Longevity Swaps

Longevity swaps are used where a pension fund that owes pensions moves the cost of pensioners living longer to a taker, and where an insurer moves the same risk to a reinsurer.

What a longevity swap exchanges

Longevity risk is the risk that pensioners, policyholders, and similar beneficiaries, taken together, live longer than expected. The longer they live, the longer pensions must be paid, so the burden on the party that owes them grows¹. A longevity swap moves this risk to a taker in the form of a swap.

The mechanism is an exchange of a fixed payment for the actual pension payments. A pension fund or similar party makes a fixed payment, based on an agreed longevity assumption, to the taker, and the taker pays the fund an amount equal to the actual pension payments². Takers are insurers, reinsurers, capital market participants, and others³. The basic form of a swap is covered in How Swaps Work.

The fund keeps paying pensions to its pensioners. Once it receives the actual-pension amount from the taker and makes the fixed payment, its net cost is replaced by the fixed payment. If the two sides are settled net, the only money that moves is the difference.

The fixed payment is based on the longevity assumption the taker has agreed to, plus an amount for the taker's profit and expenses. An article by the SOA (Society of Actuaries, a US body) describes it as a fixed monthly payment from an insurer to a reinsurer². For a pension fund and a taker, the same exchange of a fixed side for an actual side is applied in the explanation here². The example below uses one payment a year to keep the numbers easy to read.

A payment example

Consider a hypothetical example in which the pension fund of Company Z enters a longevity swap with a taker, covering the pensions of 1,000 pensioners for the next five years. Pensioners die over the years, so the fixed payment falls each year. The fixed payments that Company Z's fund makes to the taker are shown in the table below. Actual pensions are shown for two cases: pensioners live longer than expected, and they die earlier.

The unit is 100 million yen (0.1 billion yen). A negative difference means the fund pays the taker.

Figure description

These are the yearly payments between the fund and the taker when pensioners live longer than assumed. The amounts are the same as in the table above. Each year the fund makes the fixed payment and receives the amount equal to the actual pensions. From Year 2, what it receives exceeds what it pays, and the gap widens each year.

If pensioners live longer than expected, actual pensions are 4.70 billion yen, 0.20 billion yen more than the fixed payments. The fund receives 0.20 billion yen from the swap, so its net cost stays at the fixed payments of 4.50 billion yen. If they die earlier, actual pensions are lower at 4.30 billion yen, but the fund keeps making the fixed payments of 4.50 billion yen, so it pays 0.20 billion yen to the taker. The net cost is 4.50 billion yen in both cases.

For the fund, the longer-lived case is a gain because the increase in its burden is held down. The shorter-lived case is a loss because the fund does not benefit from the lower burden it would have had without the swap. For the taker, gains and losses are the reverse.

Indemnity-based and index-based swaps

There are two ways to set the amount the taker pays. An indemnity-based swap follows the actual pension payments to the covered pensioners. An index-based swap follows an agreed population index⁴. A paper from the Pensions Institute at City, University of London (Cairns et al., 2012) calls the form that corresponds to the former a customised swap, tailored to the demographics and benefit structure of the pension fund⁵.

The liquidity row rests on the descriptions in the paper and the IMF (International Monetary Fund) report of April 2012: the index swap is standardized and easier to unwind, while terms differ by contract in the indemnity-based form⁶.

The SOA article (February 2023) says indemnity-based deals take effort to price, so they are mostly large, above USD 500 million in present value of benefits⁴. It also says that, of the seven longevity swaps announced in 2022 (up to the date of the article), six were for UK pension funds⁴.

An index-based swap has a standardized structure, needs less due diligence, and costs less, but a gap remains because the fund's pensioner population differs from the index population⁴. The paper's case study found that a fund with more than about 10,000 pensioners over age 50 could reduce longevity risk substantially with an index-based hedge. This is an estimate that uses the mortality of men in England and Wales⁷.

What changes the value

The value of a longevity swap depends on the future survival of the pensioners. A pension is paid only while the pensioner is alive, so the value of the actual-pension side is the present value of future yearly survival probabilities, multiplied by discount factors and summed. If the discount rate is a constant $r$ per year, the value at time $T$ of an annuity that pays 1 at the end of each year is given by the formula below⁸.

$$a(T,x)=\sum_{s=1}^{\infty}(1+r)^{-s}\,{}_{s}p^{\mathrm{fwd}}(T,x)$$

Here $x$ is the age at time $T$, and ${}_{s}p^{\mathrm{fwd}}(T,x)$ is the estimate, based on information at time $T$, of the probability that a person aged $x$ is still alive $s$ years later. The fixed side can be expressed as an annuity of the same form, so the value of the swap is the value of the actual-pension side minus the value of the fixed side⁸. If the estimate of the future changes so that pensioners live longer than expected, the value of the actual-pension side rises, which favors the fund and hurts the taker.

