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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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
Solutions - no Detail q or b
)/,/( 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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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
Solutions - no Detail q
2bqA
2)1( bqqA
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Set 1 - q ≈ 1 since q is small. Use avg q.
)(
)(
)(
)( 222
bE
bEC
bE
bEbqA
Solutions - no Detail q
)(
)( 2
bE
bECA
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Which gives you
F
bCA
2
Solutions - no Detail q or b
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
Solutions - no Detail q or b
qnb
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Can be restated as follows:
n
FCqnbbqnb
Using C = bnq and b = F / n
Other term
Solutions - no Detail q or b
qnb
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Can also be restated as follows:
N
CCqnbbqnb
Using C = bnq and b = C / N
Other term
Solutions - no Detail q or b
)/,/( 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
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