Title: Casualty Exposure Rating
1Casualty Exposure Rating
Chris Svendsgaard, Swiss Re Casualty Exposure
Rating CARe Boot Camp 7-28-05
2Outline
- Basics of Exposure-Rating
- Practical Issues
Chris Svendsgaard, Swiss Re Casualty Exposure
Rating CARe Boot Camp 7-28-05
3Basics of Exposure-Rating
- What is exposure-rating?
- Why do it?
- How
Chris Svendsgaard, Swiss Re Casualty Exposure
Rating CARe Boot Camp 7-28-05
4What 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
5Typical Submission Data
Chris Svendsgaard, Swiss Re Casualty Exposure
Rating CARe Boot Camp 7-28-05
6Typical output of exposure rating
Chris Svendsgaard, Swiss Re Casualty Exposure
Rating CARe Boot Camp 7-28-05
7Why 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
8Why 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
9How 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
10Estimate 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
11Estimate 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
12Estimate 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
13Estimating 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
14Use 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
15What 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
16What 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
17What 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
18What 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
19What 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
20Contribution 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
21Contribution 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
22What 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
23Contribution 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
24LEV(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
25LEV(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
26Why 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
27Why use LEV function (cont)
Chris Svendsgaard, Swiss Re Casualty Exposure
Rating CARe Boot Camp 7-28-05
28LEV(k) shortcut
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
29Why 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
30Practical 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
31Submission Data Typical Submission Data
Chris Svendsgaard, Swiss Re Casualty Exposure
Rating CARe Boot Camp 7-28-05
32Submission 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
33Submission 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
34ISO 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
35Policy Limit Trend
- Policy limits trend with inflation
- How trend round numbers?
Chris Svendsgaard, Swiss Re Casualty Exposure
Rating CARe Boot Camp 7-28-05
36Question
- You are covering the 1 x 1 layer By how much
will your exposure change if policy limits are
trending at 5 per annum?
37Avg Policy Limit over time (fake ISO data)
38Simple Example
39Treatment of ALAE
- Ways reinsurance can cover ALAE
- Pro-rata
- Added To
- other
- How to handle
40Joint 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
41Simpler (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
42Gaps 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
43How 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
44How 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