Chris Svendsgaard, FCAS, CPCU, MAAA Swiss Re 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

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

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

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

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

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

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

Policy Reinsurance Exposure Rating Concepts Reinsurance Limit Policy Limit Retention Deductible

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

Deductible = 100 Policy Limit = 1,000,000 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

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

Cost at Reinsurance Top - Cost at Reinsurance Bottom 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

Cost function Cost Retained Part

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

ILFs are meant for all costs, not just losses + ALAE Using ISO ILFs: 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

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

Limited Expected Value Average limited severity

Sample ELF Calculation

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

ISO ILF Definition Ratio of Costs at policy limit sold Costs at basic limit

Costs (expressed per occurrence) 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)

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

Property Scale 100% 100%

Sometimes people use “EML” instead of TIV 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