Transcript Download Handout 3

Solving the Puzzle:
The Hybrid Reinsurance
Pricing Method
John Buchanan
CAS Ratemaking Seminar – REI 4
March 17, 2008
CAS RM 2008 – The Hybrid Reinsurance Pricing Method
1
Agenda
• Traditional Methods Recap
• Hybrid Method: Experience / Exposure
–
–
–
–
Reserving analogy
Fundamental assumptions
Basic steps of the paper
Case studies
• Hybrid roll-ups
– Testing default parameters
Appendix
– Other considerations in attempting to solve the puzzle
– Underwriting cycle: soft market experience model bias
2
Traditional Methods Recap
Experience
• Relevant parameter
defaults/overrides for:
– LDFs (excess layers)
– Trends (severity, frequency,
exposure)
– Rate changes
– LOB/Hazard Grp indicators
• Adjust for historical
changes in:
– Policy limits
– Exposure differences
o Careful “as-if”
Exposure
• Relevant parameters
defaults/overrides for:
–
–
–
–
ILFs (or ELFs, PropSOLD)
Direct loss ratios (on-level)
ALAE loads
Policy profile (LOB, HzdGrp)
o Limit/subLOB allocations
• Adjust for expected
changes in:
– Rating year policy limits
– Rating year exposures
expected to be written
3
Hybrid Pricing Method
Reserving Analogy
Responsiveness
Mix
Stability
Reserving
LDF
Older Years
BF
---->
ELR
Newer Years
Pricing
Experience
Lower Layers
Hybrid
Exposure
Upper Layers
From paper accepted by CAS Variance
---->
– John Buchanan / Mike Angelina
THE HYBRID REINSURANCE PRICING METHOD: A PRACTITIONER’S GUIDE
4
Fundamental Assumptions
of the Hybrid Method
• In theory, with perfect modeling and sufficient data
the results under the Experience and Exposure
methods will be identical. (never attainable)
• In practice,
– if the model and parameter selections for both
Experience and Exposure methods are proper and
relevant,
– then the results from these methods will be similar,
– except for credibility and random variations.
• Lower layer experience helps predict higher less
credible layers.
• Frequency is a more stable indicator than total burn
estimates.
5
Basic Steps of The Hybrid Method
1. Estimate Experience burns & counts
2. Estimate Exposure burns & counts
3. Calculate Experience/Exposure frequency ratio by
attachment point
4. Review Hybrid frequency ratio patterns
- Adjust experience or exposure models if needed and
re-estimate burns
5. Similarly review excess severities and/or excess
burns
6. Combine Hybrid frequency/severity results
7. Determine overall weight to give Hybrid
6
Step 4-Review Hybrid Frequency Ratios
(Example #1 from Paper)
Exposure Method
Indicated
Benchmark
Exposure Burn Excess Claim
(%)
Counts
Layer
50,000
100,000
150,000
500,000
250,000
1,000,000
xs
xs
xs
xs
xs
xs
Total
200,000
250,000
350,000
500,000
750,000
1,000,000
1.51%
1.92%
1.33%
1.54%
0.27%
0.27%
1.81%
38.05
29.80
15.34
6.00
1.90
0.77
Hybrid Method
Indicated
Exper/Expos
Freq Ratio
71.1%
82.3%
78.6%
44.8%
28.3%
46.8%
75.1%
Important Selection
Selected
Selected Excess
Exper/Expos
Claim Counts
Freq Ratio
80.0%
80.0%
80.0%
80.0%
80.0%
80.0%
80.0%
80.0%
30.44
23.84
12.27
4.80
1.52
0.61
6.00 expos x 80.0%
7
Steps 1-7: Bringing it All Together
A. Experience Method - Traditional Burning Cost (USD)
C. Experience / Exposure Indicated and Selected Ratios
Subject Premium: 111,000,000
1
2
3
5
6
7
8
10
11
12
13
14
15
Implied
Severity
Indicated
Exper/Expos
Freq Ratio
Selected
Exper/Expos
Freq Ratio
Base Layer
Weights
Devt/Trended
# of Claims
Actual # of
Claims
Weight to
Experience
Severity
[6/7]
[A7/B7]
48,874
68,919
81,695
169,751
176,822
86,177
71.1%
82.3%
78.6%
44.8%
28.3%
46.8%
75.1%
80.0%
80.0%
80.0%
80.0%
80.0%
80.0%
80.0%
39.9%
36.5%
18.1%
4.5%
0.6%
0.4%
100.0%
189.4
173.4
85.8
21.3
3.1
2.1
475.0
178
129
54
11
2
0
374
100.0%
100.0%
85.0%
22.5%
5.0%
2.5%
12
13
Experience Method - TBC
Layer
(Limit xs Retention)
Indicated
Experience
Burn (%)
Ultimate Loss Excess Claim
(USD)
Counts
[5xSPI]
1
2
3
4
5
6
50,000
100,000
150,000
500,000
250,000
1,000,000
xs
xs
xs
xs
xs
xs
200,000
250,000
350,000
500,000
750,000
1,000,000
Total
1.19%
1.52%
