ArticlePDF Available

Longevity: a new asset class


Abstract and Figures

A little over a decade ago, a new asset class emerged, one linked to longevity risk, i.e., unanticipated changes in life expectancy. The Life Market has two segments: a macro-segment with assets linked to groups of lives, such as members of a pension plan or a book of annuitants; and a micro-segment with assets linked to individual lives, such as life settlements. For the market to become global, certain market requirements need to be satisfied, such as understanding the causal factors underlying longevity and the development of market indices and mortality forecasting models. The government has a role in contributing to the development of the market, as do pricing models. By addressing these issues, as well as understanding the needs of investors better, the asset class can become global, by attracting new groups of investors seeking returns that are uncorrelated with existing financial instruments.
Content may be subject to copyright.
Longevity: A New Asset Class
Professor David Blake
Pensions Institute
Cass Business School
June 2018
A little over a decade ago, a new asset class emerged, one linked to longevity risk, i.e., unanticipated
changes in life expectancy. The Life Market has two segments: a macro segment with assets linked
to groups of lives, such as members of a pension plan or a book of annuitants; and a micro segment
with assets linked to individual lives, such as life settlements. For the market to become global
certain market requirements need to be satisfied, such as understanding the causal factors
underlying longevity and the development of market indices and mortality forecasting models. The
government has a role in contributing to the development of the market, as do pricing models. By
addressing these issues, as well as understanding the needs of investors better, the asset class can
become global, by attracting new groups of investors seeking returns that are uncorrelated with
existing financial instruments.
Keywords: longevity risk, longevity-linked assets, uncorrelated returns
JEL classifications: G15, J11
1. Introduction ........................................................................................................................................ 1
2. Longevity risk: The key risk to quantify ............................................................................................... 1
3. The birth of a new capital market: The Life Market ........................................................................... 5
3.1 What are the conditions for a new capital market succeed? ....................................................... 5
3.2 Quantifying the potential size of the longevity risk transfer market ............................................ 5
3.3 The structure of the longevity market .......................................................................................... 5
4. Market requirements .......................................................................................................................... 6
4.1 Causal factors underlying longevity .............................................................................................. 7
4.2 Mortality indices and mortality forecasting models ................................................................... 10
4.2.1 Mortality indices .................................................................................................................. 10
4.2.2 Mortality forecasting models ............................................................................................... 10
5. The macro-longevity risk market ...................................................................................................... 13
5.1 Bonds .......................................................................................................................................... 13
5.2 Derivatives .................................................................................................................................. 14
5.2.1 Mortality forwards ............................................................................................................... 14
5.2.2 Longevity (or survivor) swaps .............................................................................................. 15
5.2.3 Longevity bull call spreads (or tail-risk protection) .............................................................. 16
5.3 Total size of the macro-longevity market ................................................................................... 20
6. The micro-longevity risk market ....................................................................................................... 20
7. A role for government? ..................................................................................................................... 24
8. Pricing ................................................................................................................................................ 25
9. Investor engagement ........................................................................................................................ 27
9.1 Investor segmentation ................................................................................................................ 28
9.2 Expanding the asset class ............................................................................................................ 30
9.3 A new vehicle reinsurance sidecars ......................................................................................... 32
9.4 Longevity assets in a diversified portfolio ................................................................................... 33
10. Conclusion ....................................................................................................................................... 33
11. References ...................................................................................................................................... 34
A new global capital market, known as the Life Market, is developing, one which trades longevity-
linked assets and liabilities that are related to changes in human life expectancy (LE). One of the
main attractions of longevity-linked assets is that they are to a first-order uncorrelated with financial
assets, such as equities and bonds. This makes them an attractive asset to hold in a diversified
portfolio. Nevertheless, the risk is unusual in terms of financial assets, since it is a trendriska risk
that increases with time. Most financial risks do not trend, but instead are cyclical such as the
equity premium, the credit premium, the liquidity premium, and the real risk-free interest rate. The
price level is one of the few trend risks in finance as a consequence of persistent positive inflation.
There have been previous historical examples of longevity-linked assets being traded. For example,
Tontine bonds were issued by European governments in 17th and 18th Centuries and a secondary
market in life insurance policies began in mid-19th Century when Foster & Cranfield auctioned an
endowment life insurance policy in UK in 1844. However, the new market which began in the UK
in 2006 has the potential to become global.
The market started because a new risk emerged, namely longevity risk.1 Previously actuaries had
assumed that human life expectancy was fairly predictable. But from the 1990s, actuaries, first in the
UK and then elsewhere, noticed that they had been systematically underestimating how long people
are going to live. Instead, they came to realize that longevity is a trend risk.
As a consequence of this, there is the danger of individuals outliving their savings. Pension plans
must provide retirement income security for however long people live and corporate pension plan
sponsors face the risk of having to divert resources away from dividend and investment programmes
to fill plan deficits. Similarly, life offices selling life annuities face the risk of inadequately reserving.
It is possible to decompose longevity risk into two components as follows:
Total longevity risk = Systematic longevity risk [Trend risk]
+ Specific longevity risk [Idiosyncratic and modelling risks].
Specific longevity risk is itself the sum of idiosyncratic risk (different individuals from the same
population of interest have different lengths of lifetime) and modelling risk (different models will
project different lifetimes for these individuals) see Figure 1. But these risks get diversified in
sufficiently large populations of interest.
But systematic longevity risk is a slowly developing trend risk and getting the trend right is key to the
successful management of this risk. Figure 2 shows that, for almost two centuries, life expectancy
has been increasing in advanced economies by 2.5 years per decade. Figure 3 shows the variability
for UK males aged 65 and 85.
Turning to the future, will longevity continue to improve? There are alternative expert views. On the
one hand, there are the ‘pessimists’ led by Jay Olshansky (see, e.g., Olshansky et al (2001), Carnes et
al (2003), and Olshansky et al (2005)) who suggest that life expectancy might level off or decline due
to the impact of obesity, global warming etc. On the other hand, there are the ‘optimists’ led by Jim
1 This is the risk that people will live longer than expected, so that pension plans and annuity providers (and
reinsurers) make payments to members and policy holders for much longer than anticipated.
Vaupel (see, e.g., Oeppen and Vaupel (2002)) who argue there is no natural upper limit to human
life, pointing to future scientific and medical advances, such as regenerative medicine.
Figure 1: Longevity risk is driven by three underlying risks
Source: Prudential
Figure 2: Life expectancy in developed countries since 1840
Source: Oeppen and Vaupel (2002) Broken limits to life expectancy
Figure 3: Variability in life expectancy
Source: PNMA00 medium cohort
Official projections have underestimated recent improvements in life expectancy see Figure 4.
Figure 5 shows that mortality is a stochastic process. Mortality rates in the UK have been declining
since the 1970s, but the declines have been volatile. Mortality modelling needs to account for this.
There are a range of stakeholders who bear longevity risk: individuals; company pension funds;
annuity providers, principally insurance companies; the government through public pension
systems; and investors in longevity-linked products.
Those bearing longevity risk face a range of responses. They can accept longevity risk as legitimate
business risk, although this only makes sense if they earn a suitable longevity risk premium. They can
share longevity risk, e.g., through participating annuities with survival credits, conditional indexation,
and caps. They can use reinsurance to lay-off or hedge the risks: key examples are buy-outs and
buy-ins.2 Finally, they can manage the risk with longevity-linked products or securitize the risk.
These last two options constitute the Life Market.
2 With a buy-out, an insurance company buys out the liabilities of a pension plan which is paid for with the
pension plan assets and a loan if the plan is in deficit at the time. Both the pension plan assets and liabilities are
removed from the corporate sponsor’s balance sheet. Each member has a personal annuity from the insurer who
takes over responsibility for paying their pension. This contrasts with a buy-in, where the liabilities remain on
the sponsor’s balance sheet, but the plan buys bulk purchase annuities (BPAs) from an insurance company and
pays members’ pensions from the annuity payments it receives from the insurer. The BPA is an asset of the
plan, not the members. The world’s first specialist buy-out company was Paternoster which was established in
the UK in 2006. This was closely followed by the Pension Insurance Corporation (also in 2006) and Lucida and
Rothesay Life (both 2007). Paternoster executed the first buy-out in November 2006 of the Cuthbert Heath
Family Plan, a small UK plan with just 33 members. It also executed the first pensioner buy-in with Hunting
PLC in January 2007. Paternoster was bought by Rothesay Life in 2011, while Lucida was acquired by Legal &
General in 2013.
Figure 4: Poor accuracy of official projections - Actual and projected period life expectancy at birth,
UK males, 1966-2031
Source: Shaw (2007, Figure 5)
Figure 5: Mortality is now recognized as being a stochastic process
Source: UK Office for National Statistics
3.1 What are the conditions for a new capital market succeed?
There are five conditions for a new capital market to succeed:
It must provide an effective exposure, or hedging, to a state of the world that is
economically important
and cannot be hedged through existing market instruments.
It must use a homogeneous and transparent contract to permit exchange between agents
in a way that provides an attractive investment exposure.
Loeys et al (2007) argue that ‘longevity meets the basic conditions for a successful market
innovation’. In fact, two Life Markets are developing: a macro-longevity market, dealing with
corporate pension plan liabilities and annuity books; and a micro-longevity market, dealing with
individual life insurance policies (or life settlements). Both markets will be built around indices. A
reference population underlying the calculation of a mortality index is central to both the viability
and liquidity of contracts.
3.2 Quantifying the potential size of the longevity risk transfer market
The potential size of the global longevity risk market for (state and private sector) pension liabilities
is estimated at between $60trn and $80trn.3 The main countries with private corporate sector
pension liabilities are: US ($14.460trn), UK ($2.685trn), Australia ($1.639trn), Canada ($1.298trn),
Holland ($1.282trn), Japan ($1.221trn) and Switzerland ($0.788trn).
However, only the UK, US, Canada and Holland currently have the conditions for a longevity risk
transfer market to develop. These conditions are: low interest rates which, by increasing the present
value of more distant pension payments, has exposed the real extent of longevity risk in pension
plans; inflation uplifting of pensions in payment (especially in the UK and Holland); constant
updating by the actuarial profession of longevity projections; the introduction of market-consistent
valuation methods; increased accounting transparency of pension assets and liabilities; and
increased intervention powers by the pensions regulator.
3.3 The structure of the longevity market
Figure 6 shows the structure of the longevity market. The supply of longevity comes from longevity
‘hedgers’, entities that hold longevity risk and want to offload it (known as ‘cedants’ in the
reinsurance industry). Examples include a defined benefit (DB) pension plan and an annuity provider
that are looking to transfer/reinsure their longevity risk. Both institutions will consider buying
longevity protection, including a hedge related to a reference population, such as the national
population. However, if the reference population is very different from hedger’s specific population,
then the hedger will be exposed to significant basis risk’,4 and might conclude that longevity
hedging is ineffective.
