**Hendrik Rogge and Dr. Albert Jürgen Enders discuss index-based longevity risk transfer**

**Is the time right?**

Although insurers and re-insurers are "natural" longevity risk takers, they have limited capacities. Thus, the capital market with its enormous ability to absorb risk provides an obvious alternative.

On the one hand, for a long time the problem was that the market suffered from information asynchronism, i.e. the different parties involved in a transaction often do not have the same level of information. On the other hand, however, insurers and pension funds clearly have a very deep understanding of longevity risks.

But over the last years almost all of the relevant risk taking institutions have caught up in longevity knowledge and since 2008 the number of longevity transactions has increased steadily. Solvency II requirements, which have become more concrete on longevity risk transfer, are also impacting longevity risk hedging.

**Is longevity risk a big threat?**

Historically low interest rates on low-risk assets are currently the largest problem for insurers and pension funds. Obviously, low interest rates will make it very difficult to meet the required returns on assets. Hence, other liability risks which negatively impact returns cannot be ignored.

As longevity is increasing it becomes more significant for all insurers and pension funds. In general, longevity risk is a trend risk compared to interest rate risk which is a volatile risk. On the other hand, we are starting to see volatility in longevity risk. For example, the life expectancy of young women in the Netherlands seems not to increasing any more. Also, US longevity seems to be going against the trend meaning that longevity has reached a plateau or is even declining within some groups.

Our analysis of longevity data reveals that it is correlated to socio-demographic factors. In our work we even came across a pension portfolio of mainly blue collar workers that was overfunded due to higher than expected mortality rates.

**Developing a longevity index**An index reflects a defined underlying e.g. a basket of stocks, weather parameters or macroeconomic indicators. As we know, it is rather the trend of an index that is of interest than the index value itself. The deviation of the unexpected to the expected trend of the index provides the relevant risk coefficient.

Indices can be composed using prices (e.g. stock prices) or they can be parametric (based on a physical value, e.g. temperature, consumer spending or even longevity). Capital markets use parametric indices in the absence of transparent prices of the underlying.

As prices for longevity risk transactions are not published we decided to start with parametric longevity indices. The goal was to develop regularly updated longevity indices that reflect the longevity trend over a longer period of time.

Deutsche Börse's "Xpect Cohort Indices" represent the normalised number of survivors (lx) for each defined cohort group. lx is defined as the actual age specific number of survivors from the starting population of 100,000 per year of birth. This metric is similar to the survivor rate starting at 100% at age zero.

Using Xpect Cohort Indices as a benchmark for longevity has the following advantages:

* Xpect Indices are based on effective realised mortality rates and are updated monthly

* Xpect Indices show actual longevity per defined country or segment

* The number of survivors / survivor ratio covers the cumulated mortality rate to each index date

* This way of measuring survivors allows users to compose indices over multiple cohorts and to compare indices and index trends

* The run of the index reflects the ideal run of cash flows of a pension fund over time and can be customized

**Figure 1: View on Xpect Cohort Indices (1945-1949), which among others is published monthly: ****www.xpect-index.com**

In spite of the advantages, basis risk remains an issue when using an index to transfer longevity risk. Therefore Deutsche Börse has developed longevity indices that cover basis risk relevant parameters.

Studies of Deutsche Börse and Club Vita, London, demonstrate that longevity correlates with pension payments, i.e. the higher the annuity, the higher the life expectancy. Xpect-ClubVita Indices reduce basis risk because they reflect socio-demographic mortality rates provided from a pool of real pension fund data. Deutsche Börse will be launching Xpect Pensiongroup longevity indices for the UK together with Club Vita soon.

Club Vita provides pension group specific longevity data that will be transformed to longevity correction factors to calculate Xpect-ClubVita Indices for the following pension groups:

UK Males:

* <5k £ pension p.a.

* 5-10k £ pension p.a.

* > 10k £ pension p.a.

