Casualty Exposure Rating Chris Svendsgaard, Swiss Re Casualty Exposure Rating CARe Boot Camp...
-
Upload
christine-haynes -
Category
Documents
-
view
222 -
download
5
Transcript of Casualty Exposure Rating Chris Svendsgaard, Swiss Re Casualty Exposure Rating CARe Boot Camp...
Page 2
Outline
Basics of Exposure-Rating
Practical Issues
Chris Svendsgaard, Swiss ReCasualty Exposure RatingCARe Boot Camp 7-28-05
Page 3
Basics of Exposure-Rating
What is exposure-rating?
Why do it?
How
Chris Svendsgaard, Swiss ReCasualty Exposure RatingCARe Boot Camp 7-28-05
Page 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 ReCasualty Exposure RatingCARe Boot Camp 7-28-05
Page 5
Typical Submission Data
Chris Svendsgaard, Swiss ReCasualty Exposure RatingCARe Boot Camp 7-28-05
Policy Limit Range
Bottomto Top
Policy Count
Premium ($000)
1 0 250,000 7 20
2 250,001 500,000 100 250
3 500,001 1,000,000 200 700
4 1,000,001 2,000,000 700 3,500
5 2,000,001 5,000,000 30 500
Page 6
Typical output of exposure rating
Chris Svendsgaard, Swiss ReCasualty Exposure RatingCARe Boot Camp 7-28-05
Policy Limit RangeLayer = 500x500
Bottom to Top
Loss To Layer ($000)
1 0 250,000 0
2 250,001 500,000 0
3 500,001 1,000,000 200
4 1,000,001 2,000,000 700
5 2,000,001 5,000,000 100
Page 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 ReCasualty Exposure RatingCARe Boot Camp 7-28-05
Page 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 ReCasualty Exposure RatingCARe Boot Camp 7-28-05
Page 9
How to exposure-rate
How
– Estimate fgu loss
– Use severity distribution to allocate to layers
Chris Svendsgaard, Swiss ReCasualty Exposure RatingCARe Boot Camp 7-28-05
Page 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 ReCasualty Exposure RatingCARe Boot Camp 7-28-05
Page 11
Estimate fgu loss
Fac: 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 ReCasualty Exposure RatingCARe Boot Camp 7-28-05
Page 12
Estimate fgu loss
Treaty: 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 ReCasualty Exposure RatingCARe Boot Camp 7-28-05
Page 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 ReCasualty Exposure RatingCARe Boot Camp 7-28-05
Page 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 ReCasualty Exposure RatingCARe Boot Camp 7-28-05
Page 15
What exposes the layer?
Chris Svendsgaard, Swiss ReCasualty Exposure RatingCARe Boot Camp 7-28-05
A B C
Policy Limit A
Policy Limit B
Policy Limit C
Page 16
What exposes the layer?
Chris Svendsgaard, Swiss ReCasualty Exposure RatingCARe Boot Camp 7-28-05
A B C
Top of Layer
Bottom of Layer
Policy Limit A
Policy Limit B
Policy Limit C
Page 17
What exposes the layer?
Chris Svendsgaard, Swiss ReCasualty Exposure RatingCARe Boot Camp 7-28-05
A B C
Top of Layer
Bottom of Layer
Policy Limit A
Policy Limit B
Policy Limit C
Page 18
What exposes the layer?
Chris Svendsgaard, Swiss ReCasualty Exposure RatingCARe Boot Camp 7-28-05
A B C
Top of Layer
Bottom of Layer
Policy Limit A
Policy Limit B
Policy Limit C
“Top”
Page 19
What exposes the layer?
