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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 Implied SeveritiesBurns 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 Frequencies Implied SeveritiesAttachment 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 Weights, & Selected Exper/Expos Ratio

Unrealistic experience severity

CARe 2004 – A Hybrid Experience / Exposure Method


Step 7 selected overall burn
Step 7: Selected Overall Burn Weights, & Selected Exper/Expos Ratio

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 Weights, & Selected Exper/Expos Ratio

  • 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 Weights, & Selected Exper/Expos Ratio

  • 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 Weights, & Selected Exper/Expos Ratio(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 – Weights, & Selected Exper/Expos RatioExample 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 – Weights, & Selected Exper/Expos RatioExample 2

Exposure curve too light with higher attachment points?

CARe 2004 – A Hybrid Experience / Exposure Method


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