Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk*

By Andrew J. G. Cairns, David P. Blake, Kevin Dowd. ASTIN Bulletin: The Journal of the International Actuarial Association, 2006

392 citations recorded by the source corpus.

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.

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Citations in the corpus

An Optimal Product Mix for Hedging Longevity Risk in Life Insurance Companies: The Immunization Theory Approach (2009, unknown): “Alternatives to the mortality model appear in Cairns et al. (2007), who offer a comparative analysis of eight stochastic models based on English, Welsh, and U.”
Living with Mortality: Longevity Bonds and Other Mortality-Linked Securities (2006, background): “For further discussion of this risk premium, the reader is referred to Cairns et al. (2005) and Cairns et al. (2006a).”
Mortality Risk Modeling: Applications to Insurance Securitization (2010, unknown): “A number of recent studies have sought to model mortality trend involving both age-dependent and time-dependent terms (Lee and Carter 1992, Renshaw et al. 1996, Lee 2000, Sithole et al. 2000, Milevsky and Promislow 2001, Olivieri and Pitacco 2002, Dahl 2004, Cairns et al. 2006).”
Pricing of Ratchet Equity-Indexed Annuities under Stochastic Interest Rates ? (2007, background): “As in Cairns et al. (2006), we make the assumption that mortality risk and financial risk are independent, i.e. τx is independent of the processes S(t) and r(t).”
Stochastic Mortality: The Impact on Target Capital (2009, background): “See, for example, Biffis (2005), Biffis and Millossovich (2006), Dahl (2004), Dahl and Møller (2006), Cairns et al. (2006).”
Valuation and hedging of life insurance liabilities with systematic mortality risk (2006, background): “Marocco and Pitacco (1998), Milevsky and Promislow (2001), Dahl (2004), Cairns, Blake and Dowd (2004) , Biffis and Millossovich (2004)and references therein.”
Delta–Gamma hedging of mortality and interest rate risk (2012, methodology): “Cairns, Blake, and Dowd (2006) add that no one of the previous criteria dominates the others.”
Mortality-Indexed Annuities Managing Longevity Risk Via Product Design (2011, methodology): “Cairns et al. (2006). 7 For example, the Lee-Carter model served as a starting point for mortality forecasting models used by the U.”
Longevity Bond Premiums: The Extreme Value Approach and Risk Cubic Pricing (2010, unknown): “Cairns et al. (2006) provide a detailed overview of stochasticmortalitymodels.”
On systematic mortality risk and risk-minimization with survivor swaps (2008, background): “Marocco and Pitacco (1998), Milevsky and Promislow (2001), Dahl (2004), Bi‐s (2005), Cairns, Blake and Dowd (2006) , Bi‐s and Millossovich (2006), Schrager (2006), Miltersen and Persson (2006) and references therein.”
Longevity/Mortality Risk Modeling and Securities Pricing (2012, unknown): “We apply the approach in Cairns, Blake, and Dowd (2006b), which assumes the market price of mortality risk is constant and estimates it from the EIB/BNP LB in November, 2004.”
Stochastic mortality under measure changes (2010, unknown): “The calibration approach is adopted, for example, by Cairns et al. (2006a), who restrict their attention to the case f 0.”
A Two-Factor Model for Stochastic Mortality With Parameter Uncertainty: Theory and Calibration (2006, unknown): “For a full discussion of the EIB/BNP bond as well as other types of mortality-linked security, the reader is referred to Cowley and Cummins (2005), Cairns, et.”
Mortality-dependent financial risk measures (2006, methodology): “Cairns et al. (2006b) also show that if we use the UK Government Actuary’s Department (GAD) data for English and Welsh males over 1961–2002, then the least squares estimates of our parameters are:”
Natural Hedging of Life and Annuity Mortality Risks (2007, unknown): “ Cairns et al. (2004) discuss a theoretical framework for pricing mortality derivatives and valuing”
Mortality risk via affine stochastic intensities: calibration and empirical relevance (2008, background): “Cairns et al. (2006) report a list of criteria that a good mortality model should meet: 8The difference between tp65 of the observed table and S65(t) of each model is positive for t ≤ 10 approximately, negative between t = 10 and t = 20 approximately, then again positive for t ≥ 20.”