Casualty Exposure Rating

1
Casualty Exposure Rating
Chris Svendsgaard, Swiss Re Casualty Exposure
Rating CARe Boot Camp 7-28-05
2
Outline

• Basics of Exposure-Rating
• Practical Issues

Chris Svendsgaard, Swiss Re Casualty Exposure
Rating CARe Boot Camp 7-28-05
3
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
4
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
5
Typical Submission Data
Chris Svendsgaard, Swiss Re Casualty Exposure
Rating CARe Boot Camp 7-28-05
6
Typical output of exposure rating
Chris Svendsgaard, Swiss Re Casualty Exposure
Rating CARe Boot Camp 7-28-05
7
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
8
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
9
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
10
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
11
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 LOBs 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
12
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
13
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
14
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
15
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
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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
17
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
18
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
19
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
20
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
21
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
22
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
23
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
24
LEV(k)

• LEV(k)
• X random severity amount
• x realization of X
• F(x) cdf of x Prob (X ltx)
• f(x) pdf of x
• k limit

Chris Svendsgaard, Swiss Re Casualty Exposure
Rating CARe Boot Camp 7-28-05
25
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
26
Why use LEV function

• Difference LEVs to get losses in layer
• If expect ? 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
27
Why use LEV function (cont)
Chris Svendsgaard, Swiss Re Casualty Exposure
Rating CARe Boot Camp 7-28-05
28
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
29
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

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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
31
Submission Data Typical Submission Data
Chris Svendsgaard, Swiss Re Casualty Exposure
Rating CARe Boot Camp 7-28-05
32
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
33
Submission Data More things to look out for

• Policy Limit Warrant
• No information about ILF table breakdown
• Or, worse, underwriters vague feeling

Chris Svendsgaard, Swiss Re Casualty Exposure
Rating CARe Boot Camp 7-28-05
34
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
35
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
36
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?

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Avg Policy Limit over time (fake ISO data)
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Simple Example
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Treatment of ALAE

• Ways reinsurance can cover ALAE
• Pro-rata
• Added To
• other
• How to handle

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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
41
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
42
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
43
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
• ILFs 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
44
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