Reinsurance and rating agency models
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Reinsurance and Rating Agency Models. Thomas M. Mount, ACAS, MAAA A.M. Best Company. Reinsurance Products Requiring Adjustments to Capital Model:. Capped Quota Share Aggregate Stop Loss Loss Portfolio Transfers Adverse Development Covers Catastrophe Bonds Sidecars.

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Reinsurance and rating agency models

Reinsurance and Rating Agency Models

Thomas M. Mount, ACAS, MAAA

A.M. Best Company


Reinsurance products requiring adjustments to capital model

Reinsurance Products Requiring Adjustments to Capital Model:

  • Capped Quota Share

  • Aggregate Stop Loss

  • Loss Portfolio Transfers

  • Adverse Development Covers

  • Catastrophe Bonds

  • Sidecars


Where do frequent adjustments to bcar occur due to reinsurance

Where do Frequent Adjustments to BCAR Occur due to Reinsurance?

  • NWP capital factors

  • Net loss & LAE reserve capital factors

  • Surplus

  • Credit risk

  • Potential Shock Loss (PMLs)

  • Stress Tests


Origin of nwp risk capital factors

Origin of NWP Risk Capital Factors

Capital factor


Origin of reserve risk capital factors

Industry Reserve Capital Factor Calc.

2.5

2

1% in tail

1.5

1

0.5

0

-30%

-20%

-10%

0%

10%

20%

30%

40%

(Favorable)/Adverse Reserve Development % of Original Reserves

capital factor

zero

99%

defic.

Origin of Reserve Risk Capital Factors


Impact of traditional quota share on nwp risk capital factors

Impact of Traditional Quota Share on NWP Risk Capital Factors


Impact of capped quota share on nwp risk capital factors

Impact of Capped Quota Share on NWP Risk Capital Factors


Capped quota share summary of impact on bcar

Capped Quota ShareSummary of Impact on BCAR

  • NWP capital factors increased to reflect retained risk in excess of retained premium

  • Additional premium charges, sliding scale contingent commissions, etc can also increase retained risk

  • Smaller impact on reserve capital factors

  • Reinsurance dependence factor may increase

  • Credit risk required capital increases

  • Overall BCAR is Improved - due to transfer of risk to reinsurer but at a rate lower than cession percentage


Impact of aggregate stop loss on aphs and reserve risk required capital

Impact of Aggregate Stop Loss on APHS and Reserve Risk Required Capital


Aggregate stop loss summary of impact on bcar

Aggregate Stop LossSummary of Impact on BCAR

  • ASL can impact premium and reserve risks

  • Benefit to premium and reserves depends on layer ceded

  • Always need to add back ceded premium

  • Need to increase reserve required capital by amount of required capital on ceded reserve

  • Schedule P may be distorted, Deficiency distorted

  • Reinsurance recoverables increased

  • Reinsurance dependence factor increased

  • Credit risk required capital increased

  • Overall BCAR improves depending on the layer ceded


Impact of adverse development cover on reserve risk required capital

Impact of Adverse Development Cover on Reserve Risk Required Capital


Adverse development cover summary of impact on bcar

Adverse Development CoverSummary of Impact on BCAR

  • Surplus increased for prepaid deficiency

  • Surplus reduced for cost of ADC

  • Reserve required capital reduced

  • Reinsurance recoverables increased

  • Reinsurance dependence factor increased

  • Credit risk required capital increased

  • Overall BCAR is Improved - due to transfer of reserve risk to reinsurer


Effect of reinsurance on modeled pml

Effect of Reinsurance on Modeled PML

  • Published capital score (BCAR)

    • Surplus reduced by first event

      • Greater of 1/100 Wind,1/250 EQ, Recent actual loss

      • Per Occurrence curve

      • Net of reinsurance

      • Gross of reinstatement prem

      • Net of 35% FIT

    • Direct impact on balance sheet strength & FSR


Effect of reinsurance on stress test

Effect of Reinsurance on Stress Test

  • What does BCAR score look like after first event happens?

    • Potentially Main driver of our view of balance sheet strength

  • Look at Impact of 1st event on insurer’s balance sheet:

    • Surplus reduced by 1st event

    • Recoverables go up by ceded portion of 1st event loss (we use 80% of recoverable)

    • Downgrade reinsurers one FSR level (incr credit risk)

    • Net reserves increase by pre-tax net loss

      • Add to reserve page if exposed to potential development on the booked loss

      • Use 80% of net loss


Effect of reinsurance on stress test1

Effect of Reinsurance on Stress Test

  • After all those adjustments:

    • STILL EXPOSED TO A SECOND EVENT !!!

  • Reduce surplus by second event

    • Larger of 1/100 Wind, 1/100 EQ, or Recent actual event

      • Net of reins, gross of reinstate, net of 35% FIT, per occur

      • Direct Impact on balance sheet strength and FSR

  • Wanted 2 separate large per occurrence events

    • Better than aggregate season

    • Validated in 2004, 2005


Effect of reinsurance on stress test2

Effect of Reinsurance on Stress Test

  • Stressed BCAR can fall up to 30 points from current required capital as determined by committee

    • 15 points for most cos (i.e. 1 FSR level)

    • 30 points for cos with

      • Good Catastrophe management

      • Financial Flexibility

  • Potentially Greater Flexibility for Dedicated Subs of Strong Parent Companies

    • Issue is willingness to recapitalize


Cat bonds why does ambest measure basis risk

CAT Bonds:Why Does AMBest Measure Basis Risk?