This formula holds interest rates constant and isolates longevity risk. The paper analyzes the swap under the same assumption⁸. In practice interest rates move, and when the discount rate falls, the present values of both the fixed side and the actual-pension side rise. The IMF report gives an estimate for a model pension plan: with a discount rate of 6% a year, a three-year increase in average life expectancy raises liabilities by 8%, and with 2% a year it raises them by almost 14%⁹.

The report also says that the value of instruments for transferring longevity risk is correlated with interest rate levels through discounting, so the view that longevity risk can be treated as independent of interest rates and other risks may hold less well than expected¹⁰. Cases where interest rates change, or where longevity and interest rates move together, fall outside the assumptions of the formula above.

Deep diveEstimating survival probabilities and choosing a model

Survival probabilities are estimated by fitting a mortality model to past mortality rates and generating future paths of mortality. The paper lists the factors that affect hedge effectiveness as differences between populations (such as basis risk), the simulation model that generates future mortality, the model that values the liabilities at a future date, and the structure of the hedge¹¹.

At the valuation date, the model's parameters are refitted using the deaths observed up to that point. The result of the refit differs across the individual paths of future mortality, which adds variation to the values of the liabilities and the swap. The paper calls this recalibration risk and says it also depends on the length of the period used for fitting¹². For small groups, small-sample risk (Poisson risk), where observed deaths deviate from the underlying mortality rate, also matters¹². Model risk, the risk that the model itself is wrong, also remains, but the paper does not analyze it¹³.

The choice of mortality model changes the estimate of survival probabilities, and so it changes the price¹⁴. The paper's case study uses simulation: it generates many scenarios of future mortality and values the swap and the liabilities in each scenario¹⁵.

Uses and regulation

The users are pension funds that owe pensions and insurers that pay pensions. Pension liabilities grow with longer lives, and the swap moves that increase to the taker³². Among takers, reinsurers and insurers that carry life insurance risk can offset part of the risk they already hold by taking on longevity risk. When people live longer, annuity liabilities rise but life insurance liabilities fall¹⁶.

A longevity swap mainly covers longevity risk and does not cover asset-side risk. For plans with indexed benefits, it can also be structured to offset both longevity and the inflation risk related to longevity¹⁷.

On the regulatory side, the Prudential Regulation Authority (PRA) of the Bank of England sets out its expectations for UK insurers and others that carry out longevity risk transfers (November 2024 version). Large or complex transactions are subject to prior notification, and others are reported after the transaction. The PRA says it is concerned that firms may enter this market for reasons other than risk transfer¹⁸.

Risks

Several risks remain for the taker and the fund.

Basis risk is the gap between the amount the taker pays and the fund's actual pension payments. It is larger for index-based swaps, and it remains even for indemnity-based swaps because of differences between the contract terms and the actual benefit terms¹⁹. The paper says that population basis risk, the gap that arises because the fund's population differs from the index population, has a large effect on hedge effectiveness²⁰.

Counterparty credit risk is the risk that the taker cannot pay partway through a long contract. One way to cover this is collateral. The IMF report says that posting more collateral costs money because high-quality liquid assets must be provided, but that a swap needs collateral only for the net difference²¹. The PRA says that an insurer dealing with only a few counterparties can face large counterparty credit risk, and asks it to manage this beyond holding capital²².

Liquidity risk comes from the difficulty of standardizing. A party that wants to give up the risk seeks a contract tailored to its own terms. A buyer seeks a standardized product that is easy to trade. Standardizing adds liquidity for buyers, but it widens the gap between the fund's pensioners and the index population, which adds to the seller's basis risk²³.

Differences in information also matter. A fund knows more than the taker about its pensioners' health, so funds whose pensioners are likely to live long may be keener to hedge²⁴.

Differences from a pension buy-out

There are other ways to move pension liabilities besides a longevity swap.

The paper calls a buy-out a solution in which all risks move to the insurer (an insurance indemnification solution). A swap, combined with interest rate and inflation swaps and similar contracts, is a way to produce a result close to a buy-out at lower cost. However, basis risk does not disappear completely because of the individual circumstances of the fund's pensioners²⁵. Insurance-Linked Securities and Cat Bonds, which transfer disaster risk, cover a different risk²⁶.