3 Michaelson and Mulholland (2015).
4 Basis risk is the residual risk associated with imperfect hedging where the movements in the underlying
exposure are not perfectly correlated with movements in the hedging instrument.
Figure 6: Supply and demand in the longevity market
Source: Coughlan (2011)
The demand for longevity comes from longevity ‘investors’, entities that take longevity risk and
receive a risk premium for it. There are a number of potential types of investor. First, there are the
life insurers and reinsurers via the insurance markets. Such organisations are willing to sell longevity
protection as part of their business model, e.g., by writing annuities. Second, there are medium- and
long-term investors, via the capital markets. These include insurance-linked securities (ILS)
investors, other hedge funds, and other (longer term) investors, such as sovereign wealth funds,
endowments and family officesall seeking assets that have low correlation with existing financial
instruments. Next there are other institutions naturally long longevity, such as pharmaceutical
companies and long-term care homes, that might in due course consider selling longevity protection.
Then there are pension plans that have not hedged their longevity risk: they are also (possibly
reluctant) investors. Finally, there are short-term investors or speculators which might become
interested in the market if there is sufficient liquidity.
What is needed for the Life Market to operate? There are two main market requirements: analysis
of causal factors underlying longevity; and quantifying longevity risk using mortality indices and
mortality forecasting models.
4.1 Causal factors underlying longevity
There are five key causal factors underlying longevity differences:
Gender: female life expectancy is higher than that of males, but the difference is narrowing,
as Figure 7 shows for both England & Wales and for the US.
Geographical location: there are significant differences in life expectancy depending on
geographical location, even down to the level of post code as Figure 8 shows.
Social class: Figure 9 shows that life expectancy is positively related to social class and that
the difference is widening in England & Wales.
Income/wealth. Life expectancy is positively related to income and wealth as Figure 10
shows for Danish males aged 65.
Year of birth (cohort): In some countries there is evidence of a cohort effect (see, e.g.,
Willets (2004)). Life expectancy is linked to year of birth: some birth cohorts have higher life
expectancy than the birth cohorts on either side for reasons that are not fully understood.
Figure 11 shows the so-called UK male 1930 golden cohort which has exhibited higher
annual improvements in mortality rates than adjacent birth cohorts. Possible explanations
include good diets between 1939-1945 and the introduction of the National Health Service
in 1948.
Figure 7: Life expectancy at age 65 in England & Wales and the US, 1960-2010
1960 1970 1980 1990 2000 2010
65 EW Males
65 US Male
65 US Female
Period life expectancy at age 65 (years)
Source: J.P. Morgan LifeMetrics data
Figure 8: Male life expectancy at birth in different parts of the UK
Source: Office for National Statistics
Figure 9: Differences in life expectancy due to social class
Source: Longitudinal Study, Office for National Statistics
Life expectancy for men at 65 by Social Class, England and Wales
1972-76 1977-81 1982-86 1987-91 1992-96 1997-01 2002-05
Figure 10: Differences in life expectancy due to income/wealth in Denmark
Source: Cairns et al (2017)
Figure 11: Differences in life expectancy due to year of birth with the UK male 1930 golden cohort
Source: Office for National Statistics
4.2 Mortality indices and mortality forecasting models
4.2.1 Mortality indices
As has been shown in other markets, such as the equity and bond markets, trading is built around
market indices. In the context of the Life Market, mortality indices will depend on the availability of
timely high-quality mortality data.
Credit Suisse introduced a Longevity Index in 2005, but it lacked transparency and no transactions
were executed using it. In 2007, the LifeMetrics Indices were introduced by J.P. Morgan, Towers
Watson and the Pensions Institute. They covered the UK, the US, Holland and Germany and were
fully transparent and objective. The indices were transferred to the Life & Longevity Markets
Association (LLMA)5 in 2011. Deutsche Börse introduced monthly Xpect-Indices on mortality and life
Indices were also introduced in the life settlements market. For example, Goldman Sachs started the
QxX Life Settlements Index in 2007, but there was insufficient trading and it was discontinued. In
2010, the Fasano Longevity Life Settlements Index was launched.
4.2.2 Mortality forecasting models
It is essential to get unbiased estimates of future life expectancies. This requires good mortality
forecasting models. These are divided into three different classes.
The first is ‘process-based’ models which model either the causes of death or the processes
underlying mortality improvements. These models use research from demography, medical science,
and healthcare economics to: improve understanding of the drivers of historical mortality change;
and build models to predict how social change and medical improvements will influence future
With cause-of-death models, the total mortality rate is decomposed amongst a number of diseases.
Models are fit and projected stochastically for each underlying cause. Causes are then re-aggregated
to give a forecast for total mortality or life expectancy. These models are highly subjective. A large
number of competing processes need to be calibrated from sparse data and decisions on the likely
path of medical progress need to be made.
An example of the second type of model in this class is the Risk Management Solutions (RMS)
Longevity Risk Model. This uses ‘vitagion categories’ or individual sources of mortality improvement:
changing lifestyle trends, such as reduced smoking prevalence; improvements in the general health
environment; progress in medical intervention; regenerative medicine, such as stem cell research,
gene therapy and nanomedicine; and retardation of ageing, including telomere shortening and
caloric restriction. Figure 12 shows a stylized representation of the impact of successful
interventions in each of these ‘vitagion categories’.
Figure 12: Timeline into the future
Source: RMS (2010) ‘Longevity Risk’
The second is ‘explanatory’ and ‘causal’ models which model death using exogenous explanatory
variables, such as macro-economic variables or socio-economic indicators. Mortality rates for
different causes are regressed on different macro-economic variables such as GDP growth, inflation
and unemployment. GDP growth is directionally correlated with mortality improvements. Allowing
for macro health indicators (smoking history) can account for most of the mortality differences
between men and women. Post code is used as an indicator of social class.
The third is ‘extrapolative’ projection models. These are purely data-driven, and will only be reliable
if past trends continue. Clearly, medical advances can invalidate extrapolative projections by
changing the trend.
The main extrapolative models are the Lee-Carter model (which assumes no smoothness across ages
or years), the P-spline model (which assumes smoothness across years and ages) and the Cairns-
Blake-Dowd (CBD) model (which assumes smoothness across ages in same year).6 Figure 13 shows a
longevity fan chart7 for 65-year old UK males. UK male life expectancy at age 65 is expected to be 26
years in 2050, within a possible range of 21 to 32 years. Figure 14 presents a survivor fan chart8 for
65-year old UK males. The figure shows that there is little longevity risk up to age 75: we can be fairly
confident that around 18% of 65-year olds will have died before 75. Longevity risk reaches a peak at
age 90, and then there is a long tail out to age 115.
6 See Cairns et al (2006, 2009).
7 See Dowd et al (2010).
8 See Blake et al (2008).
Figure 13: Longevity fan chart for 65-year old UK males (CBD model)
Figure 14: Survivor fan chart for 65-year old UK males (CBD model)
The key macro-longevity assets are longevity-linked bonds and derivatives, principally forwards,
swaps and options. Since the instruments are not publicly traded, it is hard to get reliable
information on investor returns, but industry insiders suggest returns in the range 12-18% for
investments in swap format and 5-8% for investments in bond format. Recently, a new vehicle the
reinsurance sidecar has been introduced.
5.1 Bonds
The first longevity bond was proposed in November 2004.9 The proposed issuer was the European
Investment Bank. The structurer of the bond was BNP Paribas, with PartnerRe as reinsurer of the
longevity risk. The issue size was £540m, the maturity 25 years, and the initial coupon was £50m.
Future coupon payments would be linked to a mortality index of 65-year-old males from England &
Wales. Figure 15 shows the projected cash flows on the bond; there would be no return of principal.
The bond was targeted at UK pension funds and would have provided a hedge against the systematic
longevity risk that they faced. Unfortunately, the bond failed to attract sufficient investor interest
and was withdrawn.10
Figure 15: Projected cash flows on the EIB longevity bond
More successful was the Swiss Re mortality catastrophe bond launched in December 2003. It was
designed to hedge Swiss Re’s own holding of mortality risk.11 Known as Vita I, it was a 3-year
contract (maturing on 1 January 2007) which allowed the issuer to reduce its exposure to
9 It was based on the bond design in Blake and Burrows (2001).
10 For further details, see Blake et al (2006).
11 This is the risk that people die sooner than expected, so that insurance companies that sold life policies (and
reinsurance companies that reinsured them) make payouts under these policies sooner than was anticipated,
before the full set of projected premiums had been collected.
catastrophic mortality events, such as a severe outbreak of influenza, a major terrorist attack (using
weapons of mass destruction), and a natural catastrophe. The mortality index (MI) was: US (70%),
UK (15%), France (7.5%), Italy (5%), Switzerland (2.5%); male (65%), female (35%); also with age
bands. The bond was a principal-at-risk bond and holders would have their principal reduced if MI
exceeded an attachment point and lost altogether if it exceeded an exhaustion point. Similar
mortality catastrophe bonds were subsequently issued by both Swiss Re and other insurers.12
A Swiss Re longevity spread bond, called Kortis, was issued in December 2010. The issue size was
$50m and the maturity was 8 years. Bond holders were exposed to the risk of an increase in the
spread (Longevity Divergence Index Value (LDIV)) between the annualized mortality improvements
in English & Welsh males aged 75-85 v US males aged 55-65. The bond’s purpose was to hedge Swiss
Re's own exposure to longevity risk. The bond was also a principal-at-risk bond.13
5.2 Derivatives
5.2.1 Mortality forwards
A mortality forward rate contract is also referred to as a ‘q-forward’ because the letter ‘q’ is the
standard actuarial symbol for mortality rate. It is the simplest type of instrument for transferring
longevity (and mortality) risk. It was the first capital markets derivative to be executed (in January
2008): the hedger was Lucida, the hedge provider was J.P. Morgan, and the payments were linked to
the LifeMetrics index based on England & Wales national male mortality for a range of different
Figure 16: A q-forward which exchanges fixed mortality for realized mortality at the maturity of the
Specifically, a q-forward is a contract between two parties in which they agree to exchange an
amount proportional to the actual realized mortality rate of a given population (or subpopulation),
in return for an amount proportional to a fixed mortality rate that has been mutually agreed at
inception to be payable at a future date (the maturity of the contract): see Figure 16. In the case of
hedging longevity risk in a pension plan using a q-forward, the plan will receive the fixed mortality
rate and pay the realized mortality rate at the end of the contract (and hence locks in the future
mortality rate it has to pay whatever happens to actual rates). The counterparty to this transaction,
12 For further details, see Blake et al (2006).
13 For further details, see Hunt and Blake (2015).
Amount x
mortality rate
mortality rate
Source: Coughlan et al. (2007, Figure 1)
typically an investment bank, has the opposite exposure, paying the fixed mortality rate and
receiving the realized rate.14
5.2.2 Longevity (or survivor) swaps
A longevity swap also known as a survivor swap15 is an instrument which involves exchanging
actual pension payments for a series of pre-agreed fixed payments, as indicated in Figure 17, where
each payment is based on an amount-weighted survival rate.
