1

MORTALITY RISK FOR

LIFE INSURERS AND PENSION

FUNDS

ANDREW CAIRNS

Heriot-Watt University, Edinburgh

and

The Maxwell Institute, Edinburgh

2

PLAN FOR TALK

• Background and the mortality problem

• Possible solutions

• Stochastic mortality models

• Basis risk

• Conclusions

3

The Problem

Nothing is certain in life except death and taxes.

(1789: Franklin)

2005: What we know as the facts:

• Death is still a certainty!

• Life expectancy is increasing.

• Future development of life expectancy is uncertain.

“Longevity risk”

4

The Problem: Insurance risk

• Traditional view:

Pooling of insurance risks⇒ diversification

BUT

• Systematic risks: e.g.

– Florida hurricane risk

– Pandemic risk

– Long-term mortality improvements

5

The Problem – UK Defined-Benefit Pension Plans:

• Before 2000:

– High equity returns masked impact of longevity

improvements

• After 2000:

– Poor equity returns, low interest rates

– Decades of longevity improvements now a problem

6

The Problem – Life Insurers: annuity business

• Annuity providers:

– Risk due to unanticipated improvements in mortality.

• Equitable Life (and others): GAO’s

Guaranteed Annuity Option: becomes valuable if

– interest rates fall

– mortality rates fall

7

The Problem – Life Insurers: life business

• Short-term catastrophes

– Pandemic

– Terrorism

– Earthquake etc.

• Long-term, unanticipated deterioration in mortality

8

Insurers: What to do with systematic mortality risk?

• Ignore – risk not significant;

• Accept as a legitimate business risk;

• Diversify insurance liabilities (annuities + life);

• Replace fixed annuities with participating contracts;

• Reinsurance (downside risk);

• Securitise a line of business;

• OTC mortality-linked contracts;

• Traded mortality-linked securities.

9

Pension plans: What to do with systematic mortality risk?

• Cannot/should not:

– Ignore; Accept as business risk; Diversify.

• Purchase individual annuities from insurer;

• Bulk buyout;

• Actively manage risk using:

– OTC mortality-linked contracts;

– traded mortality-linked securities.

10

Life insurer’s perspective

1900 1920 1940 1960 1980 2000

−7.

5−

6.5

−5.

5−

4.5

England and Wales: Males age 20−29 mortality

Year

log

Mor

talit

y ra

te

Spanish flu

WW II

AIDS

11

England and Wales log mortality rates 1950-2002

1950 1960 1970 1980 1990 2000

−5.

0−

4.8

−4.

6−

4.4

−4.

2−

4.0

−3.

8−

3.6

Year

log(

mor

talit

y )

Age 60

1950 1960 1970 1980 1990 2000

−3.

0−

2.8

−2.

6−

2.4

−2.

2−

2.0

−1.

8−

1.6

Year

log(

mor

talit

y )

Age 80

12

Why do we need stochastic mortality models?

Data⇒ future mortality is uncertain

• Good risk management

• Setting risk reserves

• Life insurance contracts with embedded options

• Pricing and hedging mortality-linked securities

13

The wider picture

Life insurers and pension funds exposed to many risks

A: investment risk

B: interest-rate risk

C: mortality and longevity risk

A, B→ can hedge to reduce risk; C?

Blake, Cairns & Dowd (2006) Living with mortality ... British Actuarial Journal 12: 153-197.

14

Stochastic mortality

• Many models to choose from

• Annual mortality data

– National data; subpopulations

• Limited data⇒ model and parameter risk

15

How to compare stochastic models (*)

• Quantitative criteria

• Qualitative criteria

– parsimony and transparency

– robust relative to age and period range

– biologically reasonable

– forecasts are reasonable

(*) Cairns et al. (2007) A quantitative comparison of stochastic mortality models.... Online: www.lifemetrics.com

16

Fan charts + A plausible set of forecasts

1960 1980 2000 2020 2040

0.00

50.

020

0.05

00.

200

AGE 65

AGE 75

AGE 85

Year, t

Mor

talit

y ra

te, q

(t,x

)

Model M7 Fan Chart

AGE 65

AGE 75

AGE 85

Year, t

Mor

talit

y ra

te, q

(t,x

)

Model M7 Fan Chart

AGE 65

AGE 75

AGE 85

Year, t

Mor

talit

y ra

te, q

(t,x

)

Model M7 Fan Chart

17

Model risk

1960 1980 2000 2020 2040

0.00

50.

010

0.02

00.

050

0.10

00.

200

AGE 65

AGE 75

AGE 85

Year, t

Mor

talit

y ra

te, q

(t,x

)

Model M5 Fan Chart

18

Model risk

1960 1980 2000 2020 2040

0.00

50.

