Pricing Aggregate Risk and Credit Risk for Risk

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Pricing Aggregate Risk and Credit Risk for Risk Sharing Entities John D. Deacon CAS

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

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.

Our Context: • Deals involving insurance entities which: >SHARE RISK (RSE) >DESIRE AGGREGATE REINSURANCE

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

Our Context con’t: • Why would an entity want to share risk? • How

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

Example of a Deal Parameters: • Homogeneous captive • Per occurrence limit = $500

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

Aggregate Risk Simulation Basics: • Methods of simulation: 1. Frequency/severity - complex and precise

Aggregate Risk Simulation 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

Aggregate Risk Example Historical Results:

Aggregate Risk Example Historical Results:

Aggregate Risk Graphical Simulation Results: Captive Loss Agg Loss 60% expected Limited Loss Ratios

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

Aggregate Risk Pricing: 90% LR agg attach pt

Aggregate Risk Pricing: 90% LR agg attach pt

Are we done yet? • What about credit risk? • What IS credit risk?

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

Credit Risk Fundamentals Balance: Credit Risk Aggregate Attachment Point • Reducing risk of credit

Credit Risk Fundamentals Balance: Credit 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

Credit Risk Fundamentals LR outcomes and how covered “GAP” RSE Loss Funds Collateral incl.

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

Credit Risk Pricing Steps: Easy as ABC(D) Determine: A Size of the gap B

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

Credit Risk Pricing: Probability wtd Loss [(Prem x Gap) x Prob[LR>loss funds] less Probability

Credit Risk Pricing: Probability wtd Loss [(Prem x Gap) x Prob[LR>loss funds] less Probability wtd Equity RSE Equity x Creditworthiness ] A B $7 M x 36% x 35. 5% - - C $3 M x 25% x x D divided by prem =1. 7%

Credit Risk Assumptions: • Loss distribution accurately depicts reality • Credit risk is easily

Credit Risk Assumptions: • Loss distribution accurately depicts reality • Credit risk is easily modeled • Accurate liabilities on RSE financial stmts

Future Enhancements Acknowledge multi-year exposures: – incorporate risk of RSE uncertain liabilities – equity

Future Enhancements Acknowledge multi-year exposures: – incorporate risk of RSE uncertain liabilities – equity not allocated to current year

Close When pricing deals risk with agg cover: • Price the agg • Structure

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

Questions?

Questions?