  • AMBest’s objective in measuring basis risk is to determine how much reinsurancecredit should be given to certain types of parametric* Cat Bonds in the BCAR analysis.

*For the purpose of this document and discussion, AMB considers non-indemnity catastrophe bonds as parametric catastrophe bonds.


Measuring basis risk mechanical steps

Measuring Basis Risk: Mechanical Steps

AMBest’s method of estimating basis risk:

  • Calculate a score based on a scoring table and correlate the score to a reinsurance credit table*.

  • Calculate a ratio based on PML impact that directly ties to reinsurance credit*.

  • Take the lesser of the results from steps 1 and 2.

  • Other considerations.

* Information used in this calculation is provided by the peril modeler or sponsor.


Complete step 1 basis risk score

Complete Step 1: Basis Risk Score

Index Re Basis Risk Scoring Table

  • Sum up weighted score (ie, 1.70)

  • Determine Basis Risk Score based on the following AMB table:

Score

Weight

Wt x Score

Shortfall10.350.35

Exhaustion prob.10.250.25

Peril30.100.30

Peril modeler30.100.30

Data quality30.100.30

Certainty of bus.20.100.20

Total1.70

Scoring-based reins credit81%

AMB Scoring-Based

Reinsurance Credit Scale

Summed

Basis Risk

Score

Credit

90%1

75%2

50%3

30%4

10%5

81%

1.70

  • Scoring-based reinsurance credit is 81%.


Step 2 capital effectiveness ratio

Step 2 - Capital Effectiveness Ratio

PML Before Adding the Effect of the Bond – PML After Adding the Effect of the Bond

Capital

Effectiveness =

Ratio

90% x

Bond Principal Balance

$800,000,000 – $700,000,000

= 90% x

$125,000,000

= 90% x 80.0%

= 72%


Step 3 absolute reinsurance credit

Step 3: Absolute Reinsurance Credit

81%

  • Absolute reinsurance credit is the lower of:

    • Scoring-based reinsurance credit (step 1)

    • Capital effectiveness ratio (step 2)

  • The reinsurance credit is 72% of Cat Bond issue, calculated as follows:

    72% x $125 mil = $90.0 mil

72%

  • The adjusted per Occurrence PML is:

    = per Occurrence PML - Reinsurance Credit Amount

    = $750 mil - $90 mil

    = $660 mil

  • Compare to:

    • Taking full limit credit = $625 = $750 - $125

    • Taking modeled credit = $650 = $750 - $100


Reinsurance and rating agency models

Cat Bond Summary

  • Indemnity based – 100% credit for modeled impact in PML layer

  • Parametric/Indexed/Modeled – reduced credit due to basis risk

  • Amount of reins credit given to Cat Bond IMPACTS balance sheet strength & FSR of issuer


Sidecars role of structured finance group

Sidecars – Role of Structured Finance Group

  • Rate the debt of sidecars and, where appropriate, issue ICRs.

  • Calculate the “tail risk” to insure the appropriate reinsurance credit is given to the sponsor of the sidecar


Determining tail risk

Determining Tail Risk?

  • Tail Risk is the risk that must be borne by the sponsor if the sidecar is not sufficiently capitalized to support the reinsurance transaction.

  • In order to determine Tail Risk, the following question must be asked: “What capital level is required in order to maintain a sidecar’s assumed FSR?”

  • The “shadow rating” for the sidecar is the same as that of the sponsoring company.


Ambest s assumed one yr average impairment rates

AMBest’s Assumed One -Yr Average Impairment Rates

A++

A+

A

A-

FSR Rating

Annual Default Probability

Return Period

Confidence Interval

0.03%

3,333

99.97%

0.06%

1,667

99.94%

0.21%

476

99.79%

0.27%

370

99.73%


Sidecar s aggregate exceedence curve

Sidecar’s Aggregate Exceedence Curve

ReturnPeriod

Stressed*Losses

(Stress factor: 110%)

ConfidenceInterval

Losses

90.00%

96.00%

98.00%

99.00%

99.60%

99.73%

99.80%

10

25

50

100

250

370

500

100,000

150,000

200,000

250,000

300,000

330,000

350,000

110,000

165,000

220,000

275,000

330,000

363,000

385,000

*Use stressed losses if not confident with modeled loss.


Calculating tail risk illustration

Calculating Tail Risk: Illustration

Previous page

A-

0.27%

99.73%

$363,000

$110,000

$53,000

$163,000

$200,000

v

  • Aggregate Exceedence Curve

  • Shadow Rating of the sidecar

  • Annual Default Probability assoc with FSR

  • Confidence Interval

  • Obtain the Required Collateral

  • Initial Sidecar Collateral

  • Retained Cash

  • Total Sidecar Collateral (step 6 + step 7)

  • Tail Risk:

    = Max 0, Required Collateral (step 5) – Total Collateral (step 8)

u

u

u

v

w

w

Source: AMBest’s Assumed 1-Year Average Impairment Rates table

u

Source: Sidecar Aggregate Exceedence Curve table

v

Source: Sidecar’s pro-forma Financial Statements

w


Sidecar summary

Sidecar Summary

  • Modeling of AEP curves extremely important

  • Direct impact on the balance sheet strength & FSR of the sponsor


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