010

0.02

00.

050

0.10

00.

200

AGE 65

AGE 75

AGE 85

Year, t

Mor

talit

y ra

te, q

(t,x

)

Combined M5, M7 Fan Chart

19

Model risk

1960 1980 2000 2020 2040

0.00

50.

010

0.02

00.

050

0.10

00.

200

AGE 65

AGE 75

AGE 85

Year, t

Mor

talit

y ra

te, q

(t,x

)

Combined M5, M7, M8A Fan Chart

20

Model M2 Forecast robustness problems

1960 1980 2000 2020 2040

0.00

50.

020

0.05

00.

200

1961−2004 data: M2B full1961−2004 data: M2B limited1981−2004 data: M2B

Model M2B (ARIMA(1,1,0)) projections

Year of birth

Coh

ort e

ffect

x=65

x=75

x=85

21

Modelling Conclusions

• Be aware of model and parameter risk

• Use a full range of quantitative and qualitative criteria

Uses include:

• Risk assessment and pricing of mortality-linked

securities

22

MORTALITY-LINKED SECURITIES

• Short-term catastrophe bonds (Swiss Re, 2003, 2005)

• Survivor swaps (some OTC contracts)

swap fixed for floating mortality-linked cashflows

• Long-term longevity bonds (EIB/BNP, Nov. 2004)

cashflows linked to survivorship index

ultimately unsuccessful

23

What makes a proposed security successful?

• Attractive capital structure for hedgers

• Transparent and trustworthy underlying index

• Low basis risk for hedgers

• Good understanding of the risks being traded

⇒ need a good model

• Need receivers of longevity risk

⇒ natural hedgers; hedge funds etc.

24

November 2004: EIB/BNP Paribas longevity bond

• Payments linked to survivor index S(t)

• S(t) = proportion of cohort age 65 at time 0 surviving

to time t.

• Bond pays 50M×S(t) at time t

• Reference population: England and Wales, males

• Issuer=European Investment Bank

• Structurer and Manager=BNP Paribas

25

BNP Paribas / EIB Bond

European Investment Bank = Issuer

BNP Paribas = Manager and Structurer

EIB-

¾Bond Holders

t = 1, 2, . . . , 25

S(t)×50M

t = 0:Issue Price∼ $540M

S(t) = proportion still alive at t out of

males aged 65 in 2003

26

EIB’s perspective

• Likes to issue floating-rate notes in Euros

• Does not like floating-mortality bonds in GBP

27

EIB

Bond Holders

BNP

Partner Re

¾

Issue Price

?

¾

Survivor Swap

Issue Price

-¾Interest-rate swap

6Floating S(t)

+ Credit Insurance ???

28

0 5 10 15 20 25

0.0

0.2

0.4

0.6

0.8

1.0

Time, t

S(t

)

Longevity bond coupon payments

E[S(t)] without parameter uncertainty5/95−percentile with parameter uncertainty

• Too much capital up front for limited risk transfer

• Perceived basis risk

• Price not obviously a problem

29

What still needs to be done?

Longevity-linked securities:

• Right capital structure

– Survivor swaps (standardised?)

– Survivor caps and caplets

– Capital-at-risk bonds

• Need to understand basis risk

30

Traded securities: basis risk

Basis Risk⇒mismatch between reference population and own risk

Examples:

• different population characteristics

• different age profile

• males/females

31

Traded securities: basis risk

Single, reliable reference population

⇒ high basis risk for many hedgers

⇒ security not worth holding

⇒ low demand

⇒ low liquidity

32

Traded securities: basis risk

Several reference populations

⇒ low basis risk for hedgers

BUT too many reference populations

⇒ poor transparancy or reliability

⇒ low liquidity

Tradeoff required to get the right balance

33

Basis risk

• More work to be done

• Relatively little data

⇒ need to work hard to extract stylised facts

• Role for biological reasonableness

34

Conclusions

• Life Insurance and Pensions liabilities are huge

($ Trillions)

• Life insurers and pension plans are exposed to

significant systematic longevity risk

• Options:

– bear the risk internally

– transfer the risk to the financial markets

35

Conclusions

• Requirement for good risk management⇒ Potential huge demand for mortality-linked

securities

• Challenges for the future:

– to improve statistical models;

– to develop a substantial, liquid market in

mortality-linked securities

⇒ need to design products that are attractive forboth buyers and sellers

36

Andrew Cairns

Department of Actuarial Mathematics and Statistics

Heriot-Watt University

Edinburgh, EH14 4AS, UK

E-mail: A.Cairns@ma.hw.ac.uk

WWW: http://www.ma.hw.ac.uk/∼andrewc