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Casualty Exposure Rating

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Chris Svendsgaard, Swiss Re. Casualty Exposure Rating. CARe Boot Camp 7-28-05. Page 2 ... DOES NOT pick up all exposure to highest layers. Chris Svendsgaard, Swiss Re ... – PowerPoint PPT presentation

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Title: 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
16
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

30
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?

37
Avg Policy Limit over time (fake ISO data)
38
Simple Example
39
Treatment of ALAE
  • Ways reinsurance can cover ALAE
  • Pro-rata
  • Added To
  • other
  • How to handle

40
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
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