Chris Svendsgaard, Swiss ReCasualty Exposure RatingCARe Boot Camp 7-28-05
A B C
Top of Layer
Bottom of Layer
Policy Limit A
Policy Limit B
Policy Limit C
“Bottom”
Page 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, SIRChris Svendsgaard, Swiss ReCasualty Exposure RatingCARe Boot Camp 7-28-05
Page 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 ReCasualty Exposure RatingCARe Boot Camp 7-28-05
Page 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 ReCasualty Exposure RatingCARe Boot Camp 7-28-05
Page 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 ReCasualty Exposure RatingCARe Boot Camp 7-28-05
Page 24
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 ReCasualty Exposure RatingCARe Boot Camp 7-28-05
k
kFkdxxxf0
)](1[)(
Page 25
LEV(k)
LEV(k) =
Chris Svendsgaard, Swiss ReCasualty Exposure RatingCARe Boot Camp 7-28-05
k
kFkdxxxf0
)](1[)(
Limit
Loss amount below limit
“Probability” of loss amount below limit
Limit
Probability of loss amount at (or above) limit
Page 26
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 ReCasualty Exposure RatingCARe Boot Camp 7-28-05
))](1[)()(
BA
B
BAFAdxxfBx
Page 27
Why use LEV function (cont)
Chris Svendsgaard, Swiss ReCasualty Exposure RatingCARe Boot Camp 7-28-05
))](1[)()(
BA
B
BAFAdxxfBx
)](1[)](1[)()( BFBBAFAdxxfxBA
B
)]()([ BLEVBALEV
Page 28
LEV(k) shortcut
LEV(k) =
k
kFkdxxxf0
)](1[)(
Chris Svendsgaard, Swiss ReCasualty Exposure RatingCARe Boot Camp 7-28-05
k
dxxF0
)(1
Use integration by parts
•Good for Pareto, etc. where F(x) = 1 - ….?...
and “?” is easily integrated.
Page 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
Page 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 ReCasualty Exposure RatingCARe Boot Camp 7-28-05
Page 31
Submission Data
Typical Submission Data
Chris Svendsgaard, Swiss ReCasualty Exposure RatingCARe Boot Camp 7-28-05
Policy Limit Range
Bottomto Top
Policy Count Prem %
1 0 250,000 7 0.1%
2 250,001 500,000 100 2%
3 500,001 1,000,000 200 10%
4 1,000,001 2,000,000 700 80%
5 2,000,001 5,000,000 30 2%
Page 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 ReCasualty Exposure RatingCARe Boot Camp 7-28-05
Page 33
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 ReCasualty Exposure RatingCARe Boot Camp 7-28-05
Page 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 ReCasualty Exposure RatingCARe Boot Camp 7-28-05
Page 35
Policy Limit Trend
“Policy limits trend with inflation”
How trend round numbers?
Chris Svendsgaard, Swiss ReCasualty Exposure RatingCARe Boot Camp 7-28-05
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?
Page 37
Avg Policy Limit over time (fake ISO data)
0
100
200
300
400
500
600
700
1980
1982
1984
1986
1988
1990
1992
1994
1996
AvgLimit
Page 38
Simple Example
Limit 1,000,000 2,000,000 Average Limit
2001 Weight
95% 5% 1,050,000
2002 Weight
90% 10% 1,100,000
Page 39
Treatment of ALAE
Ways reinsurance can cover ALAE
– Pro-rata
– “Added To”
– other
How to handle
Page 40
Joint model
Chris Svendsgaard, Swiss ReCasualty Exposure RatingCARe Boot Camp 7-28-05
0
0 0
),(),(
),(),(
PL
tPolicyLimi
dIdAAIfAPLg
dIdAAIfAIg
g(I,A) = reinsurance payment given indemnity I and ALAE A.
Expected reinsurance payment per fgu claim is
Good Luck.
Page 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 ReCasualty Exposure RatingCARe Boot Camp 7-28-05
Page 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 ReCasualty Exposure RatingCARe Boot Camp 7-28-05
Page 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 20042005
Non-bureau:
– No distribution
– ILF’s from client: do they care? Are they ept?
- Is “ept” a word?Chris Svendsgaard, Swiss ReCasualty Exposure RatingCARe Boot Camp 7-28-05