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Exposure Rating

Exposure Rating. Chris Svendsgaard, FCAS, CPCU, MAAA Swiss Re. Outline. Definition of exposure rating Applications of exposure rating Steps in exposure rating. Definition of Exposure Rating . Use exposure information to price a reinsurance risk Don’t use risk’s loss information.

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Exposure Rating

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  1. Exposure Rating Chris Svendsgaard, FCAS, CPCU, MAAA Swiss Re

  2. Outline • Definition of exposure rating • Applications of exposure rating • Steps in exposure rating

  3. Definition of Exposure Rating • Use exposure information to price a reinsurance risk • Don’t use risk’s loss information

  4. Applications of exposure rating 1. Casualty excess of loss treaties 2. Casualty excess of loss facultative certificates 3. Property per risk excess of loss treaties 4. Property per risk facultative certificates 5. Property catastrophe programs

  5. Applications of exposure rating 1. Casualty excess of loss treaties 2. Casualty excess of loss facultative certificates • These two are rated similarly. • Differences • Treaty starts with subject premium, cert starts with exposures • Treaty is mix of policy limits, increased limits tables

  6. Applications of exposure rating 3. Property per risk excess of loss treaties 4. Property per risk facultative certificates • Rated similarly--Differences: • Treaty starts with subject premium, cert starts with exposures • Treaty is mix of occupancies, has more total insured values • Certs are exposure-rated only, usually • Certs usually cover more perils

  7. Applications of exposure rating 5. Property catastrophe programs • Extensive exposure information • Engineering/meteorological/geophysical models • Not covered in this talk

  8. Basic Reinsurance Pricing Concept • Calculate expected losses and expenses in layer • Discount for the time value of money • Load the expected losses for internal expenses, commission, brokerage, and risk • Express as a percentage of premium, if necessary

  9. Basic Formula Loss in layer = Premium x Expected Loss Ratio x Excess Layer Factor = (Premium x Expected Loss Ratio) x Excess Layer Factor • = (Expected Primary Loss & ALAE) x Excess Layer Factor

  10. Exposure Rating Concepts Policy Reinsurance Reinsurance Limit PolicyLimit Retention Deductible

  11. Exposure Rating Concepts Policy Reinsurance Exposes Layer Reinsurance Limit PolicyLimit Retention Graphic Design by Piet Mondrian Deductible

  12. Concepts: Example • Deductible = 100 Policy Limit = 1,000,000 • Retention = 250,000 R. Limit = 750,000 Ground-up Primary Reinsurance Loss Payment Payment 250,001 249,901 0 250,101 250,001 1 500,000 499,900 249,900 1,000,000 999,900 749,900 1,000,100 1,000,000 750,000 5,000,000 1,000,000 750,000

  13. General Equation ELF = Expected losses & ALAE for exposed layer Expected losses & ALAE for primary policy

  14. General Equation ELF = Cost at Reinsurance Top - Cost at Reinsurance Bottom Cost at Policy Top - Cost at Policy Bottom Cost at Top = Cost of claims limited to “Top” , etc. R. Top = Highest ground-up claim amount where R. pays = Min (Deductible + Pol. Limit, Ded. + Retention + R. Limit) usually P. Top = Policy Limit + Deductible P. Bottom = Deductible

  15. Cost function Cost Retained Part

  16. General Equation (wrong version) ELF = ILF(Ded+RT+LIM) - ILF(Ded+RT) ILF(Ded+PL) - ILF(Ded) Where: LIM = Reinsurance Limit RT = Retention Ded = Deductible PL = Policy Limit

  17. Problems with ILFs • ILFs are meant for all costs, not just losses + ALAE • Using ISO ILFs: • ISO Risk Load gets in • ULAE creeps in • Aggregate limits distort values (depending on which ILFs you use) • ALAE drops out (because is loaded 100% in basic limit) • Reinsurance treatment of ALAE not reflected

  18. A Solution • Use Limited Expected Value function for “Cost” function • Adjust separately for ALAE

  19. Limited Expected Value • Average limited severity

  20. Sample ELF Calculation ELF = (12,300 - 8,200) / (12,300 - 99) = 4,100 / 12,201 = 34%

  21. ISO ILF Definition • By Table • Prem/Ops • 1, 2, 3 x State Group • Products • A, B, C • C. Auto • Wt Class x State Group

  22. ISO ILF Definition • Ratio of • Costs at policy limit sold • Costs at basic limit

  23. ISO ILF Definition • Costs (expressed per occurrence) • Expected Losses, limited by policy per-occurrence limit • Expected ALAE (same for all limits) • ULAE (fixe % of sum of loss + ALAE) • Risk Load (increases with policy limit)

  24. Property Cost Function • “Scales” • Often by peril • Fire, Wind, EQ • Lloyd’s/Salzmann/Y (Swiss Re)/Ludwig (Hartford) • PSOLD (ISO)

  25. Property Scale 100% 100%

  26. Property Scale • USUALLY • x axis is Retention/Total Insured Value • y axis is Limited Expected Value(Ret)/Expected Value • These are for the severity distribution • Sometimes people use “EML” instead of TIV

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