2007 annual meeting ● assemblée annuelle 2007 vancouver

2007 Annual Meeting ● Assemblée annuelle 2007

Vancouver

2007 Annual Meeting ● Assemblée annuelle 2007

Vancouver

Canadian Institute

of Actuaries

Canadian Institute

of Actuaries

L’Institut canadien desactuaires

L’Institut canadien desactuaires

John Have

Group Life and AD&D MCCSR IP-18 & IP-27

GL MCCSR - Contents

• Working Group• Previous formulae• Current formulae• Some issues• Proposed solutions• ER surplus credits • Your input

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GL MCCSR – Task Force

Committee on Risk Management and Capital Requirements initiated Work Group to review Group Approximations

• Wally Bridel – Munich Re• Daniel Mayost - OSFI• Les Rehbeli – Oliver Wyman (Mercer)• John Have – Have Associates

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The GL MCCSR Change

From

.0005 x Insured amount x Stats Fact

To

Volatility + Catastrophic Components

where

V(olatility) = 2.5 x Std Dev next yr’s claims

Phase In Period

Dec 2005 +12 quarters ending Sep 2008

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GL MCCSR – Prior Formulae

Active GL .0005 x Net Insured Amt (guar <=1yr) (.001 and .002 for longer guar)AD&D – 30% of GLWP mortality – above using .002WP morbidity – new claim and ongoing

-> morbidity MCCSR

Adjustments• X .15 if hold harmless agreement• reduce ER policy component by surplus

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GL MCCSR – Prior Formulae

Mortality Component X Stats Factor1.25 at $1 million

1.00 at $10 million

.60 at $1 billion

Based on total individual / group mortality component20

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GL MCCSR Current Volatility

Volatility for Specfic SET

S = 2.5 x A x B x E / F

A – Std Dev next yr’s exp claims

B – Max(ln(D1),1) of exp claims - for prem guar period

E – Net amt at risk (Face – Reserve)

F – Face Amt

2.5 is CTE(95%) ≈ Normal Dist 97.5%

+ margin (ie: ongoing risk)

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GL MCCSR Current Volatility20

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007 2)1( bqqA

b - certificate amountq - certificate mortality rate

If b and q unknown use:

n

CA

39

C - next year’s net claimsn – number of lives

AD&D MCCSR Current Volatility20

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GESS GL /3. 2 E - AD&D net amount

G – GL net amount

If no comparable GL use:

n

CA

78

C - next year’s net claimsn – number of lives

Combined Volatility20

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Combined Volatility component for all basic death and AD&D products.

- Both Group and Individual SETs

DADBasicDeath

Total SSV&

22

MCCSR Current Catastrophic 20

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Catastrophic Component for each SET

FECCAT /05. E – net amount at risk

F – face amount

Use .10 if rate guaranteed > 1year

MCCSR Current 20

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Adjustments X .15 if hold harmless agreement .05 if Fed or Prov Government Reduce ER policy component by surplus

to maximum of

GECATSSV GroupDADINDINSINDTotal /)( 2&_

2_

E – AP for GL and AD&D for ER policy

G – AP for all GL and AD&D policies

MCCSR Approx Issues20

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CA

39

Does not scale properly with mortality level since the factor 39 assumes a certain level of mortality. If mortality rate doubles, A should increase by factor of not 2.2

Solutions - no Detail q

2bqA

2)1( bqqA

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Set 1 - q ≈ 1 since q is small. Then using avg q we have

then with avg q = C / F

F

bCA

2

Solutions - no Detail q or b20

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Set 1-q ≈ 1 since q is small.Since no detail, use average q or average b instead. Then

2)1( bqqA

2bqkA

Where K is factor necessary to increase volatility lost by using averages.

Solutions - no Detail q or b

2bqkA

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Summing this becomes

qnbkA

With N = nq, C = bnq and F = nb


)/,/( NCnFMaxCkA

),( ClaimFace bbMaxCkA

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OR

bFace is average insured amount

bClaim is average claim amount

And K is evaluate from camparison SET

C

CC C

NAk

Solutions - no Detail q or b20

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007 Limitation on the use of K:

If number lives exceed comparison set must use intercompany value of K.

Intercompany value of K can be developed by using detailed GL bill data from 5-6 large insurers.

Allowed for both GL and AD&D

Approximation Solutions20

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Proposed Effective Date

Jan 1, 2008

Cuurent ER Surplus Credits

Does it properly reflect reduction is capital needs??

John Have:

There are many types of ER formulae using various types of risk sharing methods.

An extra $1 of claim, over expected, is not always offset by $1 from ER surplus.

May need to develop metric to test the sensitivity of an extra, say, 5-10% of claims on an INSURER’s capital.

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Your Input?

• • • •

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Appendix20

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Detail Proposed Formula Derivations


2bqA

2)1( bqqA

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Set 1 - q ≈ 1 since q is small. Use avg q.

)(

)(

)(

)( 222

bE

bEC

bE

bEbqA


)(

)( 2

bE

bECA

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Which gives you

F

bCA

2


qnbkA

C

CC C

NA

qn

qn

qnb

Ak

1

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Since N = nq and C = bnq

With AC, NC and CC derived from comparison SET


qnb

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Can be restated as follows:

n

FCqnbbqnb

Using C = bnq and b = F / n

Other term


qnb

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Can also be restated as follows:

N

CCqnbbqnb

Using C = bnq and b = C / N

Other term


)/,/( NCnFMaxCkA

),( ClaimFace bbMaxCkA

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OR

BFace is average insured amount

bClaim is average claim amount

And K is evaluate from camparison SET

C

CC C

NAk

2007 annual meeting ● assemblée annuelle 2007 vancouver

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