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Casualty Exposure Rating. Chris Svendsgaard, Swiss Re Casualty Exposure Rating CARe Boot Camp 7-28-05. Outline. Basics of Exposure-Rating Practical Issues. Chris Svendsgaard, Swiss Re Casualty Exposure Rating CARe Boot Camp 7-28-05. Basics of Exposure-Rating. What is exposure-rating?

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casualty exposure rating

Casualty Exposure Rating

Chris Svendsgaard, Swiss Re

Casualty Exposure Rating

CARe Boot Camp 7-28-05

outline
Outline

Basics of Exposure-Rating

Practical Issues

Chris Svendsgaard, Swiss Re

Casualty Exposure Rating

CARe Boot Camp 7-28-05

basics of exposure rating
Basics of Exposure-Rating
  • What is exposure-rating?
  • Why do it?
  • How

Chris Svendsgaard, Swiss Re

Casualty Exposure Rating

CARe Boot Camp 7-28-05

what is exposure rating
What is Exposure Rating?
  • An estimate of the covered Loss + ALAE in an excess layer
  • Based on reinsured information
    • Policy Limits
    • Insured characteristics (hazard)
  • But not
    • Reinsured loss experience

Chris Svendsgaard, Swiss Re

Casualty Exposure Rating

CARe Boot Camp 7-28-05

typical submission data
Typical Submission Data

Chris Svendsgaard, Swiss Re

Casualty Exposure Rating

CARe Boot Camp 7-28-05

typical output of exposure rating
Typical output of exposure rating

Chris Svendsgaard, Swiss Re

Casualty Exposure Rating

CARe Boot Camp 7-28-05

why exposure rate
Why Exposure-Rate
  • Provide complement of credibility for experience rate
  • Relate higher layer to lower (credible) layer
  • Price “Free Cover”
    • Layer higher than largest trended claim in the experience
  • Adjust experience rate for shift in limits/deductibles
  • “Use eclectic methods”
    • Armstrong, Long-Range Forecasting

Chris Svendsgaard, Swiss Re

Casualty Exposure Rating

CARe Boot Camp 7-28-05

why exposure rate1
Why Exposure-Rate
  • Why experience rate not 100% credible/relevant
    • Volume
    • Shift in business
    • Difficulties in estimating
      • Trend, Development, On-leveling, Data problems
  • Pricing “Free Cover” is a case where experience rate given 0% credibility

Chris Svendsgaard, Swiss Re

Casualty Exposure Rating

CARe Boot Camp 7-28-05

how to exposure rate
How to exposure-rate
  • How
    • Estimate fgu loss
    • Use severity distribution to allocate to layers

Chris Svendsgaard, Swiss Re

Casualty Exposure Rating

CARe Boot Camp 7-28-05

estimate fgu loss
Estimate fgu loss
  • Fac: Extend exposures
    • (Projected Exposures) x (Manual Rate)
  • Treaty: Loss ratio approach
    • (Projected Subject Premium) x (Estimated Loss Ratio)

Chris Svendsgaard, Swiss Re

Casualty Exposure Rating

CARe Boot Camp 7-28-05

estimate fgu loss fac extend exposures
Estimate fgu lossFac: Extend exposures
  • Manual Rate contains provisons for
    • ALAE
    • ULAE
    • Profit
    • Internal and external expense

which must be stripped out.

  • Should you INCLUDE (primary) experience mod?
  • Some LOB’s and some classes of business must be judgementally estimated
    • E.g., “a-rated” Products

Chris Svendsgaard, Swiss Re

Casualty Exposure Rating

CARe Boot Camp 7-28-05

estimate fgu loss treaty projected subject premium x loss ratio
Estimate fgu lossTreaty: Projected subject premium x loss ratio
  • Loss ratio sources
    • Client internal data
    • Client Annual Statement data
    • Peer group AS data
    • Industry AS data
    • Rate filings?
    • Underwriting audit

Chris Svendsgaard, Swiss Re

Casualty Exposure Rating

CARe Boot Camp 7-28-05

estimating loss ratios issues
Estimating Loss Ratios-Issues
  • Problems with Annual Statement data
    • AS LOB, not program
    • Net (mostly)
  • Reliability of data
    • Relevance
    • Predicted vs achieved rate-level changes
    • As-if data
  • Is the loss ratio the same for all policy limits?
  • (ditto) tables

Chris Svendsgaard, Swiss Re

Casualty Exposure Rating

CARe Boot Camp 7-28-05

use severity distribution to allocate fgu expected loss to layers
Use severity distribution to allocate fgu expected loss to layers
  • What exposes the layer?
  • Using the “LEV” function
  • Why not use ILFs?