0.89%
0.41%
0.09%
0.03%
1,322,008
1,691,358
984,586
456,121
95,024
30,874
0.44%
486,996
27.05
24.54
12.05
2.69
0.54
0.36
2.69
181,241
[f/ 13]
80.0%
B. Exposure Method (USD)
1
2
3
Layer
(Limit xs Retention)
D. Hybrid Method (USD)
5
Indicated
Exposure
Burn (%)
6
7
Exposure Method
Benchmark
Indicated
Ultimate Loss Excess Claim
(USD)
Counts
[5xSPI]
8
10
Benchmark
Severity
Selected Excess
Claim Counts
11
Hybrid Method
Selected
Selected
Hybrid
Severity (Wtd)
Burn (%)
Selected
Ultimate Loss
[6/7]
[B7xC11]
[f/ A8,B8,C15]
[13/SPI]
[10x11]
1
2
3
50,000
100,000
150,000
xs
xs
xs
200,000
250,000
350,000
1.51%
1.92%
1.33%
1,671,633
2,134,498
1,481,529
38.05
29.80
15.34
43,937
71,616
96,588
30.44
23.84
12.27
48,874
68,919
84,218
1,487,569
1,643,296
1,033,439
4
500,000
xs
500,000
1.54%
1,709,680
6.00
285,088
4.80
259,137
5
250,000
xs
750,000
0.27%
296,553
1.90
156,416
1.52
157,436
6
1,000,000
xs
1,000,000
0.27%
304,773
398,338
0.61
390,534
1.81%
2,014,454
0.77
6.00
1.34%
1.48%
0.93%
1.12%
0.22%
0.22%
1.34%
1,482,284
Total
335,909
1,243,242
238,790
239,042
8
Exposure vs. Experience
(Example #2 from REI-3 Case Study)
# of Excess Claims
25.0
23.5
20.3
Exposure
Experience -BC
20.0
15.0
10.2
10.0
9.6
5.6 6.2
5.0
4.1
5.6
0.0
75,000
•
•
•
100,000
150,000
Attachment Point
200,000
In this case study, there is an inconsistent relationship as move
up the attachment points
While the low layer Experience is about half of Exposure, the
upper layers are about equal to Exposure
Need more investigation to reconcile and help solve the puzzle
9
Adjusting Experience for historically higher policy limits
(Example #2 from paper)
Hybrid Analysis - Example #2 (before investigation)
1
2
3
Layer
(Limit xs Retention)
4
5
6
Experience
Excess Claim
Counts
Exposure
Excess Claim
Counts
Indicated
Exper/Expos
Freq Ratio
7
8
Indicated
Devt &
Exper/Expos Trended #
Burn Ratio
of Claims
[4/5]
1
2
3
4
125,000
100,000
350,000
300,000
xs
xs
xs
xs
75,000
100,000
150,000
200,000
10.2
9.6
6.2
5.6
23.5
20.9
5.6
4.1
Total / Average
43.4%
45.8%
110.1%
135.5%
72.9%
43.4%
47.3%
86.3%
96.1%
61.9%
54.8
51.3
32.9
28.4
Hybrid Summary - Example #2 (after investigation)
1
2
3
Layer
(Limit xs Retention)
4
5
6
Experience
Excess Claim
Counts
Exposure
Excess Claim
Counts
Indicated
Exper/Expos
Freq Ratio
7
8
Indicated
Devt &
Exper/Expos Trended # of
Burn Ratio
Claims
[4/5]
1
2
3
4
125,000
100,000
350,000
300,000
xs
xs
xs
xs
75,000
100,000
150,000
200,000
10.2
9.1
3.7
2.2
23.5
20.9
5.6
4.1
Total / Average
Selected Hybrid frequency ratio
43.4%
43.5%
66.1%
54.2%
49.7%
50.0%
43.4%
44.9%
56.1%
38.4%
45.5%
54.8
51.3
32.9
28.4
10
Adjusting Exposure for clash potential
(Example #3 from Paper)
Hybrid Analysis - Example #3 (before investigation)
1
2
3
4
Experience
Excess Claim
Counts
Layer
(Limit xs Retention)
5
6
7
Experience Method - TBC
Exposure
Indicated
Indicated
Excess Claim
Exper/Expos
Exper/Expos
Counts
Freq Ratio
Burn Ratio
8
Developed &
Trended # of
Claims
[4/5]
1
2
3
4
5
6
7
8
1,000,000
1,000,000
1,500,000
2,500,000
2,500,000
10,000,000
15,000,000
25,000,000
xs
xs
xs
xs
xs
xs
xs
xs
1,000,000
2,000,000
3,500,000
5,000,000
7,500,000
10,000,000
20,000,000
35,000,000
16.0
7.5
3.4
2.1
1.06
0.64
0.43
0.00
23.5
8.8
4.5
3.0
1.32
0.48
0.11
0.03
Total / Average
67.9%
84.5%
76.3%
71.9%
81.0%
134.0%
386.4%
0.0%
78.8%
77.9%
85.6%
91.7%
73.9%
74.8%
212.9%
372.7%
0.0%
90.7%
106.7
48.1
22.3
14.7
8.5
4.4
2.5
0.0
7
8
Hybrid Analysis - Example #3 (after investigation)
1
2
3
Layer
(Limit xs Retention)
4
Experience
Excess Claim
Counts
5
6
Experience Method - TBC
Exposure
Indicated
Indicated
Excess Claim
Exper/Expos
Exper/Expos
Counts
Freq Ratio
Burn Ratio
Developed &
Trended # of
Claims
[4/5]
1
2
3
4
5
6
7
8
1,000,000
1,000,000
1,500,000
2,500,000
2,500,000
10,000,000
15,000,000
25,000,000
xs
xs
xs
xs
xs
xs
xs
xs
1,000,000
2,000,000
3,500,000
5,000,000
7,500,000
10,000,000
20,000,000
35,000,000
16.0
7.5
3.4
2.1
1.06
0.64
0.43
0.00
22.2
8.8
4.5
3.0
1.47
1.07
0.48
0.13
Total / Average