Figure 17: A longevity swap involving the regular exchange of actual realized pension cash flows and
pre-agreed fixed cash flows
The Swiss Re Friends’ Provident longevity swap was the world’s first publicly announced swap in
April 2007. It was a pure longevity risk transfer, but in the form of an insurance contract not a
capital markets instrument. The swap was based on FriendsProvident’s £1.7bn book of 78,000
pension annuity contracts written between July 2001 December 2006. Swiss Re makes payments
and assumes longevity risk in exchange for an undisclosed premium.16
The J.P. Morgan Canada Life longevity swap was the world’s first capital markets longevity swap in
July 2008. Canada Life hedged £500m of its annuity book, representing 125,000 lives, using a 40-year
swap customized to insurer’s longevity exposure. The longevity risk was fully transferred to
investors, which included ILS and hedge funds. J. P. Morgan acted as the intermediary and assumed
the counter-party credit risk.17
14 For further details, see Coughlan et al. (2007) and Blake et al (2013).
15 See Dowd et al (2006).
16 For further details, see Blake et al (2013).
17 For further details, see Blake et al (2013).
Cash payment (£ millions)
Pension plan receives
actual pen sion payments
reflecting realized l ongevity
Pension plan makes
fixed payments
reflecting f ixed longevity
5.2.3 Longevity bull call spreads (or tail-risk protection)
To date there have been five publicly announced deals involving tail risk protection. The first two
involved Aegon: one in 2012 was executed by Deutsche Bank and another in 2013 by Société
Générale. The second two involved Delta Lloyd and Reinsurance Group of America (RGA Re) in 2014
and 2015, respectively. The most recent occurred in December 2017 between NN Life and Hannover
Re and is similar to the Société Générale deal discussed below.
Société Générale’s tail risk protection structure was described in Michaelson and Mulholland
(2015).18 It is an index-based hedge using national population mortality data, but with minimal basis
risk,19 and is designed around the following set of principles (p.30-31):
In general, capital markets will be most effective in providing capital against the most remote
pieces of longevity risk, called tail risk. This can be accomplished by creating ‘out-of-the-money’
hedges against extreme longevity outcomes featuring option-like payouts that will occur if
certain predefined thresholds are breached. These hedges would be capable of alleviating
certain capital requirements to which the (re)insurers are subject, thereby enabling additional
risk assumption.
However, a well-constructed hedge programme must perform a delicate balancing act to be
effective. On the one hand, it must provide an exposure that sufficiently mimics the performance
of the underlying portfolio so as not to introduce unacceptable amounts of basis risk; while, on
the other hand, it must simplify the modelling and underwriting process to a level that is
manageable by a broad base of investors. Further, the hedge transaction must compress the
60+ year duration of the underlying retirement obligations to an investment horizon that is
appealing to institutional investors.
Basis risk will reduce hedge effectiveness and this will, in turn, reduce the allowable regulatory
capital relief. However, basis risk can be minimized if the hedger can customize three features of the
hedge exposure:
The hedger is able to select the age and gender of the ‘cohorts’ (also known as model points)
they want in the reference exposure. For example, the hedger selects an exposure totalling
70 cohorts males and females aged 6599 to cover all the retired lives in the pension
The hedger is able to choose the ‘exposure vector’, i.e., the ‘relative weighting’ of each
cohort over time. This will equal the anticipated annuity payments for each cohort in each
year of the risk period (see Table 1 for an example).
The hedger is able to select an ‘experience ratio matrix’, based on an experience study of its
underlying book of business. For each cohort, in each year of the risk period, a fixed
adjustment is applied to the national-population mortality rate to adjust for anticipated
differences between the mortality profile of the hedger’s book of business and the
corresponding reference population. So if the hedger’s underlying lives are healthier than
the general population, they will assign experience ratios of less than 100% to ‘scale down’
the mortality rate applied in the payout (see Table 2 for an example).
18 See, also, Cairns and El Boukfaoui (2018) for a more detailed description.
19 Basis risk is the residual risk associated with imperfect hedging where the movements in the underlying
exposure are not perfectly correlated with movements in the hedging instrument.
Table 1: Exposure vector: Relative weighting of cohorts over time
Source: Michaelson and Mulholland (2015, Exhibit 1)
Table 2: Experience ratio matrix
Source: Michaelson and Mulholland (2015, Exhibit 2)
A risk exposure period of 55 years as shown in Tables 1 and 2is unattractive to capital markets
investors for a number of reasons. Liquidity in this market is still low and would be completely
absent at these horizons. The maximum effective investment horizon is no more than 15 years. Just
as important, the risks are too great. The likely advances in medical science suggests that the range
of outcomes for longevity experience will be very wide for an investment horizon of more than half a
To accommodate both an ‘exposure period’ of 55 years or more and a ‘risk period’ (or transaction
length) of 15 years, the hedge programme uses a ‘commutation function’ to ‘compress’ the risk
period. As explained in Michaelson and Mulholland (2015, pp.32-33):
This is accomplished by basing the final index calculations on the combination of two elements:
(i) the actual mortality experience, as published by the national statistical reporting agency,
applied to the exposure defined for the risk period; and (ii) the present value of the remaining
exposure at the end of the risk period calculated using a ‘re-parameterized’ longevity model that
takes into account the realized mortality experience over the life of the transaction. This re-
parameterization process involves:
Selecting an appropriate longevity risk model and establishing the initial
parameterization of the model using publicly available historical mortality data that exist
as of the trade date. For a basic longevity model, the parameters that may be
established, on a cohort-by-cohort basis, are (i) the current rate of mortality; (ii) the
expected path of mortality improvement; and (iii) the variability in the expected path of
mortality improvement.
‘Freezing’ the longevity risk model, with regard to the related structure; but also
defining, in advance, an objective process for updating the model’s parameters based on
the additional mortality experience that will be reported over the risk period. A
determination needs to be made as to which parameters are subject to updating, as well
as the relative importance that will be placed on the historical data versus the data
received during the risk period.
Re-parameterizing the longevity model by incorporating the additional mortality data
reported over the life of the trade. This occurs at the end of the transaction risk period,
once the mortality data for the final year in the risk period have been received.
Calculating the present value of the remaining exposure using the re-parameterized
version of the initial longevity model. This is done by projecting future mortality rates,
either stochastically or deterministically, and then discounting the cash flows using
forward rates determined at the inception of the transaction.
The benefit of this approach to the hedger is that ‘roll risk’20 is reduced, since, by taking account of
actual mortality rates over the risk period, there will be a much more reliable estimate at the end of
the risk period of the expected net present value of the remaining exposure than if only historical
mortality rates prior to the risk period were used. The benefit to the investor is that the longevity
model is known and not subject to change, so the only source of cash flow uncertainty in the hedge
is the realization of national population mortality rates over the risk period see Figure 18.
The hedge itself is structured using a long out-of-the money call option bull spread on future
mortality outcomes. The spread has two strike prices or, using insurance terminology, an attachment
point and an exhaustion point. The spread is constructed using a long call at the lower strike price
and a short call at the upper strike price see Figure 19. These strikes are defined relative to the
distribution of ‘final index values’ calculated using the agreed longevity model. The final index value
will be a combination of:
The ‘actual’ mortality experience of the hedger throughout the risk period which is
calculated by applying the reported national population mortality rates to the predefined
‘exposure vector’ and ‘experience ratio matrix’ for each cohort in each year of the risk
period, and accumulating with interest, using forward interest rates defined on the trade
The ‘commutation calculation’ which estimates the expected net present value of the
remaining exposure at the end of the risk period, calculated using the re-parameterized
version of the initial longevity model.
20 This is the risk that arises when a hedger is not able for some reason to put on a single hedge that covers the
full term of its risk exposure and is forced to use a sequence of shorter term hedges which are rolled over when
each hedge matures, with the risk that the next hedge in the sequence is set up on less favourable terms than the
previous one.
Figure 18: Mortality rates before, during and after the risk period
Note: Projected mortality rates are calculated using experience data available at end of the risk period.
Source: Michaelson and Mulholland (2015, Exhibit 3)
Figure 19: Bull call spread payoff to hedger
Note: Both axes in $m
Given the distribution of the final index, the attachment and exhaustion points are selected to
maximize the hedger’s capital relief, taking into account the investors’ (i.e., risk takers’) wish to
maximize the premium for the risk level assumed. Investors might also demand a ‘minimum
Attachment point
Exhaustion point
premium’ to engage in the transaction. The intermediary e.g., the investment bank therefore
needs to carefully work out the optimal amount of risk transfer, given both the hedger’s strategic
objectives and investor preferences.
The hedger then needs to calculate the level of capital required to cover possible longevity
outcomes with a specified degree of confidence. For example, if the ‘best estimate’ of the longevity
liability is $1bn, the (re)insurer may actually be required to issue $1.2bn, $200m of which is reserve
capital to cover the potential increase in liability due to unanticipated longevity improvement with
99% confidence.
The (re)insurer may then decide to implement a hedge transaction with a maximum payout of
$100m. This transaction would begin making a payment to the hedger in the event the attachment
point is breached, and then paying linearly up to $100m if the longevity outcome meets or exceeds
the exhaustion pointsee Figure 19. This hedge provides a form of ‘contingent capital’ from
investors (up to $100m of the $200m required), enabling the hedger to reduce the amount of
regulatory capital it must issue see Figure 20.
Figure 20: Distribution of the final index value and the potential for capital reduction
Source: Michaelson and Mulholland (2015, Exhibit 3) not drawn to scale
5.3 Total size of the macro-longevity market
Figure 21 shows that $366bn of longevity risk transfers have taken place between 2007 and 2017.
The principal product subject to micro-longevity risk is a life settlement. This is a life insurance policy
sold by its owner for more than the surrender value21 but less than face value.
