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A Hybrid Experience / Exposure Method Presented by John Buchanan - Platinum Reinsurance Seminar on Reinsurance – Advanced Experience Rating June 7 & 8, 2004

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A Hybrid Experience / Exposure Method Presented by John Buchanan - Platinum Reinsurance Seminar on Reinsurance – Advanced Experience Rating June 7 & 8, 2004. Agenda. Overriding Assumptions Traditional Methods Experience Rating Exposure Rating Credibility Weighting

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A Hybrid Experience / Exposure MethodPresented byJohn Buchanan - Platinum ReinsuranceSeminar on Reinsurance – Advanced Experience RatingJune 7 & 8, 2004

CARe 2004 – A Hybrid Experience / Exposure Method

agenda
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
Overriding Assumptionsof 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
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
      • Careful “as-if”
  • Exposure
  • Relevant parameters defaults/overrides for:
    • ILFs (or ELFs, PropSOLD)
    • Direct loss ratios (on-level)
    • ALAE loads
    • Policy profile (LOB, HzdGrp)
      • 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
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 weighting1
Classical Credibility Weighting

Credibility weights judgmentally selected

CARe 2004 – A Hybrid Experience / Exposure Method

basic steps of the hybrid 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
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
Estimation of Experience CountsExample - 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
Step 1B: Estimation of Experience CountsYear 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
Step 1B: Estimation of Experience CountsYear 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
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
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
Step 3: Review Exper/Expos FrequenciesAttachment 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
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
Step 6: Selected Severity

Unrealistic experience severity

CARe 2004 – A Hybrid Experience / Exposure Method

step 7 selected overall burn
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
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
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
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
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

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Test of Default Rating Factors – Example 2

Exposure curve too light with higher attachment points?

CARe 2004 – A Hybrid Experience / Exposure Method

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