finite reinsurance reserving
DESCRIPTION
Finite Reinsurance Reserving. Nick Giuntini, FCAS, MAAA CLRS, September 2003. General Approach. Generally Reserved on an Individual Contract Basis Lack of Homogeneity LPTs, Agg XOLs, Q/Ss Varied Terms Varied Underlying Often Large Contracts Underlying Exposure and Deal Modeling - PowerPoint PPT PresentationTRANSCRIPT
Finite Reinsurance Reserving2
General Approach
Generally Reserved on an Individual Contract Basis Lack of Homogeneity
LPTs, Agg XOLs, Q/Ss Varied Terms Varied Underlying
Often Large Contracts Underlying Exposure and Deal Modeling Accounting May Vary
Risk Transfer – Reinsurance Accounting Can Reinsurer Discount Reserves?
“No Risk Transfer” – Deposit Accounting
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Hypothetical Aggregate XOL
Whole Account
$1 Billion Est. Subject Premium
10% xs 75% Loss Ratio or $100M xs $750M of Losses
Additional Premium = 55% of Covered Loss
Funds Withheld Balance (FWB)
Crediting Interest Rate = 8.5%
Effective 1/1/2000 (2000 Underwriting Year)
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Aggregate XOL
Retention = 75% l/r or $750M
LAYER OF
COVERAGELimit + Retention = 85% l/r or $850M
Retained Losses
Retained Losses
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Aggregate XOL FWB
Premium
= $55M
Limit
= $100M
INTEREST CREDIT COVERED LOSSES
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Mean or Mode
Assume:
Reinsurer can Discount Losses
Cedent Reports a 80% loss ratio
FWB Expected to Cover Ceded Loss Payout ($27.5M of Premium + Interest for $50M Losses)
Should Reinsurer Set up a Reserve for Obligations in Excess of FWB?
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Credit Risk
If Cedent becomes Insolvent, Reinsurer’s Funds are at Risk:
Premiums and Interest “Paid” into FWB Funds Transferred Triggers on Certain Events If not transferred offset generally believed to hold
Premiums not yet Paid into FWB Offset Probably Holds
Future Interest Credits Offset Questionable
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Credit Risk – Interest Income
Assume:
Reserving at 12/31/2003
Expected Loss Ratio = 85%
$736M Paid to Date (Paid Losses still in Retention)
FWB = $76M (for $100M of Ceded Losses)
What is the Magnitude of the Reinsurer’s Credit Risk?
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Credit Risk – Interest Income
Current Interest % Credit Risk*
2% $16 M
3% $13 M
4% $9 M
5% $6 M
6% $4 M
7% $1 M
8% 0
8.5% 0
* PV of Shortfall if FWB is transferred to Reinsurer and only earns Current Interest %.
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Credit Risk – Under-Reporting
Assume:
Same as before, but
Expected Loss Ratio = 85%,
Reported Loss Ratio = 80%
FWB = $38M (for $50M of Reported but ultimately $100M of Reported Losses)
Now What is the Magnitude of the Reinsurer’s Credit Risk?
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Credit Risk – Under-Reporting
Current Interest %
Credit Risk w/o Offset on Future APs
Credit Risk with Offset on Future APs
2% $54 M $27 M
3% $51 M $23 M
4% $48 M $20 M
5% $45 M $17 M
6% $42 M $14 M
7% $39 M $12 M
8% $37 M $9 M
8.5% $36 M $8 M
* PV of Shortfall if FWB is transferred to Reinsurer and only earns Current Interest %.
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Tail Factor Selection
Generally Higher Tail Factors are “Conservative” for the Reinsurer
For this Cover, an Increase in Paid Losses After 8 Years is Good for Reinsurer
Assume: Reserving at 12/31/2003 Expected Loss Ratio = 80% (given tail factor) $694M Paid to Date (Paid Losses still in Retention)
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Amount of APs
Payment Date AP with Interest
2000 55%
2001 60%
2002 65%
2003 70%
2004 76%
2005 83%
2006 90%
2007 97%
2008 106%
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Tail Factor Selection
108 mos. 120 mos. 132 mos. 144 mos. 156 mos. 168 mos. 180 mos.
1.001 1.005 1.003 1.001 1.002 1.0051.005 1.003 1.002 1.002 1.0031.005 1.005 1.002 1.0021.004 1.002 1.0031.003 1.0041.003
1.004 1.004 1.003 1.002 1.003 1.005TAIL
1.004 1.004 1.003 1.002 1.003 1.005 ????
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Tail Factor Selection
Tail Factor FWB Cushion*
1.000 - $2.4 M
1.005 - $0.7 M
1.010 $0.6 M
1.015 $1.4 M
1.020 $2.2 M
* Negative Numbers are PV Reinsurers Loss at 4%.