21 This is the value paid by the original life company to cancel the policy.
Figure 21: Cumulative Pension Risk Transfers by Product and Country, 2007-17
Sources: LIMRA, Hymans Robertson, LCP and PFI analysis as of 31 December 2017
2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
$22 bn
Canada All
UK Longevity
UK Buy-outs
and Buy-ins
US All
The secondary market in life insurance policies is dominated by the US. The US market took off in
the 1990s when viatical settlements were introduced. Viators are owners of life policies who are
very close to dying, such as AIDS sufferers who needed to sell their policies to pay for medical
treatment. That market ceased suddenly in 1996 when protease inhibitors were introduced. It was
replaced by a senior life settlements (SLS) market which deals with the whole life policies22 of elderly
high net worth individuals. Two medical doctors or underwriters are used to assess each
policyholder’s life expectancy (LE). The most important criterion for successful investment in life
settlements is a good estimate of LE. The investor purchasing the life settlement has to continue
paying the premiums on the underlying policy while the original policyholder is still alive.
LE estimates vary widely. A study by A.M. Best of 909 life portfolio underwritten by the three major
LE underwriters found that there was an average spread of 8 months between the longest and
second longest underwriter, and an average spread of 24 months between longest and shortest
underwriter. These differences can have a significant effect on investor returns. The implied return
on the portfolio based on the shortest LE underwriter was 12.4%, while it was 8.3% based on second
longest underwriter and 6.5% based on longest underwriter.
Underestimating LE is the key micro-longevity risk faced by investors in life settlements, since this
makes the promised returns on life settlements more attractive than the realized returns. The SLS
market experienced a significant setback when, in 2008, the shortest of the LE underwriters revised
upwards their LEs by between 20 and 25%, while the second longest revised upwards by between 5
and 10%. LE providers were forced to respond by establishing the Life Expectancy Providers Focus
Group in October 2010 with the aim of offering a comprehensive and consistent set of best practices
and performance standards to all life markets that make use of life expectancy and mortality
information. The group also addresses issues such as privacy, fraud, and confidentiality policies. The
group’s founding members were Advanced Underwriting Solutions, AVS Underwriting, Examination
Management Services, Inc., ISC Services and 21st Services.
A number of solutions have been put forward to hedge micro-longevity risk or ‘extension risk’ as it is
more commonly known. One is a hedge offered by certain investment banks based on a synthetic
index of life settlements. Another is known as FAIRE and consists of both individual and portfolio
extension risk hedges, priced off the LE underwriter Fasano’s LEs. FAIRE is provided by Fasano
Associates and Augur Capital, a German investment manager of life insurance and life settlement
In 1994, the Life Insurance Settlement Association (LISA) was established in Orlando, Florida as a
trade association for viatical and life settlement companies.23
In 2005, the Life Exchange was established with an objective ‘to provide the secondary life insurance
market with the most advanced and independent electronic trading platform available by which to
conduct life settlement transactions with the highest degree of efficiency, transparency, disclosure,
and regulatory compliance’. This was not a success and later delisted.
22 A whole life policy has two components, a life insurance component and an investment component: periodic
premiums (monthly, quarterly, annual, single, for example) cover the cost of the life insurance, with the surplus
going into an investment fund. In the US market, the insurance company typically invests the surplus premium
in fixed-income securities to build up a ‘cash value’. The cash value is separate from the ‘face value’ of the
policy, which is the guaranteed insurance value.
In 2007, the Institutional Life Markets Association (ILMA), started in New York with the mission ‘to
expand and apply capital market solutions in life insurance, educate consumers that their insurance
may be a valuable asset, expand consumer choices about how to manage it, and support the
responsible growth and regulation of the industry. We believe that expanded consumer choice and
full disclosure of all fees is good for the consumer and for the industry’.24
In 2008, Institutional Life Services (ILS) and Institutional Life Administration (ILA), a life settlements
trading platform and clearing house, were launched by Goldman Sachs, Genworth Financial, and
National Financial Partners. ILS/ILA was designed to modernize dealing in life settlements and meet
the needs of consumers (by ensuring permanent anonymity of the insured) and of the capital
markets (by providing a central clearing house for onward distribution of life settlement assets,
whether individually or in structured form). In 2010, National Financial Partners became the sole
owner of ILS/ILA.25
One of the latest developments is the attempt to introduce a synthetic life settlements market. This
is to avoid some of the costs, monitoring, and ethical issues associated with the physical life
settlements market.26 The synthetic market would be based on indices and the returns will depend
on the performance of the pool of lives in the index. The first attempt to do this was by Goldman
Sachs which introduced a QxX Life Settlements Index in 2007. This market failed to take off the
spreads offered were too wide to making trading profits and the index was discontinued in 2009.
In 2008, Credit Suisse initiated a longevity swap with Centurion Fund Managers, whereby Centurion
acquired a portfolio of synthetic life policies, based on a longevity index built by Credit Suisse. In
2010, the Fasano Longevity Life Settlements Index was introduced. In April 2011, the International
Society of Life Settlement Professionals (ISLSP)27 formed a life settlement and derivatives committee
and announced that it was developing a life settlement index. The purpose of the index is to
benchmark net asset values in life settlements trading. Investors need a reliable benchmark to
measure performance and the index will help turn US life insurance policies into a tradable asset
class according to ISLSP. The calculation agent for the index is AA Partners.
There are a number of other much smaller secondary markets in life insurance policies, including:
Traded endowment policies in the UK. The maturity date of policies is fixed, but the maturity
value of the policy depends on the performance of an investment fund. The policy premiums
are invested in a risk-graded with-profits fund established by the life company selling the
policy. There is a fixed minimum return in the event of policy holder dying during term.
Secondary market for life insurance in Germany. German consumers have been able to sell
life and pension insurance policies to professional policy buyers since 1999. The trade body
26 It is an expensive process to acquire suitable life policies for settlement with a range of intermediaries who
need paying. In addition, premiums need to be financed. There is also a laborious process of monitoring policy
holders between the purchase and policy maturity dates. In addition, there are ethical issues associated with the
sale of policies by elderly individuals: these issues were considered by, amongst others, Blake and Harrison
for the secondary market in life insurance is the Bundesverband Vermogensanlagen im
Zweitmarkt Lebensversicherungen (BVZL).28 There is also the European Life Insurance
Settlement Association (ELSA).29
In principle, longevity bonds could be issued by private-sector organizations. As previously
mentioned, pharmaceutical companies would be natural issuers, because their revenues are
positively linked to survivorship: the longer people live, the more they will spend on medicines.
Although this is true, the scale of the demand for longevity bonds far exceeds conceivable private-
sector supply from companies such as pharmaceuticals. Further, there would be significant credit
risk associated with the private-sector issuance of an instrument intended to hedge a systematic risk
many years into the future.
In practice, therefore, the only realistic issuer of longevity bonds in scale is the government. The UK
Pensions Commission also suggested the government should consider the use of longevity bonds to
absorb tail risk for those over 90 or 95, provided it exits from other forms of longevity risk pre-
retirement, which it has done by linking state pension age to increases in life expectancy and by
raising the future state pension age from 65 to 69 by 2050: ‘One possible limited role for
government may, however, be worth consideration: the absorption of the ‘extreme tail’ of longevity
risk post-retirement, i.e., uncertainty about the mortality experience of the minority of people who
live to very old ages, say, beyond 90 or beyond 95’.30
Blake et al (2014) argue that there are three important reasons why the government should engage
in sharing longevity risk with the private sector:
It has an interest in ensuring there is an efficient annuity market.
It has an interest in ensuring there is an efficient capital market for longevity risk transfers.
It is best placed to engage in intergenerational risk sharing, such as providing tail risk
protection against systematic trend risk, and in exchange earn a longevity risk premium.
There are two areas where government support is required.
First, the government can help with the construction of national longevity indices. It is for reasons of
accuracy that longevity indices would most likely have to be based on national mortality data
which only the government collects. A key component of the success of the new capital market will
be the timely publication of accurate and independently calculated longevity indices. The longevity
indices would cover mortality rates, survivor rates, and life expectancies for both males and females.
Second, the government can make an important contribution by issuing longevity bonds to facilitate
price discovery, thereby encouraging capital market development. Longevity risk is not currently
actively traded in the capital markets, so we do not have a good estimate of its market price or
premium. But if the government issued a small number of longevity bonds, this would help to
establish and maintain the market-clearing ‘price points’ for longevity risk at key ages and future
dates, and hence establish a market price for longevity risk. In other words, the bonds would help to
30 Pension Commission (2005, p. 229).
establish the riskless term structure for survivor rates for ages above 65 for future years. There is a
clear analogy with the fixed-income and index-linked bond markets. In these markets, the issue of
government bonds helped to establish the riskless term structures for interest rates and inflation
rate expectations, respectively, for terms out to 50 years or more. The private sector was then able
to issue corporate fixed-income and index-linked bonds with different credit risks (AAA, AA, etc.) and
establish credit term structures above the riskless benchmark curves.
The longevity risk term structure is more complex than either the interest rate or inflation term
structures, since it is two dimensionalinvolving age as well as time whereas the latter are one-
dimensional, involving only time. The longevity risk term structure is therefore a two-dimensional
surface, rather than a line: cohorts move diagonally across the surface over time, getting one year
older with every passing year, with some members of the cohort dying each year. This is
demonstrated in Figure 22, which shows the cash flows on two deferred longevity bonds: one bond
based on male lives from the national population aged 65 and one bond based on male lives from
the national population aged 75. Each bond is specified by four dates: the birth year of the cohort
being tracked (e.g., 1945), the issue date (e.g., 2010), the first payment date (e.g., 2020), and the last
payment date (e.g., 2050). There is a corresponding mortality term structure for females, so
longevity bonds are also identified by gender (M or F).
Figure 22: Longevity bond cash flows across ages and time
Source: Blake et al (2014)
In developed markets, prices are determined by the market forces of supply and demand. While
those forces are present in the longevity market see, e.g., Figure 6 they are not yet sufficiently
well developed to generate a deep, liquid market in which longevity-linked instruments can trade on
the basis of market-determined prices. Instead, prices are still determined by theoretical models.
This has been the experience of new financial markets for a number of decades. For example, most
financial derivatives with complex payoff structures initially traded on the basis of prices generated
by theoretical models.
The same will be true of the Life Market to begin with. In this section, we consider the pricing of a
fairly simple longevity-linked instrument, namely a longevity bond issued by the government,
following the framework outlined in Blake et al (2014). Clearly the demand for longevity bonds will
depend on their price. Demand will be higher the closer the government offers the bonds at true
economic cost, that is, charges a fair, but not excessive, longevity risk premium.
Blake et al (2014) accept it is appropriate that the government seeks to charge a fair risk premium
on longevity bonds because this ensures intergenerational fairness. The expected cost of the
longevity risk should be borne by those whose retirement incomes will be derived from the bonds.
