Transcript A Hybrid Experience / Exposure Method

A Hybrid
Experience / Exposure Method
Presented by
John Buchanan - Platinum Reinsurance
Seminar on Reinsurance – Advanced Experience Rating
June 7 & 8, 2004
CARe 2004 – A Hybrid Experience / Exposure Method
Agenda
• Overriding Assumptions
• Traditional Methods
– Experience Rating
– Exposure Rating
– Credibility Weighting
• Hybrid: Experience / Exposure Method
– Highlight differences between traditional
methods
• Testing Default Parameters
CARe 2004 – A Hybrid Experience / Exposure Method
Overriding Assumptions
of Hybrid Experience / Exposure Method
• With perfect modeling and data the results under the
experience and exposure methods will be identical.
• 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.
CARe 2004 – A Hybrid Experience / Exposure Method
Traditional Methods
Experience
• Relevant parameter
defaults/overrides for:
– LDFs (excess layers)
– Trends (severity, frequency,
exposure)
– Rate changes
– LOB/HzdGrp 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
CARe 2004 – A Hybrid Experience / Exposure Method
Classical Credibility Weighting
• Estimate separate Experience and Exposure
burns
• Select credibility weights using combination of:
– Judgment
– Formulaic Approach
• Expected # of Claims / Variability
• Exposure ROL (or burn on line)
– Questionnaire Approach
• Apriori Neutral vs. Experience vs. Exposure
• Need to be careful of unintended weighted burn
patterns
CARe 2004 – A Hybrid Experience / Exposure Method
Classical Credibility Weighting
Credibility weights
judgmentally selected
CARe 2004 – A Hybrid Experience / Exposure Method
Basic Steps of The Hybrid Method
Step 1: Estimate Experience burns & counts
–
–
–
–
Select base attachment points above data threshold
Estimate total burns using projection factors
Estimate counts using frequency trends, claim count LDFs
Calculate implied severities
Step 2: Estimate Exposure burns & counts
– Use same attachment points/layers as Experience
– Bifurcate burns between counts, average severity
Step 3: Calculate experience/exposure
frequency ratio by attachment point
CARe 2004 – A Hybrid Experience / Exposure Method
Basic Steps of The Hybrid Method (cont.)
Step 4: Estimate base layer weights
– Possibly use number of claims/variability by
attachment
Step 5: Review frequency ratio patterns
– Adjust underlying experience or exposure
models if needed and re-estimate burns (!!)
– Select indicated exper/expos frequency ratio
Step 6: Similarly review excess severities
Step 7: Combine frequency/severity results
– Using experience adjusted exposure
frequencies and severities
CARe 2004 – A Hybrid Experience / Exposure Method
Estimation of Experience Counts
Example - Step 1
A: Select base attachment points above data
threshold
– Example: threshold=150k; reins layers=500x500k, 1x1mm
– Select 200k, 250k, 350k, 500k, 750k, 1mm attachment points
B: Review year by year patterns
– At lower attachment points, should be variable about some
mean
– For example, if upward trend, then perhaps:
• Overdeveloping or trending later years
C: Review attachment point patterns
– Should be relatively stable until credibility runs out
CARe 2004 – A Hybrid Experience / Exposure Method
Step 1B: Estimation of Experience Counts
Year Variability: >350,000 Attachment
Apparently random pattern
around selection of #=12.05
CARe 2004 – A Hybrid Experience / Exposure Method
Step 1B: Estimation of Experience Counts
Year Variability: >1,000,000 Attachment
Credibility runs out;
indication is #=.36
CARe 2004 – A Hybrid Experience / Exposure Method
Step 1-Recap: Estimation of Experience
Burns, Counts and Implied Severities
To be compared to
exposure counts
CARe 2004 – A Hybrid Experience / Exposure Method
Step 2-Recap: Estimation of Exposure
Burns Bifurcated Between Counts and Severities
12.05 exper / 15.34 expos
= 78.6%
CARe 2004 – A Hybrid Experience / Exposure Method
Step 3: Review Exper/Expos Frequencies
Attachment Point Variability: 200k…1mm
Expos and Exper counts relatively
consistent - IF experience very credible
through 350k, then perhaps pressure to
reduce exposure L/R; check out spikes
CARe 2004 – A Hybrid Experience / Exposure Method
Steps 3-5: Calculate Exper/Expos Frequency Ratio,
Base Layer Weights, & Selected Exper/Expos Ratio
6.00 expos x 80.0%
Important Selection
CARe 2004 – A Hybrid Experience / Exposure Method
Step 6: Selected Severity
Unrealistic experience severity
CARe 2004 – A Hybrid Experience / Exposure Method
Step 7: Selected Overall Burn
Hybrid: Experience adjusted
Exposure count & severity…
100% credibility to burn??
CARe 2004 – A Hybrid Experience / Exposure Method
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
• Well constructed frequency / severity method can
sometimes be given 100% weight if credible
• Can review account by account, and aggregate
across accounts to evaluate pressure on industry
defaults
CARe 2004 – A Hybrid Experience / Exposure Method
Test of Default Parameters
• Aggregate across “similar” accounts to evaluate
pressure on industry defaults
– May want to re-rate accounts using e.g. default rate
changes, ILFs, premium allocations, LDFs, trends, etc.
• Each individual observation represents a
cedant/attachment point exper/expos ratio
• Review dispersion of results and overall trend
– E.g. if weighted and/or fitted exper/expos ratios are well
below 100% (or e.g. 90% if give some underwriter credit)
then perhaps default L/Rs overall are too high (or
conversely LDFs or trends too light)
– If trend is up when going from e.g. 100k to 10mm att pt,
then perhaps expos curve is predicting well at lower
points but is underestimating upper points
CARe 2004 – A Hybrid Experience / Exposure Method
Test of Default Parameters (cont.)
• Before making overall judgments, must
consider
– UW contract selectivity (contracts seen vs. written),
– Sample size (# of cedants/years),
– Impact “as-if” data (either current or historical)
– “Lucky”
CARe 2004 – A Hybrid Experience / Exposure Method
Test of Default Rating Factors – Example 1
Well below 100%,
pressure to reduce expos
params or increase exper
params…but credible??
CARe 2004 – A Hybrid Experience / Exposure Method
Test of Default Rating Factors – Example 2
Exposure curve too light
with higher attachment
points?
CARe 2004 – A Hybrid Experience / Exposure Method