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Pricing Aggregate Risk and Credit Risk for Risk Sharing Entities

Pricing Aggregate Risk and Credit Risk for Risk Sharing Entities. John D. Deacon CAS Ratemaking Seminar Ratemaking Call Paper Tampa, FL March 7-8, 2002. Quotation:. ”The best and safest thing is to keep BALANCE in your life…If you can do that and live that way, you are really a wise man”

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Pricing Aggregate Risk and Credit Risk for Risk Sharing Entities

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  1. Pricing Aggregate Risk and Credit Risk for Risk Sharing Entities John D. Deacon CAS Ratemaking Seminar Ratemaking Call Paper Tampa, FL March 7-8, 2002

  2. Quotation: ”The best and safest thing is to keep BALANCE in your life…If you can do that and live that way, you are really a wise man” -Euripides 406 B.C.

  3. Our Context: • Deals involving insurance entities which: >SHARE RISK (RSE) >DESIRE AGGREGATE REINSURANCE • Focus on deals with <$10M annual losses • Goal: price adequately for aggregate and credit risk

  4. Our Context con’t: • Why would an entity want to share risk? • How do these entities share risk? • Examples of entities which share risk...

  5. Example of a DealParameters: • Homogeneous captive • Per occurrence limit = $500k • Annual aggregate limit = 90% gross prem

  6. Aggregate RiskSimulation Basics: • Methods of simulation: 1. Frequency/severity - complex and precise 2. Loss ratios - simple and accurate • To simulate loss ratios we need: • distribution (Lognormal) • mean • variance

  7. Aggregate RiskExample Historical Results:

  8. Aggregate RiskGraphical Simulation Results: Captive Loss Agg Loss 60% expected 90% agg attach pt Limited Loss Ratios (% gross prem)

  9. Aggregate RiskPricing: 90% LR agg attach pt

  10. Are we done yet? • What about credit risk? • What IS credit risk? • When do we get to BALANCE?

  11. Credit Risk FundamentalsBalance: Credit Risk Aggregate Risk Aggregate Attachment Point Reducing risk of credit losses by decreasing attachment increases agg risk Reducing risk of agg losses by increasing agg attachment increases credit risk

  12. Credit Risk FundamentalsLR outcomes and how covered “GAP” Collateral incl. Inv Inc RSE Loss Funds Agg Loss Potential Credit Risk Probable RSE Equity RSE Expected Losses Agg Attach Point %ile 0% 50% 100%

  13. Credit RiskPricing Steps: Easy as ABC(D) Determine: Size of the gap Probability of losses above loss funds How much equity the entity (RSE) has “Creditworthiness” - Probability of tapping into this equity A B C D

  14. Probability wtd Loss less Probability wtd Equity [(Prem x Gap) x Prob[LR>loss funds] less RSE Equity x Creditworthiness ] Credit RiskPricing: A $7M x 36% x x B 35.5% - - $3M C x x 25% D divided by prem =1.7%

  15. Credit RiskAssumptions: • Loss distribution accurately depicts reality • Credit risk is easily modeled • Accurate liabilities on RSE financial stmts

  16. Future Enhancements Acknowledge multi-year exposures: • incorporate risk of RSE uncertain liabilities • equity not all allocated to current year

  17. Close When pricing deals risk with agg cover: • Price the agg • Structure a deal with BALANCE • Price the credit risk x - x A B C D

  18. Questions?

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