×

Pricing death frameworks for the valuation and securitization of mortality risk. (English) Zbl 1162.91403

Summary: It is now widely accepted that stochastic mortality - the risk that aggregate mortality might differ from that anticipated - is an important risk factor in both life insurance and pensions. As such it affects how fair values, premium rates, and risk reserves are calculated. This paper makes use of the similarities between the force of mortality and interest rates to examine how we might model mortality risks and price mortality-related instruments using adaptations of the arbitrage-free pricing frameworks that have been developed for interest-rate derivatives. In so doing, the paper pulls together a range of arbitrage-free (or risk-neutral) frameworks for pricing and hedging mortality risk that allow for both interest and mortality factors to be stochastic.The different frameworks that we describe - short-rate models, forward-mortality models, positive-mortality models and mortality market models - are all based on positive-interest-rate modelling frameworks since the force of mortality can be treated in a similar way to the short-term risk-free rate of interest. While much of this paper is a review of the possible frameworks,the key new development is the introduction of mortality market models equivalent to the LIBOR and swap market models in the interest-rate literature. These frameworks can be applied to a great variety of mortality-related instruments, from vanilla longevity bonds to exotic mortality derivatives.

MSC:

91B30 Risk theory, insurance (MSC2010)
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] DOI: 10.1080/10920277.2000.10595882 · Zbl 1083.62535
[2] Credit Derivatives Pricing Models: Models, Pricing and Implementation (2003)
[3] Working paper (2005)
[4] DOI: 10.2143/AST.30.2.504635
[5] (2001)
[6] Insurance: Mathematics and Economics 33 pp 29– (2003)
[7] Credit Risk Modeling: Theory and Applications (2004)
[8] Financial Analysts Journal pp 52– (1991)
[9] Working paper (2005)
[10] Methods of Mathematical Finance (1998) · Zbl 0941.91032
[11] ASTIN Bulletin 33 pp 57– (2003) · Zbl 1098.91551
[12] Working paper (2004)
[13] DOI: 10.1017/S0020268100048988
[14] DOI: 10.2143/AST.32.2.1027 · Zbl 1090.91555
[15] Insurance: Mathematics and Economics 37 pp 443– (2005)
[16] DOI: 10.1007/s007800050026 · Zbl 0888.60038
[17] DOI: 10.2307/253675
[18] Global Association of Risk Professionals 4 pp 26– (2004)
[19] Interest Rate Modelling (2000)
[20] DOI: 10.2143/AST.26.1.563234
[21] DOI: 10.1111/j.1467-9965.1995.tb00064.x · Zbl 0866.90047
[22] DOI: 10.2307/2951677 · Zbl 0751.90009
[23] DOI: 10.1016/0304-405X(77)90016-2 · Zbl 1372.91113
[24] DOI: 10.1093/rfs/15.1.243
[25] DOI: 10.1016/S0304-405X(97)00037-8
[26] Risk 9 pp 46– (1996)
[27] DOI: 10.2143/AST.29.1.504608 · Zbl 1162.91433
[28] DOI: 10.1111/j.1467-9965.1996.tb00123.x · Zbl 0915.90014
[29] DOI: 10.1080/135048697334782 · Zbl 1009.91020
[30] DOI: 10.1111/1467-9965.00029 · Zbl 0884.90046
[31] DOI: 10.1111/j.1539-6975.2006.00163.x
[32] DOI: 10.1111/1539-6975.00002
[33] Insurance: Mathematics and Economics 33 pp 255– (2003)
[34] DOI: 10.2307/253893
[35] Modern Pricing of Interest-Rate Derivatives (2002)
[36] Presented at the third annual CeRP conference ”Developing an Annuity Market in Europe” (2002)
[37] Insurance: Mathematics and Economics 35 pp 113– (2004)
[38] DOI: 10.1017/S0020268100046680
[39] DOI: 10.1191/1471082X04st080oa · Zbl 1061.62171
[40] Insurance: Mathematics and Economics 33 pp 283– (2003)
[41] DOI: 10.1111/j.1539-6975.2005.00121.x
[42] DOI: 10.2307/1911242 · Zbl 1274.91447
[43] DOI: 10.2307/2678106
[44] The Encyclopaedia of Actuarial Science 1 pp 231– (2004)
[45] DOI: 10.2143/AST.30.1.504631
[46] DOI: 10.1111/j.1540-6261.1997.tb03823.x
[47] Continuous Mortality Investigation Reports 17 pp 89– (1999)
[48] Working paper (2005)
[49] Insurance: Mathematics and Economics 29 pp 299– (2001)
[50] Continuous Mortality Investigation Reports 3 pp 1– (1978)
[51] Proceedings of the 3rd World Congress of the Bachelier Society, Chicago, and Proceedings of the 35th International ASTIN Colloquium (2004)
[52] Life and Pensions pp 41– (2005)
[53] CMI Working Papers 1 and 2; Presented to the Staple Inn Actuarial Society on 11 March 2003 pp 46– (2003)
[54] DOI: 10.1017/S1357321700005183
[55] Interest-Rate Models: An Introduction (2004) · Zbl 1140.91039
[56] DOI: 10.1111/j.0960-1627.2004.00198.x · Zbl 1134.60355
[57] Working paper (2005)
[58] Insurance: Mathematics and Economics 31 pp 373– (2002)
[59] DOI: 10.1111/j.1539-6975.2005.00122.x
[60] Interest Rate Models: Theory and Practice (2001)
[61] Journal of the American Statistical Association 87 pp 659– (1992)
[62] DOI: 10.1111/1467-9965.00028 · Zbl 0884.90008
[63] Transactions of the Faculty of Actuaries 40 pp 98– (1987)
[64] (2000)
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.