Some might argue that the government should seek to charge a risk premium in excess of the
economic cost. For example, if, in a Solvency II world, insurance companies writing annuity business
end up having to hold capital in excess of true economic levels, because they are unable to hedge
longevity risk, then they might be prepared to pay a premium price for longevity bonds if, by doing
so, they can reduce their capital requirements. This would obviously depend on the Solvency II
treatment of longevity bonds and the capital reduction that the regulators would allow. Blake et al
(2014) argue that it would be short sighted of governments to seek to exploit this situation. If
insurance companies can reduce their capital requirements closer to economic capital levels, then
this should result in higher annuity values with the consequent benefits to government, pensioners
and savers already highlighted.
Blake et al (2014) also argue that it is most unlikely that a liquid market for longevity bonds will
develop if the government just focuses on insurers. The bonds will need to be priced to attract
defined benefit (DB) pension plans, which do not currently face solvency capital requirements. DB
plans that do not have a pressing need for a full buy-out (which will be subject to Solvency II capital
via insurers) and that want to engage in risk management will buy longevity bonds only if they
believe they are priced fairly (and cheaper than longevity swaps and other derivative longevity
hedges provided by the private sector). So, if we want to ensure DB pension plans buy longevity
bonds issued by the government, the government should not price them above AAA.
Members of defined contribution (DC) pension plans who are derisking (i.e., lifestyling or life cycling)
in the run-up to their retirement will have a choice between using long-dated bonds and longevity
bonds, and again many will be discouraged from using longevity bonds if the government looks to
charge a markup beyond the fair price. Other investors, including investment banks, will also be
discouraged from buying longevity bonds if they believe the longevity risk premium is excessive,
because they will fear that the bonds will eventually fall in value to reflect their true economic cost.
So for the market in longevity bonds to take off, Blake et al (2014) recommend that they should be
priced according to economic capital principles. They propose an approach that builds on the
insurance industry ‘cost-of-capital’ method. This determines a risk premium (or risk margin) for
capital above the best estimate of the value of the liabilities. The best estimate of the value of the
liabilities in their model is derived from the median scenario from 10,000 possible stochastic
mortality rate scenarios using the CBD model and, at any point in time, is the present value of the
expected future coupons on the bond from the median scenario discounted at the risk-free rate.
The cost-of-capital method involves four stages for determining the risk premium (RP):
Determine the required credit rating for the bond (e.g., AAA).
Project the longevity risk capital required for each year in the life of the bond to maintain
the required credit rating.
Multiply each annual longevity capital requirement (LCR) by a percentage cost of capital to
give the cost of capital in money terms.
Calculate the present value of each of these cost-of-capital (CoC) amounts using a risk-free
discount rate and sum to give the present value of the overall risk premium.31
Table 3 shows the total risk premium for a number of longevity bonds for illustrative costs of capital
of 2% and 3%. It also shows the corresponding basis points (bps) reductions from the risk-free rate.
Take the longevity bond LBM(65,75) and a 2% cost of capital, for example. This bond where the
coupon payments are linked to the mortality experience of 65-year-old UK males, but with the first
coupon delayed until this cohort reaches age 75 has a total risk premium of 3.2%. This means that
the issue price of the bond would be £103.20. The effective yield on the bond is equal to the risk-
free rate less the basis points reduction, so the effective yield on LBM(65,75) is 3.821%. The table
shows that the risk premium increases with the cost of capital, but, more significantly, increases with
the deferral period.
Table 3: Risk premiums on longevity bonds using industry cost-of-capital method to give AAA credit
Risk premiums and basis points reduction in yield on longevity bonds
2% cost of capital
3% cost of capital
Risk premium
Bps reduction
Risk premium
Bps reduction
13.4 bps
20.0 bps
17.9 bps
26.5 bps
48.7 bps
70.8 bps
16.5 bps
24.7 bps
27.6 bps
40.8 bps
42.6 bps
62.2 bps
Notes: LBM(65,75) is a longevity bond relating to UK males aged 65, with the first coupon paid at age 75, etc.
The risk premium is the total for each bond. The basis points reduction shows the annual reduction from the
assumed risk-free yield of 4%.
Source: Blake et al (2014, Table 4)
The Life Market especially the macro-longevity segment will only be a success in the long run if
sufficient investment capital is attracted to it. The macro-longevity market is currently dominated
by insurers and reinsurers, but their total capacity is small relative to the potential size of the
market. New capital must be attracted and the two key attractions are a longevity risk premium and
diversification with respect to traditional asset classes. However, these features by themselves have
not proved to be sufficient to attract new investors in the numbers required since the market
started in 2006. Much more needs to be done to understand the needs of investors and to segment
then into their ‘natural’ investor bases, as recommended by Coughlan (2011).
31  = ()
=1 where r is the risk-free discount rate.
9.1 Investor segmentation
A key element of investor segmentation is understanding what is being hedged: cash flow or value.
With a cash flow hedge, each individual cash flow in, say, a pension plan liability is hedged in each
period. This is the insurance indemnity paradigm. With a value hedge, only the value of the liability
at a future time horizon is hedged. This is the risk management paradigm and takes account of all
cash flows beyond the horizon.
Each has a different ‘naturalinvestor base: the former being suited only for investors attached to
insurers in some way, such as in a sidecar (discussed below in section 9.3), the latter being suited to
investors familiar with standard capital markets instruments, such as bonds and related derivatives.
An important dimension of segmentation is segmentation by age. Figure 23 illustrates this for cash-
flow-related longevity risks for 65-year-old males. Insurers are natural holders of this risk out to, say,
age 75. They are also comfortable in the UK holding the 75-90 age segment. However, in countries
with less well-developed insurance markets, there might be a role for government to help with this
segment, either through the issue of deferred longevity bonds or by selling annuities to individuals
who survive to these ages. But even in countries like the UK, private-sector insurers are much less
willing to assume the longevity risk of those who survive to age 90 and beyond. Further, the price of
deferred annuities from age 90 would be so high as a result of solvency capital requirementsthat
demand for them would be negligible.32 This leaves the government as the only realistic provider of
a longevity hedge for the post-90 age segment, as recognized by the UK Pensions Commission in
Figure 24 illustrates the case for value-related longevity risks for 65-year-old males. Capital markets
investors are natural holders of this risk so long as the hedge does not have a maturity beyond 10
years. Such a hedge which could be in the form of a bond, a q-forward or a value swap could be
attractive to pension funds since it does partially hedge their cash flows beyond 10 years.
How well does this segmentation fit with pension funds wishing to hedge the longevity risk exposure
of their members? Funds with pensions in payment will be looking at the insurance indemnity
paradigm. They can access this through buy-outs and buy-ins and there is currently sufficient
insurance capacity to meet their needs in full. However, if there were to be a significant increase in
demand for buy-outs and buy-ins, this capacity might no longer be there and it would be reduced,
beginning with the third segment in Figure 24. We should therefore see increasing requests for
government support for the post-90 age segment. By government support, we, in effect, mean the
next generation. Young workers are natural holders of higher age longevity risk, since their own
longevity risk will not materialize for many decades. Government support can therefore be viewed
as a form of intergenerational longevity risk sharing as mentioned in section 7 above.
For younger pre-retirement members, value hedges are the only practical near-term solution. This is
because longevity risk is long duration for this group and insurers and reinsurers are reluctant to
take this risk on its own. A value hedge is therefore natural because there is no cash flow risk until
32 As an analogy, Table 3 shows how the risk premium increases with the deferral period in the case of longevity
Figure 23: Age segmentation of investors: Provision of cash flow hedges for age 65
Source: Coughlan (2011)
Figure 24: Segmentation of investors: Provision of value hedges for age 65
Source: Coughlan (2011)
The first examples of hedges fitting this framework are given in Table 4.
Table 4: Early examples of cash flow and value hedges
Jan 2008
J.P. Morgan
Value hedge
10-year q-forward
(LifeMetrics Index)
July 2008
Canada Life
J.P. Morgan
Cash flow
40-year survivor swap
Royal Bank of
Cash flow +
value hedge
10-year collared survivor swap
+ final commutation payment
Jan 2011
Pall UK
Pension Fund
J.P. Morgan
Value hedge
10-year q-Forward
(LifeMetrics Index)
Source: Coughlan (2011)
9.2 Expanding the asset class
The next step in the process is to expand the asset class to capital markets investors. As Coughlan
(2011) points out this involves identifying supply and demand mismatches amongst capital markets
investors see Table 5 and recalling the discussion in section 3.3 above and then resolving them.
Table 5: Supply and demand mismatch (capital markets investors)
Supply-side wishes
Demand-side wishes
Customized hedges
Standardized investments
Long duration
Short duration
First, we need to address the challenges for the supply-side. Pension plans need to recognize the
extent of their implicit longevity ‘investment. This becomes easier if, as they should, they evaluate
the liability as close as possible to the true economic value, by discounting based on swaps with
realistic longevity assumptions. They also need to change their mindset about longevity hedging, by
moving from an ‘indemnification’ to a ‘risk management’ mindset. This will require them to consider
alternative hedging approaches, such as index-based hedges and shorter maturity hedges of liability
value. In turn, it requires them to understand basis risk better and why it is a much smaller risk to
bear in an index-based hedge than longevity risk itself.
Another issue is counterparty credit risk. This is the risk that one of the counterparties to, say, a
longevity swap contract defaults owing money to the other counterparty. When a swap is first
initiated, both counterparties might expect a zero excess profit or loss.33 But over time, as a result of
realized mortality rates deviating from the rates that were forecast at the time the swap started, one
counterparty’s position will be showing a profit and the other will be showing an equivalent loss.
The insurance industry addresses this issue via regulatory capital and the capital markets deal with it
via collateral. The role of regulatory capital and collateral is to significantly reduce, but not entirely
eliminate counterparty credit risk. The European Union’s Solvency II Directive, for example, sets a
solvency capital requirement (SCR) at a level which ensures that an insurance company can meet its
obligations over the next 12 months with a probability of at least 99.5%. By contrast, in the capital
33 This is the case for a transaction involving a pension plan and an insurer, where allowance is made for the
insurer’s cost of capital and normal profit etc. In a transaction involving an insurer and a reinsurer, it is typical
for fees to be added to the ‘fixed leg’, so commercially there will be a loss to the cedant on day 1.
markets, collateral in the form of high quality securities needs to be posted by the loss-making
counterparty to cover such losses. However, the collateral also has to be funded and the funding
costs will depend on the level of interest rates. Further, the quality of the collateral and the
conditions under which a counterparty can substitute one form of collateral for another need to be
agreed. This is done in the credit support annex (CSA) to the ISDA34 Master Agreement that
establishes the swap. The CSA also specifies how different types of collateral will be priced.
