Academic journal article Journal of Risk and Insurance

Longevity Bonds: Financial Engineering, Valuation, and Hedging

Academic journal article Journal of Risk and Insurance

Longevity Bonds: Financial Engineering, Valuation, and Hedging

Article excerpt

ABSTRACT

This article examines the main characteristics of longevity bonds (LBs) and shows that they can take a large variety of forms which can vary enormously in their sensitivities to longevity shocks. We examine different ways of financially engineering LBs and consider problems arising from the dearth of ultra-long government bonds and the choice of the reference population index. The article also looks at valuation issues in an incomplete markets context and finishes with an examination of how LBs can be used as a risk management tool for hedging longevity risks.

INTRODUCTION

One of the largest sources of risk faced by life companies and pension funds is longevity risk: the risk that members of some reference population might live longer, on average, than anticipated. For example, if the reference population are annuitants, longevity risk is the risk that annuitants might live longer on average than anticipated in the life companies' mortality tables used to price annuities. Longevity risk is an important problem both because of the uncertainty of longevity projections, on the one hand, and because of the large amounts of liabilities exposed to longevity risk, on the other. The uncertainty of longevity projections is illustrated by the fact that life expectancy for men aged 60 is more than 5 years' longer in 2005 than it was anticipated to be in mortality projections made in the 1980s; (1) and the amounts at risk are illustrated by the fact that state and private sector exposure to longevity risk in the United Kingdom amounted to 2,520 bn [pounds sterling] (or $4,424 bn) at the end of 2003--that is, nearly 40,000 [pounds sterling] (or $70,000) for every man, woman, and child in the United Kingdom. (2)

Exposure to longevity risk is therefore a serious issue, and yet, traditionally, life companies and pension funds have had few means of managing it: until recently, longevity risks were never securitized (3) and there were no longevity derivatives that these institutions could use to hedge their longevity risk exposures. However, this state of affairs is changing, and markets for longevity derivatives are starting to develop. Most prominent among these are longevity bonds (LBs), which are financial instruments in which payments depend on the realization of a survivor index [S.sub.t,x] for some period t. As its name suggests, the survivor index is the proportion of some initial reference population aged x at time t = 0 who are still alive at some future time t. If [q.sub.s,x] is the mortality rate between s and s + 1 for members of the reference population aged x at time t = 0 and still alive at time s, then the relationship between the sequence [q.sub.s,x] and [S.sub.t,x] is given by

[S.sub.t,x] = (1 - [q.sub.0,x]) (1 - [q.sub.1,x]) ... (1 - [q.sub.t-1,x]). (1)

Since we are dealing in this article with reference populations from a single age cohort, we will simply denote below the survivor index as [S.sub.t.]

LBs were first proposed by Blake and Burrows (2001), and the first operational mortality-linked bond (the Swiss Re mortality catastrophe bond) appeared in 2003. A second mortality-linked bond (the EIB/BNP Paribas LB) was announced in 2004 (although it failed to come to market), and various other mortality-linked products have also been issued or are in preparation. (4)

However, many actuaries are still unconvinced that LBs (and related derivatives) will have a significant part to play in the management of longevity risk. (5) Indeed, even supporters of LBs are divided on some of the key issues. For example, Blake (2003) and Dowd (2003) disagree on whether LBs should be issued by the state, (6) and on the significance of a potential natural excess demand for products that are hedges against longevity risk. (7) Thus, the subject of LBs is both novel and controversial, and much more work remains to be done on it.

Our discussion is organized as follows. …

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