, 87 (419), 659–671.Google Scholar
Li, H., Waegenaere, A. and Melenberg, B. (2017) Robust mean-variance hedging of longevity risk. Journal of Risk and Insurance, 84 (S1), 459–475.Google Scholar
Li, J.S.-H. and Hardy, M.R. (2011) Measuring basis risk in longevity hedges. North American Actuarial Journal, 15 (2), 177–200.Google Scholar
Li, J.S.-H. and Luo, A. (2012) Key q-duration: A framework for hedging longevity risk. Astin Bulletin, 42 (2), 413–452.Google Scholar
Lin, Y. and Cox, S.H. (2005) Securitization of mortality risks in life annuities. Journal of Risk and Insurance, 72 (2), 227–252.CrossRefGoogle Scholar
Lin, Y. and Cox, S.H. (2008) Securitization of catastrophe mortality risks. Insurance: Mathematics and Economics, 42 (2), 628–637.Google Scholar
Menoncin, F. (2008) The role of longevity bonds in optimal portfolios. Insurance: Mathematics and Economics, 42 (1), 343–358.Google Scholar
OECD (2013) Pension at a glance 2013. Technical report, http://dx.doi.org/10.1787/pension_glance-2013-en.Google Scholar
Strotz, R.H. (1956) Myopia and inconsistency in dynamic utility maximization. The Review of Economic Studies, 23, 165–180.Google Scholar
Wang, S. (2002) A universal framework for pricing financial and insurance risks. Astin Bulletin, 32 (2), 213–234.Google Scholar
Wong, T.W., Chiu, M.C. and Wong, H.Y. (2014) Time-consistent mean–variance hedging of longevity risk: Effect of cointegration. Insurance: Mathematics and Economics, 56, 56–67.Google Scholar
Wong, T.W., Chiu, M.C. and Wong, H.Y. (2015) Managing mortality risk with longevity bonds when mortality rates are cointegrated. Journal of Risk and Insurance, doi: 10.1111/jori.12110.CrossRefGoogle Scholar