Second, we need to address the challenges for the demand-side. Standardization is being addressed
in a number of ways, such as: industry initiatives, e.g., LifeMetrics and LLMA; and the introduction of
index-based hedges for pre-retirement pension members. Then there is the ‘long duration’ problem:
the hedger wants a long-term hedge, while the investor wants an exposure that is much shorter.
Both parties need to compromise. The way the hedger compromises is to use a value hedge and not
a cash flow. The way the investor compromises is to accept that liquidity will be limited at least in
the early stages of the market.35
The key problem with customized solutions for some participants36 is that they are not liquid and
cannot easily be reversed. By contrast, liquidity is a key advantage of deep and well-developed
capital market solutions. However, liquidity requires standardized contracts. The fewer the number
of standardized contracts traded, the greater the potential liquidity in each contract, but the lower
the potential hedge effectiveness. There is therefore an important tradeoff to be made, such that
the number of standardized contracts traded provides both adequate hedge effectiveness and
adequate liquidity. If they are ever to achieve adequate liquidity, it is likely that capital-markets-
based solutions will have to adopt either mortality indices based on the national population as the
primary means of transferring longevity risk or sub-population indices that are transparent,
trustworthy, reliable and durable. However, potential hedgers, such as life assurers and pension
funds, face a longevity risk exposure that is specific to their own policyholders and plan members:
for example, it might be concentrated in specific socio-economic groups or in specific individuals
such as the sponsoring company’s directors. Hedging using population mortality indices means that
life assurers and pension funds will face basis risk if their longevity exposure differs from that of the
national population. Herein lies the tension between index-based hedges and customized hedges of
longevity risk, and, in turn, the unavoidable tradeoff between basis risk and liquidity. Until the
market fully develops, some limited liquidity could be provided by the intermediary.
Other challenges for the demand-side include:
Improving education, such as the development of both longevity expertise and longevity
investment capabilities.
Structuring portfolios to cope with longevity positions that have longer maturity and lower
liquidity than other investments.
Developing capabilities to invest in derivative format, e.g., swaps as well as bonds.
Working with hedgers and intermediaries to develop new investment structures to address
liquidity and maturity challenges.
34 International Swaps and Derivatives Association.
35 The longevity bull call spreads in section 5.2.3 had to reflect such compromises in order to be implemented.
36 It is not an issue for a pension plan if it is doing a longevity swap as a step to buy-out.
Finally, there are challenges for intermediaries. Principally, these are to: provide liquidity to
investors, provide credit intermediation, and to develop attractive bond-like products, which is
essential to open up a larger universe of fixed-income investors. These are traditionally the areas of
expertise of investment banks. But following the Global Financial Crisis, it has become more difficult
for banks to engage in such non-core activities. Either insurers/reinsurers develop the relevant
expertise or investment banks are persuaded to re-enter the market.
9.3 A new vehicle – reinsurance sidecars
One recent way in which the insurance industry has helped to attract new investors is through the
reinsurance sidecar37 which is a way to share risks with new investors when the latter are
concerned about the ceding reinsurer having an informational advantage.38
Formally, a reinsurance sidecar is a financial structure established to allow external investors to take
on the risk and benefit from the return of specific books of insurance or reinsurance business. It is
typically set by existing (re)insurers looking to partner with or accept capital from third-party
It is established as a special purpose vehicle (SPV), with a maturity of 2-3 years. It is capitalized by
specialist insurance funds, usually by preference shares, though sometimes in the form of debt
instruments. It reinsures a defined pre-agreed book of business or category of risk. Liability is limited
to assets of the SPV and the vehicle is unrated.
The benefit to insurers is that sidecars can provide protection against exposure to peak longevity
risks,39 help with capital management by providing additional capacity without the need for
permanent capital, and can provide an additional source of income by leveraging underwriting
expertise. The benefit to investors is that they enjoy targeted uncorrelated returns relating to
specific short-horizon risks and have an agreed procedure for exiting. Investors can also take
advantage of temporary price hikes, but without facing legacy issues that could affect an investment
in a typical insurer. Figure 25 shows a typical sidecar structure.
Figure 25: Typical sidecar structure
Source: PFI
37 For further details, see Blake et al (2018) and Bugler et al (2018).
38 See, e.g., Akerlof (1970).
39 That is, specific individual cashflows that give rise to the greatest uncertainty in value terms.
There are a number of challenges to the use of sidecars in the longevity risk transfer market. There is
the tension between the long-term nature of longevity risk and investor preference for a short-term
investment horizon. There are also regulatory requirements on cedants, affecting their ability to
generate a return. These include: the posting of prudent collateral, the underlying assets in the SPV
must generate matching cash flows, the risk transfer must be genuine, and the custodian/trustee
must be financially strong. There is also a risk to cedants of losing capital relief if regulatory
requirements are not met or they change.
9.4 Longevity assets in a diversified portfolio
Figure 26 shows the benefits in terms of risk reduction from a pension fund having even a small
allocation to a longevity-linked asset, in this case a longevity swap. Since, longevity-linked assets are
to a first-order uncorrelated with financial assets, such as equities and bonds, this makes them an
attractive asset to hold in a diversified portfolio.
Figure 26: Efficient frontier with and without longevity swaps
However, it is important to note that there will some smaller second-order correlations, such as:
credit risk, e.g., if an insurance company is involved as a counter-party; liquidity and interest rate risk
if funding and leverage are used by investors; and through economic linkages, both in the short-term
e.g., suicides rise in a recession and in the long-term richer economies spend more on medical
research and development.
Longevity will become a key new asset class in 21st Century. There is insufficient capital in
insurance/reinsurance industry to deal with global longevity risk. Capital markets are more efficient
than the insurance industry in reducing informational asymmetries and in facilitating price discovery.
Returns to investors will reflect the huge need for companies to remove legacy pension liabilities
from their balance sheets and to provide the secondary market for life policies. Furthermore, the
Life Market has risks that are to a first-order uncorrelated with traditional bond and equity markets
which makes them an attractive diversifying asset.
Nevertheless, the Life Market is still a long way from being a fully mature global capital market. In
terms of Richard Sandor’s seven stages of market evolution, we are currently only at stage twosee
Table 4. But it is only a matter of time before we reach stages three and four.
Table 4: Sandor’s seven stages of market evolution
Structural change leading to a demand for capital
Development of uniform commodity/security standards
Introduction of legal instruments providing evidence of ownership
Development of informal spot and forward markets
Emergence of formal exchanges
Introduction of organized futures and options markets
Proliferation of over-the-counter (OTC) markets, deconstruction
Source: Sandor (1994, 2003, 2016)
Akerlof, G. A. (1970) The Market for 'Lemons': Quality Uncertainty and the Market Mechanism,
Quarterly Journal of Economics, 84 (3): 488500.
Blake, D., Boardman, T., and Cairns, A.J.G. (2014) Sharing Longevity Risk: Why Governments Should
Issue Longevity Bonds, North American Actuarial Journal, 18(1): 258-277.
Blake, D., and Burrows, W. (2001) Survivor Bonds: Helping to Hedge Mortality Risk, Journal of Risk
and Insurance, 68(2): 339-48.
Blake, D., Cairns, A.J.G., Coughlan, G. D., Dowd, K. and MacMinn, R. (2013) The New Life Market,
Journal of Risk and Insurance, 80: 501-558.
Blake, D., Cairns, A.J.G., and Dowd, K. (2006) Living with Mortality: Longevity Bonds and Other
Mortality-Linked Securities, British Actuarial Journal, 12: 153-197.
Blake, D., Cairns, A.J.G., and Dowd, K. (2008) Longevity Risk and the Grim Reaper’s Toxic Tail: The
Survivor Fan Charts, Insurance: Mathematics and Economics, 42: 1062-66.
Blake, D., Cairns, A.J.G., Dowd, K., and Kessler, A.R. (2018) Still Living with Mortality: The Longevity
Risk Transfer Market After One Decade, presented to the Institute and Faculty of Actuaries,
Edinburgh, 29 January.
Blake, D. and D. Harrison (2008). And Death Shall Have No Dominion: Life settlements and the Ethics
of Profiting from Mortality, Pensions Institute Report, London.
Bugler, N., Maclean, K., Nicenko, N., and Tedesco, P. (2018) Reinsurance Sidecars: The Next Stage in
the Development of the Longevity Risk Transfer Market, North American Actuarial Journal,
Cairns, A.J.G., Blake, D., and Dowd, K. (2006) A Two-Factor Model for Stochastic Mortality with
Parameter Uncertainty: Theory and Calibration, Journal of Risk and Insurance, 73: 687-718.
Cairns, A.J.G., Blake, D., Dowd, K., Coughlan, G.D., Epstein, D., Ong, A., and Balevich, I. (2009) A
Quantitative Comparison of Stochastic Mortality Models using Data from England & Wales
and the United States, North American Actuarial Journal, 13: 1-35.
Cairns, A.J.G., and El Boukfaoui, Ghali (2018) Basis Risk in Index Based Longevity Hedges: A Guide For
Longevity Hedgers, North American Actuarial Journal (forthcoming).
Cairns, A.J.G., Kallestrup-Lamb, M., Rosenskjold, C.P.T., Blake, D. and Dowd, K. (2017) Modelling
Socio-Economic Differences in the Mortality of Danish Males Using a New Affluence Index,
Pensions Institute Discussion Paper PI-1604, February.
Carnes, B.A., Olshansky, S.J., Grahn, D (2003) Biological Evidence for Limits to the Duration of Life,
Biogerontology, 4(1):31-45.
Coughlan, G.D., Epstein, D., Sinha, A., and Honig, P. (2007) q-Forwards: Derivatives for Transferring
Longevity and Mortality Risks, J. P. Morgan Pension Advisory Group, London (July).
Coughlan, G.D. (2011) Longevity as the New Asset Class, presentation to Longevity 7: Seventh
International Longevity Risk and Capital Markets Solutions Conference¸ Goethe University
Frankfurt, 9 September.
Dowd, K., D. Blake, A.J.G. Cairns, and P. Dawson (2006) Survivor Swaps, Journal of Risk and
Insurance, 73: 1-17.
Dowd, K., Blake, D., and Cairns, A. J. G. (2010) Facing Up to the Uncertainty of Life: The Longevity Fan
Charts, Demography, 47: 67-78.
Hunt, A., and Blake, D. (2015) Modelling Longevity Bonds: Analysing the Swiss Re Kortis Bond,
Insurance: Mathematics and Economics, 63: 1229.
