International Experience

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1 International Experience on Longevity Risk 數 : 林寛葉 2005 年 3 18

2 Agenda Introduction Development of Mortality Tables Capital Market Solutions Comments

3 Introduction Should the demand for individual annuity products increase in the future? US: Social security reform(db DC) Taiwan: 勞, 金率

4 Development of Mortality Tables Incorporating the Trend of Mortality Improvement. Projected Mortality=Base Mortality* Reduced Factor Example: UK, German

5 Development of Mortality Tables(Con t)

6 Development of Mortality Tables(Con t) a(55): PA90 this table was produced in about 1950, and designed to give reasonable values of annuities purchased in 1955 (purchased immediate annuities). This table is applied to both males and females. (CMIR 1, 1973.) this table is based on the experience of pensioner annuities from 1967 to 1970, and published by the CMIB in (CMIR 3, 1978.) PMA80 Base Pensioners, Male, Amounts, based on the experience from 1979 to Forecast factors allow forecasting of values for any age to any calendar year and year of birth tables applied too. This table was published in (CMIR 9, 1988 and CMIR 10, 1990.) PMA92 Base Pensioners, Male, Amounts, based the experience from 1991 to This table has the same form as the 80 series with different forecast factors, and was published in (CMIR 16, 1998 and CMIR 17, 1999.)

7 Development of Mortality Tables(Con t)- UK GMIB and GAD Base Table [q x ] Forecasting mortality rates [q x,t =q x *RF x,t ] So far, it is still deterministic.

8 Example: PMA80 Table Calculating µ : in contrast to the PMA80 base table, a single formula x for µ was used for all ages. x (, )( ) µ x = GM r s t 2 ( 2,3)( ) exp 2 ( ) GM t = a1+ a2t + b1+ b2 + b3 t 1 100a = a = b b b = = = 1.6.

9 where c = 0.13 and k = 0.55 P rojecting future q from x, t q x q = q R F x, t x x, t ( ) 1 α ( ) 1 ( ) RF x, t = α x + x f x t 20 where α c x 60 x 10 x = c 60 x x 110 ( ) ( ) and h x 60 ( 110 x) h + ( x 60) k f ( x) = 60 x k x 110

10 Development of Mortality Tables(Con t)- UK: The trend of the survival probability of British people aged above 65 for different mortality tables 1.20 (x-65)p a(55) PA90M PMA80C2010 PMA92C Age

11 Development of Mortality Tables(Con t)- German Annuity tables: mortality rates per birth year + a trend assumption relating to the future mortality improvements Published Life Annuity Table DAV1994 R, DAV 2004 R (Data Between 1995 and 2002)

12 Development of Mortality Tables(Con t)- German An age and calendar dependent mortality model was

13 Current Solutions: Actuarial Methods

14 Development of Mortality Tables(Con t)- International Comparison

15 Development of Mortality Tables(Con t)- German Note: An analysis of the observation material shows the relationship between mortality and annuity levels. weighted by annuity levels

16 How do these projecting models interpret for UK experience?

17 Capital Market Solutions Securitization of mortality risk Existing Products Swiss Re mortality bond(2003) EIB/ BNP Paribas/ PartnerRe Longevity Bond(2004) Alternatives Product Swap

18 Securitization of mortality risk 量年金金金度量來了金度度

19 Securitization of mortality risk: Products Design Survivor Bonds where coupon payment are linked to the number of survivors in a given cohort (Blake and Burrows (2001)and Lin and Cox (2004)) Survivor Swaps where counterparties swap a fixed series of payments in return for a series of payments linked to the number of survivors in a given cohort ( Dowd et al (2004)) Annuity Futures where prices are linked to a specified future market annuity rate.

20 Securitization of mortality risk: (con t) Products Design Mortality Options a range of contracts with option characteristics whose payoff depends on an underlying mortality table at the payment date. Example: Guaranteed annuity contract.

21 Securitization of mortality risk: Products Design: an example ( Lin and Cox(2004)) Reinsurer Insurance Premium Proceeds from Bond Sales V ( P ) ( ) SPC Investors Insurance Payment B t Coupon Principal D t B + D = 1000C t t

22 Securitization of mortality risk: Products Design: an example ( Lin and Cox(2004)) Reinsurer Annual Insurance Premium x Dealer Fixed payment y Investors Insurance Payment B t D t Floating payment x+ y= B + D t t

23 Existing Product Swiss Re mortality bond In December 2003, Swiss Re sponsored a $400 million securitization of mortality risk. The purpose was to get protection against extreme mortality events Life Insurance A catastrophe bond structure was used.

24 契金金率理率若益若益金率理若利金行金益金益不 Capital Market Solutions- Swiss Re mortality bond :Structure

25 Capital Market Solutions- Swiss Re mortality bond :Structure

26 Capital Market Solutions- Swiss Re mortality bond :Calculation of Loss %Loss=100 Index Value X Y X

27 Capital Market Solutions- Swiss Re mortality bond :Index Value Trigger Definition : The index value for a given year is defined to be the average death rate per 100,000 for predefined coverage area. 1. c j is the weight for country j ( 利 ) 2. g m,f is the gender weighting 3. a i is the weight for age band i 4. q i,j is the observed death per 100,000 for males and females, respectively, from country j and age band i

28 Capital Market Solutions- The EIB/ BNP Paribas longevity bond

29 Capital Market Solutions- The EIB/ BNP Paribas longevity bond : Cash Flow Profile

30 Capital Market Solutions- The EIB/ BNP Paribas longevity bond:annual Pay-off

31 Capital Market Solutions- The EIB/ BNP Paribas longevity bond : Advantages The Longevity Bond 1. It provides a better match for the liabilities of pension funds and life insurers than other available investments other than purchasing (re)insurance to cover the longevity risk. 2. Life insurers holding the longevity bond as a hedge may be able to hold lower prudential margins. The payoff is similar to a pension in payment. The longevity index is completely transparent and independent - data are published by the UK Government.

32 Capital Market Solutions- The EIB/ BNP Paribas longevity bond :Disadvantages Main sources of basis risk: Different trends in longevity among populations of the same age Age distribution of the pension fund different from that of the Reference Population. The Reference Population weights all lives equally Pension fund population includes males and females whereas the Reference Population is male only

33 Current Solutions: Financial Methods The EIB/ BNP Paribas longevity bond: Disadvantages A small scheme will find it difficult to use this bond to match its liabilities as the variance between actual and expected mortality will be quite large. The bond is a progressively worse hedge for pension liabilities related to younger or older cohorts.

34 Current Solutions: Financial Methods Implication of Existing Products A market for mortality-based securities will develop if the prices and contracting features make the securities attractive to potential buyers and sellers Revised current product: index Note: The EIB/ BNP Paribas longevity bond is similar to life annuity issued by insurer.

35 Alternatives: Mortality swaps

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