Chris Svendsgaard, Swiss Re

Casualty Exposure Rating

CARe Boot Camp 7-28-05

what exposes the layer
What exposes the layer?

Policy Limit A

Policy Limit B

Policy Limit C

Chris Svendsgaard, Swiss Re

Casualty Exposure Rating

CARe Boot Camp 7-28-05

A B C

what exposes the layer1
What exposes the layer?

Policy Limit A

Top of Layer

Policy Limit B

Bottom of Layer

Policy Limit C

Chris Svendsgaard, Swiss Re

Casualty Exposure Rating

CARe Boot Camp 7-28-05

A B C

what exposes the layer2
What exposes the layer?

Policy Limit A

Top of Layer

Policy Limit B

Bottom of Layer

Policy Limit C

Chris Svendsgaard, Swiss Re

Casualty Exposure Rating

CARe Boot Camp 7-28-05

A B C

what exposes the layer3
What exposes the layer?

“Top”

Policy Limit A

Top of Layer

Policy Limit B

Bottom of Layer

Policy Limit C

Chris Svendsgaard, Swiss Re

Casualty Exposure Rating

CARe Boot Camp 7-28-05

A B C

what exposes the layer4
What exposes the layer?

“Bottom”

Policy Limit A

Top of Layer

Policy Limit B

Bottom of Layer

Policy Limit C

Chris Svendsgaard, Swiss Re

Casualty Exposure Rating

CARe Boot Camp 7-28-05

A B C

contribution to expected losses
Contribution to expected losses

Contribution to expected layer losses from policy =

FGU losses up to “Top” – FGU losses up to “Bottom”

Contribution to all expected losses from policy =

FGU losses up to policy limit*

______________________________________________

*assuming no deductible, SIR

Chris Svendsgaard, Swiss Re

Casualty Exposure Rating

CARe Boot Camp 7-28-05

contribution to expected losses1
Contribution to expected losses

Contribution to expected layer losses from policy =

{LEV(“Top”) – LEV(“Bottom”)} x frequency

Contribution to all expected losses from policy =

{LEV(Policy Limit) – LEV(0*)} x frequency

______________________________________________

*assuming no deductible, SIR

Chris Svendsgaard, Swiss Re

Casualty Exposure Rating

CARe Boot Camp 7-28-05

what is a lev
What is a LEV?
  • Limited Expected Value function
    • LEV(k)
      • = “Losses up to k”
      • Expected loss fgu, up to the value k, per ground-up claim
      • Also written E(X; k)
      • Also written LAS(k)
        • (Limited Avg Sev)

Chris Svendsgaard, Swiss Re

Casualty Exposure Rating

CARe Boot Camp 7-28-05

contribution to expected losses2
Contribution to expected losses

Contribution to expected layer losses from policy =

{LEV(“Top”) – LEV(“Bottom”)} x frequency

Contribution to all expected losses from policy =

{LEV(Policy Limit) – LEV(0*)} x frequency

______________________________________________

The FRACTION of fgu losses that gets into the layer does not depend on the frequency. When you divide, it drops out. Only need the LEV.

Note that aggregate limits could make this statement false.

Chris Svendsgaard, Swiss Re

Casualty Exposure Rating

CARe Boot Camp 7-28-05

lev k
LEV(k)
  • LEV(k) =
  • X = random severity amount
  • x = realization of X
  • F(x) = cdf of x = Prob (X <=x)
  • f(x) = pdf of x
  • k = “limit”

Chris Svendsgaard, Swiss Re

Casualty Exposure Rating

CARe Boot Camp 7-28-05

lev k1
LEV(k)
  • LEV(k) =

Limit

Limit

Loss amount below limit

Probability of loss amount at (or above) limit

“Probability” of loss amount below limit

Chris Svendsgaard, Swiss Re

Casualty Exposure Rating

CARe Boot Camp 7-28-05

why use lev function
Why use LEV function
  • Difference LEVs to get losses in layer
  • If expect λ losses from ground-up (fgu) then loss to layer A xs B is

Chris Svendsgaard, Swiss Re

Casualty Exposure Rating

CARe Boot Camp 7-28-05

why use lev function cont
Why use LEV function (cont)

Chris Svendsgaard, Swiss Re

Casualty Exposure Rating

CARe Boot Camp 7-28-05

lev k shortcut
LEV(k) shortcut
  • LEV(k) =

Use integration by parts

•Good for Pareto, etc. where F(x) = 1 - ….?...

and “?” is easily integrated.