Selected Hybrid frequency ratio
71.9%
85.1%
75.4%
70.6%
72.4%
59.8%
88.6%
0.0%
75.2%
85.0%
81.7%
86.2%
90.4%
71.2%
66.8%
89.5%
79.9%
0.0%
82.7%
106.7
48.1
22.3
14.7
8.5
4.4
2.5
0.0
11
Benefits of Hybrid Method
• One of main benefits is questioning Experience
and Exposure Selections
– To the extent credible results don’t line up, this provides
pressure to the various default parameters
– For example, there would be downward pressure on
default exposure ILF curves or loss ratios if
• Exposure consistently higher than experience, and
• Credible experience and experience rating factors
• A well constructed Hybrid method can sometimes
be given 100% weight if credible
• Can roll-up Hybrid results across accounts to
evaluate pressure on industry defaults
12
Hybrid roll-ups: Test of Default Factors
Well below 100%,
pressure to reduce expos
params or increase exper
params…but credible??
13
Other Considerations in
Attempting to Solve the Puzzle
Appendix
14
Inspect Hybrid Ratios
Exper/
Expos
Ratio
Layers
Ideal Situation
- No noticeable slope to ratio of Experience/Exposure
- Random fluctuation around mean
From forthcoming paper
- THE HYBRID REINSURANCE PRICING METHOD:
A PRACTITIONER’S GUIDE
15
Pressure Indicators:
Inspect Burn ratios by Year
Burn
Burn
Years
Upward slope pressure indicators:
- Not enough trend
- Too much LDF
- Too much later year rate change
- Too much earlier year rate change
…
Years
Downward slope pressure indicators:
- Too much trend
- Not enough LDF
- Not enough later year rate change
- Not enough earlier year rate change
…
16
Assessing Credibility of
Exposure Method
• Assess confidence due to:
–
–
–
–
–
–
Exposure curve selected
Exposure profile
Source of hazard or sub-line information
Prediction of next years primary loss ratio
Percentage of non-modeled exposure, clash, etc.
Company strategy and ability to realize strategy
• Possibly take questionnaire / scoring
approach to mechanize (Patrik/Mashitz)
17
Assessing Credibility of
Experience Method
• Assess confidence due to:
– Overall volume of claims
– Volume of claims within layer (lucky or unlucky?)
– Stability of year by year Experience results
–
“
layer to layer Hybrid ratios
– Source of loss development, trend factors, historical rate
changes and deviations
– Changes in historical profile limits affecting claims
– Appropriateness of any claims or divisions that may have
been removed (or “as-if’d”)
– Including additional large claim(s) if feel account “lucky”
• Underwriter “as-if” scorecard – soft market
• Experience score compared to exposure score to determine
credibility weight
18
Classical Credibility Weighting
Techniques
• Select credibility weights using combination of:
– Formulaic Approach
• Expected # of Claims / Variability
• Exposure ROL (or burn on line)
– Questionnaire Approach
• Apriori Neutral vs. Experience vs. Exposure
• Patrik/Mashitz paper
– Judgment
• Need to check that burn patterns make sense
– i.e. higher layer ROL < lower ROL
– similar to Miccolis ILF consistency test
19
Classical Credibility Weighting
o Credibility weights can be judgmentally or formula selected
o Soft market pressure to give more weight to experience
indication when lower (perhaps implicitly by underwriter or
management override)
20
Underwriting Cycle
• Hard market vs. Soft market
• Calendar year vs. accident year
– Accident year – posted vs. “true” after adjusting for reserves
• Loss ratios, combined ratios, operating ratios
• Forensic analysis of cycle
– Numerator impacts (loss trends, new plateaus, shock losses)
– Denominator impacts (rate changes, terms and conditions)
• Relative magnitude of components
–
–
–
–
Losses
Rates
Reserve adequacy (no impact if able to review “true” AY results)
Which is larger impact, losses or rates? Perhaps vary by line
• Hypothesis
– Soft market bias towards Experience model results
– Could be implicit by underwriters or management override
21
Underwriting Cycle - AY
22
Underwriting Cycle – AY vs. CY
Information Gap
23