Loeys, J., Panigirtzoglou, N., and Ribeiro, R.M. (2007) Longevity: A Market in the Making, J.P. Morgan
Securities Ltd, London (2 July).
Michaelson, A. and Mulholland, J. (2015) Strategy for Increasing the Global Capacity for Longevity
Risk Transfer: Developing Transactions That Attract Capital Markets Investors, in Brian R.
Bruce (Ed) Pension & Longevity Risk Transfer for Institutional Investors, Fall: 28-37.
Oeppen, J. and Vaupel, J.W. (2002) Broken Limits to Life Expectancy, Science, 296 (5570): 1029-1031.
Olshansky, S.J., Carnes, B.A., Butler, R. 2001. If Humans Were Built to Last, Scientific American,
284(3): 50-55.
Olshansky, S.J., Passaro, D., Hershow, R., Layden, J., Carnes, B.A., Brody, J., Hayflick, L., Butler, R.N.,
Allison, D.B., Ludwig, DS. 2005. A Potential Decline in Life Expectancy in the United States in
the 21st Century, New England Journal of Medicine, 352:1103-1110.
Pension Commission (2005) A New Pension Settlement for the Twenty-first Century, HMSO, Norwich.
Sandor, R.L. (1994) In Search of Market Trees: Market Architecture and Tradable Entitlements for
CO2 Abatement, in Combating Global Warming: Possible Rules, Regulations, and
Administrative Arrangements for a Global Market in CO2 Emission Entitlements, United
Nations Conference on Trade and Development, New York.
Sandor, R.L. (2003) The First Chicago Climate Exchange Auction: The Birth of the North American
Carbon Market, in Greenhouse Gas Market 2003: Emerging but Fragmented, International
Emissions Trading Association, Geneva.
Sandor, R.L. (2016) Financial Innovation, presentation to Longevity 12: The Twelfth International
Longevity Risk and Capital Markets Solution Conference, Chicago, 29 September.
Shaw, C. (2007) Fifty Years of United Kingdom National Population Projections: How Accurate Have
They Been?, Population Trends, 128: 8-23.
Willets, R. C. (2004) The Cohort Effect: Insights and Explanations, British Actuarial Journal, 10: 833-
... In practice, the financial effects of longevity risk have been handled differently. Some institutions or individuals accept the risk in exchange for some compensation or premium, others use insurance or reinsurance to spread the likely losses, and some institutions turn to financial markets using derivative instruments to manage this risk (Blake, 2018). To a certain extent, the latter alternative has been used more in recent years because the longevity market is attractive to investors because it offers assets that are not correlated with other financial assets (Jamal & Quayes, 2004), thus providing opportunities to diversify investment portfolios and create more efficient strategies. ...
... Also, in 2014 and 2015, Delta Lloyd and Reinsurance Group of America were involved in transactions of this nature. By 2018, the size of the global longevity market was estimated to be between $60 billion and $80 billion (Blake, 2018). ...
Full-text available
The objective of this article is to show the feasibility of derivative products being used to hedge longevity risk in Latin America. To do this, a longevity index is built with Mexican data using the Lee-Carter model and several longevity-linked derivatives are simulated. Results indicate that an ecosystem of derivative instruments is feasible in Mexico for two reasons: they are effective as hedging against longevity risk and the estimated longevity index, used as an underlying asset, does not correlate with relevant stock indices, which makes it feasible as part of a comprehensive financial portfolio. The originality of this research consists in the adaptation for Mexico of novel valuation methodologies and the new estimation of a longevity index. The main limitation of this research is that the ecosystem is subject to a base risk with respect to the population structure in the future.
... En la práctica, los efectos financieros que conlleva el riesgo de longevidad se han manejado de distintas formas: algunas instituciones o personas aceptan el riesgo a cambio de cierta compensación o prima, otros utilizan seguros o reaseguros para distribuir las probables pérdidas, y algunas instituciones acuden a los mercados financieros utilizando instrumentos derivados para manejar este riesgo (Blake, 2018). Esta última alternativa se ha utilizado más en años recientes, en alguna medida porque el mercado de longevidad resulta atractivo para inversionistas, al ofrecer activos no-correlacionados con otros activos financieros (Jamal y Quayes, 2004), proporcionando así oportunidades para diversificar portafolios de inversión y crear estrategias más eficientes. ...
... También en 2014 y 2015 Delta Lloyd y Reinsurance Group of America participaron en transacciones de esta índole. Se estima que, para el año 2018, el tamaño del mercado global de longevidad se ubicaba entre 60 y 80 miles de millones de dólares (Blake, 2018). ...
Full-text available
El objetivo de este artículo es mostrar la factibilidad de que productos derivados sean utilizados como cobertura del riesgo de longevidad en Latinoamérica. Para ello, se construye un índice de longevidad con datos mexicanos usando el modelo Lee-Carter y se simulan diversos instrumentos derivados de longevidad. Se concluye que un ecosistema de instrumentos derivados es factible en México por dos razones, éstos son efectivos como cobertura del riesgo de longevidad y el índice de longevidad construido, y utilizado como activo subyacente, no presenta correlación con índices accionarios relevantes, lo que lo hace factible como parte de un portafolio financiero amplio. La originalidad de este trabajo consiste en la adaptación de metodologías de valuación inéditas para México y la estimación de un índice de longevidad propio, y la principal limitante es que el ecosistema está sujeto a un riesgo base con respecto a la estructura poblacional en el futuro
... See, e.g.,Figure 19inBlake (2018). ...
Full-text available
This Special Issue of the Journal of Demographic Economics contains 10 contributions to the academic literature all dealing with longevity risk and capital markets. Draft versions of the papers were presented at Longevity 16: The Sixteenth International Longevity Risk and Capital Markets Solutions Conference that was held in Helsingør near Copenhagen on 13-14 August 2021. It was hosted by PerCent at Copenhagen Business School and the Pensions Institute at City, University of London.
... See, e.g.,Figure 19inBlake (2018). ...
Full-text available
This special issue of the Journal of Demographic Economics contains 10 contributions to the academic literature all dealing with longevity risk and capital markets. Draft versions of the papers were presented at Longevity 16: The Sixteenth International Longevity Risk and Capital Markets Solutions Conference that was held in Helsingør near Copenhagen on 13–14 August 2021. It was hosted by PerCent at Copenhagen Business School and the Pensions Institute at City, University of London.
... Mikro uzun ömürlü risk piyasasını ise bireysel hayat sigortası poliçeleri (hayat anlaşmaları) oluşturmaktadır. Piyasanın küresel bir hale gelmesi için, uzun ömürlülüğün altında yatan nedensel faktörlerin anlaşılabilirliği ve piyasa endeksleri ile ölüm tahmini modellerinin geliştirilmesi gibi belirli piyasa gereksinimlerinin karşılanması gerekmektedir (Blake, 2018 Finansal okuryazarlığın artırılmasının öneminin yanı sıra, yaşla ilgili konularda bilgi kalitesinin iyileştirilmesi de önemlidir. Yeni finansal ürünlerin ve çözümlerin geliştirilmesini engelleyen bir konu, bireylerin yaşlanmaya bağlı risklerini tahmin etmenin zorluğudur. ...
Full-text available
GİRİŞ Yaşlanma ve demografik değişiklikler, ekonomi ve toplumdaki değişikliklerin başlıca itici güçleridir. Zamanlama ve ölçek ülkeler arasında farklılık gösterse de yaşam beklentisindeki artışlar ve doğurganlık oranlarındaki düşüşler nedeniyle kapsamlı bir küresel demografik geçiş yaşanmaktadır. Bu geçiş başta sağlık hizmetleri olmak üzere işgücü, finans piyasaları, ekonomik büyüme ve kamu maliyesinin sürdürülebilirliği üzerinde geniş kapsamlı etkilere sahiptir. Yaşlanan ve küçülen iş gücü, aynı zamanda üretkenliği, tasarruf ve yatırım davranışlarını ve faiz oranlarını da etkilemektedir. Artan emeklilik, sağlık ve uzun süreli bakım maliyetleri ile bireysel emeklilik tasarruf düzenlemesi üzerinde bir mali stres oluşturmaktadır. Dünya Ekonomik Forumu yıllık toplantısında "sağlık hizmetlerinin geleceğe uygun hale getirilmesi" konusunu en büyük on küresel zorluktan biri olarak kabul etmiştir. Ekonomistler, yaşlanan bir dünya nüfusuna bakmanın zorluğuna özellikle dikkat çekmektedirler. Önümüzdeki 10 yılda içerisinde, ülkelerdeki yaşlılık bağımlılık oranlarında ciddi ölçüde artış beklenmektedir. Başta Japonya olmak üzere Monako, İtalya, Yunanistan ve Porto Riko dünyadaki en yaşlı nüfusa sahip beş ülkedir. Türkiye'de ise yaşlı nüfus oransal olarak diğer yaş gruplarındaki nüfusa göre daha yüksek bir hız ile artış göstermektedir. Yaşlı nüfusun toplam nüfus içindeki oranı 2016 yılında %8,3 iken, 2021 yılında %9,7 ye yükselmiştir. Yaşlı nüfus oranının 2025 yılında %11,0, 2030 yılında %12,9, 2040 yılında %16,3, 2060 yılında%22,6 ve 2080 yılında %25,6 olacağı öngörülmektedir. Artan yaşlılık bağımlılık oranları, yeterli emeklilik, sağlık ve uzun süreli bakımın finansmanını yüksek baskı altına alacaktır. Oluşacak maliyetlerle başa çıkmak ve demografik değişim çağında kapsayıcı büyümeyi teşvik etmek için kapsamlı bir yaklaşıma 1 ORCID ID:0000
... Furthermore, as the present COVID-19 crisis has shown, financial portfolio managers value the opportunity to include assets that show low correlation with traditional financial assets; one example being those linked to longevity, Blake (2018). Sports betting could provide such an opportunity by playing that role, both in risk management and speculative trading. ...
This paper transfers and adapts the Black-Litterman portfolio management model and its subsequent generalizations to the characteristics and specificities of assets quoted on sports betting markets. The results show that these assets are suitable for the application of portfolio management models with possible inclusion of investors’ opinions. Information based on the variability of market prices and the attention received by NBA teams in Google Trends is successfully used to simulate the opinions expressed by a hypothetical portfolio manager. Furthermore, this makes these assets suitable for inclusion in portfolios in which managers are seeking returns uncorrelated with other assets.
