International Experience on Longevity Risk

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International Experience on Longevity Risk

報告人：東吳大學商用數學系楊曉文

工作小組: 政大風管系研究生林銘寛及葉政瑋

日期：2005年3月18日

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Agenda

Introduction

Development of Mortality Tables

Capital Market Solutions

Comments

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Introduction

Should the demand for individual annuity products increase in the future?

US: Social security reform(DBÆDC)

Taiwan: 勞退新制, 退休金所得替代率仍偏低

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Development of Mortality Tables

Incorporating the Trend of Mortality Improvement.

Projected Mortality=Base Mortality* Reduced Factor

Example: UK, German

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Development of Mortality Tables(Con’t)

age/year ……… t t+1 t+2 t+3 ………

……

x q^x(t) q^x(t+1) q^x(t+2) q^x(t+3) x+1 q^x+1(t) q^x+1(t+1) q^x+1(t+2) q^x+1(t+3) x+2 q^x+2(t) q^x+2(t+1) q^x+2(t+2) q^x+2(t+3) x+3 q^x+3(t) q^x+3(t+1) q^x+3(t+2) q^x+3(t+3)

……

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a(55):

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.)

PA90

this table is based on the experience of pensioner annuities from 1967 to 1970, and published by the CMIB in 1978. (CMIR 3, 1978.)

PMA80 Base

Pensioners, Male, Amounts, based on the experience from 1979 to 1982. 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 1990. (CMIR 9, 1988 and CMIR 10, 1990.)

PMA92 Base

Pensioners, Male, Amounts, based the experience from 1991 to 1994. This table has the same form as the 80 series with different forecast factors, and was published in 1998. (CMIR 16, 1998 and CMIR 17, 1999.)

Development of Mortality Tables(Con’t)

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Development of Mortality Tables(Con’t)- UK

GMIB and GAD

Base Table [q

_x

]

ÆForecasting mortality rates [q

_x,t

=q

_x

*RF

_x,t

]

ÆSo far, it is still deterministic.

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Example: PMA80 Table

( )( )

1 2 1 2 3 ²

Calculating : in contrast to the PMA80 base table, a single formula for was used for all ages.

,

2, 3 exp 2

x x

x

GM r s t

GM t a a t b b b t

µ µ

µ

• =

= + + + + ( − )

1

2

1

2

3

1 100 0.023

100 0.011 5.397782 6.622746 1.6.

a a b b b

⎡ ⎤

⎣ ⎦

=

= −

=

= −

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( ) ( ) ( )

( ) ( )

( ) ( ) ( )

,

, ,

2 0 ,

P r o j e c t i n g f u t u r e f r o m

1 1

w h e r e

6 0

1 1 1 0 6 0 1 1 0 1 1 0 5 0

1 1 1 0

a n d

6 0

1 1 0 6 0

6 0

5 0

x t x

x t x x t

t x t

q q

q q R F

R F x x f x

c x

x c x x

x

h x

x h x k

f x x

α α

α

•

= ⋅

= + ⎡⎣ − ⎤ ⎡⎦ ⎣⋅ − ⎤⎦

⎧ ≤

⎪ −

= ⎪⎨ + − ≤ ≤

⎪⎪ ≥

⎩

≤

− + −

= ≤ ≤ 1 1 0

1 1 0

w h e r e 0 . 1 3 a n d 0 . 5 5

k x

c k

⎧⎪

⎪⎨

⎪ ≥

⎪⎩

= =

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Development of Mortality Tables(Con’t)- UK:

The trend of the survival probability of British people aged above 65 for different mortality tables

0.00 0.20 0.40 0.60 0.80 1.00 1.20

65 69 73 77 81 85 89 93 97 101

105 109

113 Age

(x-65)P65

a(55) PA90M

PMA80C2010 PMA92C2020

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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)

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Development of Mortality Tables(Con’t)- German

An age and calendar dependent mortality model

was

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Current Solutions: Actuarial Methods

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Development of Mortality Tables(Con’t)-

International Comparison

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Development of Mortality Tables(Con’t)- German

Note: An analysis of the observation material shows the relationship between mortality and annuity levels.

Æweighted by annuity levels

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How do these projecting models interpret

for UK experience?

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Capital Market Solutions

Securitization of mortality risk

Existing Products

Swiss Re mortality bond(2003)

EIB/ BNP Paribas/ PartnerRe Longevity Bond(2004)

Alternatives

Product Swap

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Securitization of mortality risk

透過資本市場取得承保能量

人壽保險公司將年金險或退休金商品之長壽風險透過證券化的方式，

轉到金融市場上分散給投資者購買，進而分散長壽風險

Advantage

從保險角度看，保險風險證券化將再保險容量從原來保險業內部擴大

到了外部的資本市場；從金融角度看，保險風險證券化具體實施過程就是一個資產證券化過程，這裏的資產就是保險公司的負債。

Disadvantage:

保險風險證券化的透明度較差

保險風險證券化的運作成本較高

違約風險

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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.

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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.

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Securitization of mortality risk:

Products Design: an example ( Lin and Cox(2004)) Proceeds from Bond

Sales

Investors

Insurance Premium

Insurance Payment

Coupon Principal

Reinsurer

t t

1000

B + D = C

( ) ^P ( ) ^V

B

t

D

t

SPC

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Securitization of mortality risk:

Products Design: an example ( Lin and Cox(2004))

Fixed payment y

Investors

Annual Insurance Premium x

Insurance

Payment Floating payment

Reinsurer

t

D

t

x + = y B ⁺

B

t

D

t

Dealer

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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

ÆLife Insurance

A catastrophe bond structure was used.

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Capital Market Solutions-

Swiss Re mortality bond :Structure

保險公司跟SPV簽訂契約,保險公司交一筆合約金額, 約定SPV外募集一筆資金,作為保險公司當死亡率過高時所須之超額理賠的部份。

SPV在外向投資人以票據的方式，約定到期給付方

式，以死亡率index值為準，若index超過(100+x)%時投資人之收益減損，若損失到達(100+y)%時，投資人就無任何收益。投資人所損失之金額即作為保險司公司之超額賠償，用以彌補保險人因高死亡率所生之理賠損失。若index未達(100+x)%時，SPV依約給付給投資一筆加計利息之最終給付

當SPV收到在外募集之資金後，進行投資，再向另一

金融機構，SWAP以投資收益交換固定金額(內含另一

風險)，此作法之目的在於避免投資收益不佳時所生

之損失

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Capital Market Solutions-

Swiss Re mortality bond :Structure

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Capital Market Solutions-

Swiss Re mortality bond : Calculation of Loss

%Loss=

¹⁰⁰ Index Value X Y X

× −

−

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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 pre- defined coverage area.

1. c

_j

is the weight for country j

(美國、英國、法國、義大利、瑞士) 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

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Capital Market Solutions-

The EIB/ BNP Paribas longevity bond

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Capital Market Solutions-

The EIB/ BNP Paribas longevity bond : Cash Flow Profile

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Capital Market Solutions-

The EIB/ BNP Paribas longevity bond:Annual Pay-off

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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.

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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

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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.

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International Experience on Longevity Risk