Academic journal article Journal of Risk and Insurance

Canonical Valuation of Mortality-Linked Securities

Academic journal article Journal of Risk and Insurance

Canonical Valuation of Mortality-Linked Securities

Article excerpt

ABSTRACT

A fundamental question in the study of mortality-linked securities is how to place a value on them. This is still an open question, partly because there is a lack of liquidly traded longevity indexes or securities from which we can infer the market price of risk. This article develops a framework for pricing mortality-linked securities on the basis of canonical valuation. This framework is largely nonparametric, helping us avoid parameter and model risk, which may be significant in other pricing methods. The framework is then applied to a mortality-linked security, and the results are compared against those derived from other methods.

INTRODUCTION

Thanks to the combination of better health care and other factors, human mortality in developed countries has been improving steadily for many decades. While improved longevity is generally perceived as a social achievement, it can be a serious problem for actuaries, particularly when it is unanticipated. Longevity risk, that is, the risk that future mortality improvement deviates from today's assumptions, has significantly contributed to the pension crisis that has enveloped many public and corporate pension plans on both sides of the Atlantic.

Actuaries did, of course, take the possibility that people would live longer into account when valuing pensions and annuities. However, what was missed was the pace of mortality reduction. For instance, mortality reduction factors that have been widely used in Britain are found to understate the decline of UK male pensioners' mortality considerably (see Continuous Mortality Investigation Bureau, 1999, 2002). Such an error, which will lead to unforeseen pension and annuity liabilities in the future, cannot be mitigated by selling a large number of contracts, simply because it affects the entire portfolio. Although the risk may be hedged by selling life insurance to the same lives that are buying life annuities, the hedge, as Cox and Lin (2007) pointed out, is cost prohibitive and may not even be practical in many circumstances.

Securitization is seen as a solution to the problem. By securitization we mean laying off mortality or longevity risk exposures with securities that have payoffs tied to a certain mortality or longevity index. There are two main types of mortality-linked security. The first type, for example, the Swiss Re deal in 2003, aims to hedge against the catastrophic loss of insured lives that might result from natural or man-made disasters. The second type, which is the focus of this article, allows participants to mitigate longevity risk. A well-known example of this type is the 25-year longevity bond announced by BNP-Paribas and the European Investment Bank in November 2004. This bond is an annuity bond that pays coupons that are proportional to the survival rates of English and Welsh males who were aged 65 in 2002. Another example is the QxX index swap launched by Goldman Sachs in December 2007. In this swap, the random cash flows are linked to the QxX index, a longevity index for a representative sample of the U.S. senior insured population. We refer readers to Blake and Burrows (2001), Blake, Cairns, and Dowd (2006) and Blake et al. (2006) for deeper discussions on mortality-linked bonds and swaps.

A fundamental question in the study of mortality-linked securities is how to place a value on them. This is still an open question, partly because, as in valuing over-the-counter-traded options, there is a lack of liquidly traded longevity indexes or securities from which we can infer the market price of risk, a crucial element in the pricing process. The difficulty can also be seen from another viewpoint by considering the creation of a replicating portfolio. If the index on which the mortality-linked security is based is liquidly traded, then the security can be replicated by a portfolio of bonds and the index. Given the principle of no arbitrage, the price of the security is just the value of its replicating portfolio. …

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