UK Females:

* <5k £ pension p.a.

* >5k £ pension p.a.

*Figure 2: The run of the Xpect-ClubVita Pensiongroup Indices reflect the Pensiongroup specific mortality rates*

**Modelling future mortality rates**

Historic index values help market participants understand index risk parameters such as volatility and trends. In addition, actual monthly Xpect Indices support the valuation of Xpect index-linked products.

Index projections are necessary to support the price finding of index-based financial products e.g. longevity swaps and bonds. Xpect Forward Curves simply reflect the simulated developments of the number of survivors (or survivor ratio) of the defined cohort group until the number of survivors or survivor ratio is zero.

The index user has to model future mortality rates (qx) and calculates Xpect Forward Curves. The model to assess future mortality rates is essential and a model to calculate the Xpect Forward Curve is provided by Deutsche Börse.

In established derivative markets such as interest rates, the sum of many different assumptions about the future run of the index leads to a mark-to-market index forward curve. This will also happen for the Xpect and Xpect-ClubVita Indices.

**How index-linked longevity products work**

In principle, two kinds of financial products exist to transfer longevity risk based on indices:

* Index-linked swaps and forwards

* Index-linked bonds

In both cases, the involved parties accept the effective index value at maturity date as the settlement value of the contract. At the time t=0 both parties simulate the future index value at maturity or trigger date to determine their bid and ask prices.

Thus, for the maturity date of the index-linked contract, best estimates of the expected value of the Xpect Index plus required risk premiums are calculated. Following, we would like to show how a longevity swap will be priced and settled using the "Xpect Cohort Index England & Wales 1945-1949 Male".

*Graph 3: The graph shows internal swap rates (prices) based on the Xpect Index EW 1945-1949 Male Forward Curve projections: expected run and a -30% mortality rate change run.*

The following example illustrates the pricing and settlement of an Xpect Zero Coupon Swap:

**A** is the fixed rate payer at a specific maturity date = pension fund

**B** is the floating rate payer at a specific maturity data = investor

Index Value t=0: 83,628

Agreed Index Value t=20 52,680

internal Swap rate is: -2.28%

Swap nominal 100,000,000

If the Xpect index at t=20 is 52,680 the longevity swap would be settled with zero: fixed rate = floating rate (-2.28%).

If the Xpect Index at t=20 is 60,480 (-30% qx p.a. scenario) then internal rate is -1.61%:

* A owes -2.28% to B which means A receives 37,007,063 from B

100,000,000 * (( 1- 2.28%)20-1)

* B owes a floating rate of -1.61% to A

Therefore B receives 27,680,053 from A

100,000,000 *(( 1- 1,61%)20-1)

* The investor (B) incurs a loss AND the pension fund (A) receives additional payment of 9,327,009

**How to use Xpect today**

Deutsche Börse and TullettPrebon have created a tradable longevity swap market on Bloomberg and ThomsonReuters. The Bloomberg screen below shows indicative internal swap rates for a series of Xpect Cohort Indices. These indicative bid/ask prices (internal swap rates) are based on simulated Xpect Forward Curves as described in the swap example above. We expect that the more often market participants evaluate new longevity information, the more often they will adjust their Xpect swap quotes thus leading to frequent updates of the Xpect Forward Curve.

The fact that Club Vita is joining the Xpect initiative will help the market develop further. We invite other interested market participants to join our efforts in establishing a longevity risk trading market. It is our joint objective to create a market that will a) provide sufficient capacity and b) fair and transparent prices for longevity risk.

**Authors:**

Hendrik Rogge

Product Manager Xpect, Deutsche Börse AG

Frankfurt, Germany

[email protected]

Dr. Albert Jürgen Enders

Managing Director, ValueData7 GmbH

Königstein, Germany

[email protected]

*Graph 4: Bloomberg screen of Xpect Cohort Indices indicative longevity swap prices (see below)*