Notes

1. Bank of England, Prudential Regulation Authority, "Supervisory Statement SS18/16: Solvency II: longevity risk transfers" (November 2024), paragraph 1.4. ↩

2. Society of Actuaries, "Managing Longevity Risk: A Solution to Consider" (Reinsurance News, February 2023), "How a Longevity Swap Works". The application to a fund and a taker rests on the abstract and equations (2) and (3) on page 8 of Cairns et al., "Longevity Hedge Effectiveness". ↩ ↩² ↩³ ↩⁴

3. International Monetary Fund, "Chapter 4: The Financial Impact of Longevity Risk" (Global Financial Stability Report, April 2012), page 19 ("Market-Based Transfer of Longevity Risk") and page 23. ↩ ↩²

4. Society of Actuaries, "Managing Longevity Risk: A Solution to Consider", "Two Categories of Longevity Swaps". USD 500 million is the present value of benefits, and six of the seven swaps in 2022 were for UK pension funds. ↩ ↩² ↩³ ↩⁴

5. Cairns, Dowd, Blake and Coughlan, "Longevity Hedge Effectiveness: A Decomposition" (Pensions Institute DP PI-1106, August 2012), page 3 (descriptions of the customised swap and the index swap). ↩

6. Cairns, Dowd, Blake and Coughlan, same paper, page 3, and International Monetary Fund, same report, page 23. ↩

7. Cairns, Dowd, Blake and Coughlan, same paper, abstract and page 3. In the case study, the index is modeled on the mortality of men in England and Wales, and the fund's population on the mortality of male CMI assured lives (page 8). ↩

8. Cairns, Dowd, Blake and Coughlan, same paper, page 8, equations (1) to (3). The paper's a corresponds to a(T,x) in the text, and the swap value H(T) is the difference between the values of the fixed and actual-pension annuities. ↩ ↩² ↩³

9. International Monetary Fund, same report, page 15 and Figure 4.4 (the figure's source is IMF staff estimates). ↩

10. International Monetary Fund, same report, page 23, footnote 28. ↩

11. Cairns, Dowd, Blake and Coughlan, same paper, pages 4 to 5. The paper lists four categories: population differences, the simulation model, the valuation model, and hedge structure. ↩

12. Cairns, Dowd, Blake and Coughlan, same paper, page 5 ("Recalibration risk"; "Recalibration window"; "Poisson risk"). ↩ ↩²

13. Cairns, Dowd, Blake and Coughlan, same paper, page 4, footnote 6 (a note that the model risk of the simulation model is excluded from the analysis). ↩

14. Cairns, Dowd, Blake and Coughlan, same paper, page 4 ("The choice of model to be fitted to historical mortality data" is one of the factors affecting hedge effectiveness). ↩

15. Cairns, Dowd, Blake and Coughlan, same paper, pages 4 and 9 to 10 (a simulation model generates scenarios of future mortality, and each scenario is fed into a valuation model). ↩

16. International Monetary Fund, same report, page 23 ("life annuity liabilities increase when annuitants live longer, whereas life insurance liabilities decrease"). ↩

17. Society of Actuaries, same article, "Two Categories of Longevity Swaps" ("longevity swaps for either category do not cover any asset-related risk"; treatment of inflation-linked benefits). ↩

18. Bank of England, Prudential Regulation Authority, same Supervisory Statement, paragraphs 1.5 and 3.1 to 3.3. ↩

19. Bank of England, Prudential Regulation Authority, same Supervisory Statement, paragraph 2.3 (lists basis risk as an example of a residual risk). ↩

20. Cairns, Dowd, Blake and Coughlan, same paper, abstract and page 4 ("Population basis risk"). ↩

21. International Monetary Fund, same report, pages 23 to 24 (from counterparty risk through collateral on the net difference only). ↩

22. Bank of England, Prudential Regulation Authority, same Supervisory Statement, paragraphs 2.1 and 2.2. ↩

23. International Monetary Fund, same report, page 23 (the difference between the contracts that sellers and buyers seek). ↩

24. International Monetary Fund, same report, page 23 (the discussion of asymmetric information). ↩

25. Cairns, Dowd, Blake and Coughlan, same paper, pages 2 to 3 (buy-out; "insurance indemnification solution"; cost; "DIY buy-out"; basis risk remaining with the fund). ↩

26. OECD, "Fostering Catastrophe Bond Markets in Asia and the Pacific" (2024), "Introduction". ↩