Chris Svendsgaard, Swiss Re

Casualty Exposure Rating

CARe Boot Camp 7-28-05

why not use ilfs
Why not use ILFs?
  • ILFs are meant for all costs, not just losses + ALAE
    • ISO ILF = Ratio (all costs at Policy Limit) to (all costs at Basic Limit)
  • 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
practical issues
Practical Issues
  • Submission data issues
  • Trend in limits
  • Treatment of ALAE
  • Gaps in exposure-rating
  • How good is the severity distribution?

Chris Svendsgaard, Swiss Re

Casualty Exposure Rating

CARe Boot Camp 7-28-05

submission data typical submission data
Submission Data Typical Submission Data

Chris Svendsgaard, Swiss Re

Casualty Exposure Rating

CARe Boot Camp 7-28-05

submission data things to look out for
Submission Data Things to look out for
  • Policy Limit Ranges
    • But limits are round #’s
  • Numbers do not add up
    • Written premium vs. Earned
    • Historical vs. projected
  • Missing data
    • Post-merger

Chris Svendsgaard, Swiss Re

Casualty Exposure Rating

CARe Boot Camp 7-28-05

submission data more things to look out for
Submission Data More things to look out for
  • Policy Limit Warrant
  • No information about ILF table breakdown
    • Or, worse, underwriter’s vague feeling

Chris Svendsgaard, Swiss Re

Casualty Exposure Rating

CARe Boot Camp 7-28-05

iso increase limits factors
ISO Increase Limits Factors
  • By Table
    • Prem/Ops
      • 1, 2, 3 x State Group
    • Products
      • A, B, C
    • C. Auto
      • Wt Class x State Group

Chris Svendsgaard, Swiss Re

Casualty Exposure Rating

CARe Boot Camp 7-28-05

policy limit trend
Policy Limit Trend
  • “Policy limits trend with inflation”
  • How trend round numbers?

Chris Svendsgaard, Swiss Re

Casualty Exposure Rating

CARe Boot Camp 7-28-05

question

Question

You are covering the 1 x 1 layer: By how much will your exposure change if policy limits are trending at 5% per annum?

treatment of alae
Treatment of ALAE
  • Ways reinsurance can cover ALAE
    • Pro-rata
    • “Added To”
    • other
  • How to handle
joint model
Joint model

g(I,A) = reinsurance payment given indemnity I and ALAE A.

Expected reinsurance payment per fgu claim is

Good Luck.

Chris Svendsgaard, Swiss Re

Casualty Exposure Rating

CARe Boot Camp 7-28-05

simpler but less accurate ways to handle alae
Simpler (but less accurate) ways to handle ALAE
  • Pro-rata: Apply appropriate ALAE/Indmenity ratio
  • Added to:
    • Twiddle the severity distribution, and (possibly) limits, retentions, etc.
    • DOES NOT pick up all exposure to highest layers

Chris Svendsgaard, Swiss Re

Casualty Exposure Rating

CARe Boot Camp 7-28-05

gaps in traditional exposure rating
Gaps in traditional Exposure-Rating
  • Does not estimate
    • Clash
    • Extra-Contractual Obligations (ECO)
    • Declatory Judgement (DJ) expense
      • Is not ALAE?
    • “Cat” potential?
      • Asbestos, DES, . . .

Chris Svendsgaard, Swiss Re

Casualty Exposure Rating

CARe Boot Camp 7-28-05

how good is the severity distribution
How good is the severity distribution?
  • ISO data is sparse above (say) $5,000,000
    • Umbrella/XS data is often not reported to ISO
  • Mixed exponential maxes out at $10,000,000
  • Big swings in exposure rate for many tables 20042005
  • Non-bureau:
    • No distribution
    • ILF’s from client: do they care? Are they ept?
      • Is “ept” a word?

Chris Svendsgaard, Swiss Re

Casualty Exposure Rating

CARe Boot Camp 7-28-05

how good is the severity distribution1
How good is the severity distribution?
  • How reflect parameter risk?
  • How reflect possible “anti-selection” effects?
    • They buy big limits because they need to . . .?

Chris Svendsgaard, Swiss Re

Casualty Exposure Rating

CARe Boot Camp 7-28-05