Pension risk transfer and longevity risk transfer are now growing secular trends. From North America to Europe, companies are de-risking pension plans in near-record volumes and have continued to boldly do so throughout the pandemic—at or near the most favorable pricing experienced in years. The arrival of funded reinsurance on both sides of the Atlantic is bringing reinsurer capital and private assets to support the steady growth in the pension risk transfer market. Additionally, we have observed that the enduring low-rate environment and quest for uncorrelated risk has the world's largest investors directing billions into life reinsurance sidecars. How have these markets thrived during the worst global outbreak in a century? Key research on the pandemic's impact on pensioner life expectancy allowed prices to be set and transactions to proceed through a time of significant uncertainty.
Full-text available
O objetivo do artigo é o de apresentar e discutir as caraterísticas dos denominados instrumentos financeiros de longevidade, ou instrumentos do life market, nomeadamente das obrigações de longevidade e dos derivados de longevidade. A criação de tais instrumentos deveu-se à amplitude das transformações demográficas e à necessidade de cobertura do risco de longevidade por parte das entidades gestoras de produtos de previdência. O artigo sustenta-se na apreciação crítica e na sistematização dos contributos de artigos científicos, bem como na consulta de informação estatística produzida por organismos nacionais e internacionais. Para além dos fatores determinantes das sucessivas transições demográficas, apresentam-se as tendências que se perspetivam neste domínio. Mas, sobretudo, o artigo evidencia as caraterísticas dos instrumentos financeiros de longevidade, bem como sublinha as dificuldades que se colocam à sua adoção enquanto mecanismo de cobertura de risco, entre as quais se colocam a determinação do preço e a fraca adesão que podem encontrar junto dos investidores.
To mitigate the hedger’s longevity risk exposure, this paper proposes a collective longevity swap between a reinsurer (hedge provider) and a group of hedgers (pension plans and annuity providers), and an economic framework to price longevity risk and longevity swaps. Combining the appealing features of two widely discussed longevity swaps, i.e., the indemnity swap and index-based swap, the collective longevity swap requires that reinsurer’s payments are based on the longevity risk of the aggregate portfolio of all hedgers, whereas each hedger could receive indemnity payments on their own portfolio. In a general principal-agent pricing model under the incomplete market setting, we determine the optimal risk premiums and hedge rates that maximize the reinsurer’s expected profit under a set of the hedgers’ participation constraints. We find that, in a competitive market, the proposed collective swap could lead to a higher expected profit for the reinsurer than the indemnity and the index-based swap, and simultaneously improve the benefits of the majority of hedgers without worsening the benefits of the rest. Finally, using a stochastic multi-population mortality model and real-world mortality data, a series of numerical analyses are performed to verify the theoretical findings.
This paper proposes an optimal dynamic strategy for hedging longevity risk in a discrete-time setting. Our proposed hedging strategy relies on standardized mortality-linked securities and minimizes the variance of the hedging error as induced by the population basis risk. While the formulation of our proposed hedging strategy is quite general, we use a stylized pension plan, together with a specified “yearly rollingǥ trading strategy involving q-forwards and a specified stochastic mortality model, to illustrate our proposed strategy. Under these specifications, we show that the resulting hedging problem can be formulated as a stochastic optimal control framework and that a semi-analytic solution can be derived through an extended Bellman equation. Extensive Monte Carlo studies are conducted to highlight the effectiveness of our proposed hedging strategy. We also consider a scheme to approximate the semi-analytic solution in order to reduce the computational time significantly while still retaining its hedge effectiveness. We benchmark our strategy against the “delta” hedging strategy as well as its robustness to q-forwards maturity, reference age, interest rate, and stochastic mortality models. The proposed strategy has many appealing features, including its discrete-time setting which is consistent with market practice and hence conducive to practical implementation, and its generality in that the underlying hedging principle can be applied to other standardized mortality-linked securities and other stochastic models.
Full-text available
This paper updates Living with Mortality published in 2006. It describes how the longevity risk transfer market has developed over the intervening period, and, in particular, how insurance-based solutions-buy-outs, buy-ins and longevity insurance-have triumphed over capital markets solutions that were expected to dominate at the time. Some capital markets solutions-longevity-spread bonds, longevity swaps, q-forwards, and tail-risk protection-have come to market, but the volume of business has been disappointingly low. The reason for this is that when market participants compare the index-based solutions of the capital markets with the customized solutions of insurance companies in terms of basis risk, credit risk, regulatory capital, collateral, and liquidity, the former perform on balance less favourably despite a lower potential cost. We discuss the importance of stochastic mortality models for forecasting future longevity and examine some applications of these models, e.g., determining the longevity risk premium and estimating regulatory capital relief. The longevity risk transfer market is now beginning to recognize that there is insufficient capacity in the insurance and reinsurance industries to deal fully with demand and new solutions for attracting capital markets investors are now being examined-such as longevity-linked securities and reinsurance sidecars.
Full-text available
This paper considers the assessment of longevity basis risk in the context of a general index-based hedge. We develop a detailed framework for measuring the impact of a hedge on regulatory or economic capital that takes population basis risk explicitly into account. The framework is set up in a way that accommodates a variety of regulatory regimes such as Solvency II as well as local actuarial practice, attempting, therefore, to bridge the gap between academia and practice. This is followed by a detailed analysis of the capital relief resulting from a hedge that uses a call spread as the hedging instrument. We find that the impact of population basis risk on capital relief (expressed in terms of a ‘haircut’ relative to the case with no population basis risk) depends strongly on the exhaustion point of the hedge instrument. In particular, in a Solvency II setting, if the exhaustion point lies well below the 99.5% Value-at-Risk, population basis risk has negligible impact and the haircut is zero.
Full-text available
We investigate and model how the mortality of Danish males aged 55-94 has changed over the period 1985-2012. We divide the population into ten socio-economic subgroups using a new measure of affluence that combines wealth and income reported on the Statistics Denmark national register database. The affluence index, in combination with sub-group lockdown at age 67, is shown to provide consistent sub-group rankings based on crude death rates across all ages and over all years in a way that improves significantly on previous studies that have focused on life expectancy. The gap between the most and least affluent is confirmed to be widest at younger ages and has widened over time. We introduce a new multi-population mortality model that fits the historical mortality data very well and generates smoothed death rates that can be used to model a larger number of smaller sub-groups than has been previously possible without losing the essential character of the raw data. The model produces bio-demographically reasonable forecasts of mortality rates that preserve the sub-group rankings at all ages. It also satisfies reasonableness criteria related to the term structure of correlations across ages and over time through consideration of future death and survival rates.
Full-text available
We compare quantitatively eight stochastic models explaining improvements in mortality rates in England and Wales and in the United States. On the basis of the Bayes Information Criterion (BIC), we find that, for higher ages, an extension of the Cairns-Blake-Dowd (CBD) model that incorporates a cohort effect fits the England and Wales males data best, while for U.S. males data, the Renshaw and Haberman (RH) extension to the Lee and Carter model that also allows for a cohort effect provides the best fit. However, we identify problems with the robustness of parameter estimates under the RH model, calling into question its suitability for forecasting. A different extension to the CBD model that allows not only for a cohort effect, but also for a quadratic age effect, while ranking below the other models in terms of the BIC, exhibits parameter stability across different time periods for both datasets. This model also shows, for both datasets, that there have been approximately linear improvements over time in mortality rates at all ages, but that the improvements have been greater at lower ages than at higher ages, and that there are significant cohort effects.
Full-text available
A key contribution to the development of the traded market for longevity risk was the issuance of the Kortis bond, the first longevity trend bond, by Swiss Re in 2010. We analyse the design of the Kortis bond, develop suitable mortality models to analyse its payoff and discuss the key risk factors for the bond. We also investigate how the design of the Kortis bond can be adapted and extended to further develop the market for longevity risk.
Full-text available
q-forwards are simple capital markets instruments for transferring longevity and mortality risk. They are derivatives involving the exchange of the realized mortality rate of a population at some future date, in return for a fixed mortality rate agreed at inception. q-forwards form the basic building blocks from which many other more complex derivatives can be constructed. A portfolio of q-forwards can be used to provide an effective hedge of the mortality risk of a life assurance portfolio, or of the longevity risk of a pen-sion plan or annuity book. Because investors require a premium to take on longevity risk, the mortality forward rates at which q-forwards transact will be below the expected, or "best estimate" mortality rates. To create a liquid market requires, in the early stages, a limited number of standardized contracts in which liquidity can be concentrated. A set of q-forwards that settle based on the LifeMetrics Index could fulfill this role. JPMorgan is committed to developing a market in LifeMetrics q-forwards.
Full-text available
A BSTRACT The huge economic significance of longevity risk for corporations, governments, and individuals has begun to be recognized and quantified. By virtue of its size and prevalence, longevity risk is the most significant life‐related risk exposure in financial terms and poses a potential threat to the whole system of retirement income provision. This article reviews the birth and development of the Life Market, the new market related to the transfer of longevity and mortality risks. We note that the emergence of a traded market in longevity‐linked capital market instruments could act as a catalyst to help facilitate the development of annuity markets both in the developed and the developing world and protect the long‐term viability of retirement income provision globally.
The longevity risk transfer market in Europe and North America remains in its infancy despite rapid growth in recent years, and further qualitative progress is needed to develop a commoditized market. Reinsurance sidecars, which are commonly used in the property and casualty market in the United States, have enormous potential to play an important role in such development. Transaction structures involving reinsurance sidecars can be adapted to benefit cedants and sponsoring reinsurers and also to attract a broader spectrum of investors and participants by reducing the long-tail risk inherent in longevity risk transfer. While several transaction structures are possible, each would fundamentally provide additional capital to support transactions in a form that is not subject to a requirement to hold a regulatory solvency capital buffer, thereby enabling sponsoring reinsurers to offer keener pricing to cedants. As a result, a European Union-based cedant could gain considerable capital benefits by reinsuring longevity risk, market risk or both to a reinsurance sidecar.
This article considers the assessment of longevity basis risk in the context of a general index-based hedge. We develop a detailed framework for measuring the impact of a hedge on regulatory or economic capital that takes population basis risk explicitly into account. The framework is set up in a way that accommodates a variety of regulatory regimes such as Solvency II as well as local actuarial practice, attempting, therefore, to bridge the gap between academia and practice. This is followed by a detailed analysis of the capital relief resulting from a hedge that uses a call spread as the hedging instrument. We find that the impact of population basis risk on capital relief (expressed in terms of a “haircut” relative to the case with no population basis risk) depends strongly on the exhaustion point of the hedge instrument. In particular, in a Solvency II setting, if the exhaustion point lies well below the 99.5% Value-at-Risk, population basis risk has a negligible impact and the haircut is zero.
There's an iceberg dead ahead. It's called global aging, and it threatens to bankrupt the great powers. As the populations of the world's leading economies age and shrink, we will face unprecedented political, economic, and moral challenges. But we are woefully unprepared. Now is the time to ring the alarm bell..