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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

Exposure Rating

Chris Svendsgaard, FCAS, CPCU, MAAA

Swiss Re

outline
Outline
  • Definition of exposure rating
  • Applications of exposure rating
  • Steps in exposure rating
definition of 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
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 rating1
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 rating2
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 rating3
Applications of exposure rating

5. Property catastrophe programs

  • Extensive exposure information
  • Engineering/meteorological/geophysical models
  • Not covered in this talk
basic reinsurance pricing concept
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
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
slide10

Exposure Rating Concepts

Policy

Reinsurance

Reinsurance Limit

PolicyLimit

Retention

Deductible

slide11

Exposure Rating Concepts

Policy

Reinsurance

Exposes Layer

Reinsurance Limit

PolicyLimit

Retention

Graphic Design by Piet Mondrian

Deductible

concepts example
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

slide13

General Equation

ELF =

Expected losses & ALAE for exposed layer

Expected losses & ALAE for primary policy

slide14

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

slide15

Cost function

Cost

Retained Part

slide16

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

problems with 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
A Solution
  • Use Limited Expected Value function for “Cost” function
  • Adjust separately for ALAE
limited expected value
Limited Expected Value
  • Average limited severity
slide20

Sample ELF Calculation

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

iso ilf definition
ISO ILF Definition
  • By Table
    • Prem/Ops
      • 1, 2, 3 x State Group
    • Products
      • A, B, C
    • C. Auto
      • Wt Class x State Group
iso ilf definition1
ISO ILF Definition
  • Ratio of
    • Costs at policy limit sold
    • Costs at basic limit
iso ilf definition2
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
Property Cost Function
  • “Scales”
    • Often by peril
      • Fire, Wind, EQ
    • Lloyd’s/Salzmann/Y (Swiss Re)/Ludwig (Hartford)
    • PSOLD (ISO)
property scale
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