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Report of the Tail Factor Working Party. Steven C. Herman, FCAS, MAAA San Diego, California September 10-11, 2007. Tail Factor Working Party. Co-Chairs Steven C. Herman Mark R. Shapland Members. Tail Factor Working Party. Disclaimer:

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report of the tail factor working party
Report of the Tail Factor Working Party

Steven C. Herman, FCAS, MAAA

San Diego, California

September 10-11, 2007

tail factor working party
Tail Factor Working Party


Steven C. Herman Mark R. Shapland


tail factor working party1
Tail Factor Working Party


While this paper is the product of a CAS working party, its findings do not represent the official view of the Casualty Actuarial Society. Moreover, while we believe the approaches we describe are very good examples of how to address the issue of estimating development of loss and loss adjustment expense payments from a given evaluation to ultimate disposition, we do not claim they are the only acceptable ones, nor do they represent all possible applications of the specific methods presented.

the motivation
The Motivation
  • Tail factors used to estimate additional development occurring
    • after the eldest maturity in a given loss development triangle, or
    • after the eldest credible link ratio.
  • Over the years, many valuable contributions have been made to the CAS literature describing methods for calculating tail factors.
  • However no overall paper compiling these contributions existed.
the paper
The Paper
  • The CAS Tail Factor Working Party prepared this paper on the methods currently used by actuaries in estimating loss development tail factors.
  • Standard terminology for discussing aspects of link ratios and tail development is communicated within the paper.
the paper1
The Paper
  • Included are
    • Descriptions of advantages and disadvantages of each method and
    • Identification of what entities (companies, rating bureaus, or consulting firms) typically use each method.
paper description
Paper Description
  • Organized by “Type” of Method
  • Sections Describe:
    • Mechanics of each method,
    • Examples for most methods,
    • Results of our Testing, and
    • Results of our Surveys
paper description1
Paper Description
  • Standard Notation:
    • Consistency,
    • Started with Notation from Reserve Variability Working Party
    • Added new notation where lacking
  • Summarize Areas for Future Research
section description
Section Description
  • Bondy-Type Methods
  • Algebraic Methods
  • Benchmark Methods
  • Open Claim Methods
  • Curve Fitting Methods
  • Lifespan Methods
  • Miscellaneous Methods
bondy type methods description
Bondy-Type Methods Description
  • Bondy Method
    • Use last link ratio:
  • Modified Bondy Method
    • Double or square:
  • Generalized Bondy Method (Weller)
    • For 0
  • Fully Generalized Bondy Method (Gile)
    • Let Vary by Accident Year
bondy type methods description1
Bondy-Type Methods Description
  • Advantages
    • Simple to Implement
    • Pattern Described with One Factor
    • Only Requires Cumulative Paid Data
  • Disadvantages
    • Not Always Useful for Incurred Data
    • Will Fail with Increasing Development
    • May Fail with “More Complicated” Patterns
algebraic methods description
Algebraic Methods Description
  • Equalizing Paid & Incurred Loss Estimates
    • Use Cumulative Incurred / Cumulative Paid
  • Boor’s Method
    • Adjust Case Reserves
  • Mueller’s Method
    • Adjust Incremental Factors
  • NCCI Method
algebraic methods description1
Algebraic Methods Description
  • Advantages
    • Simple to Implement
    • Only Requires Cumulative Data
    • Statistically Unbiased
  • Disadvantages
    • May Not be Sophisticated Enough
    • Subject to Case Reserve Distortions
    • Some Methods Not Generally Well Known
benchmark methods description
Benchmark Methods Description
  • Benchmark Development / Link Ratios
  • Adjusted Benchmark Development / Link Ratios
    • Use Link Ratios to Adjust Tail Factor
  • Benchmark Average Severity
  • Benchmark Adjusted by Claims Audit
benchmark methods description1
Benchmark Methods Description
  • Advantages:
    • Supplement when Little Data
    • Adds Credibility
    • Various Degrees of Sophistication
  • Disadvantages:
    • Need Similar Data
    • Claim Handling Procedures
    • Relative Case Reserve Strength
open claim methods description
Open Claim Methods Description
  • Maximum Possible Loss
  • Judgment of Open Claim Costs / Audit
open claim methods description1
Open Claim Methods Description
  • Advantages:
    • Incorporates Particulars of Open Claims
    • Uses Knowledge of Claim Staff
    • Can Provide Bounds
  • Disadvantages:
    • Requires Access to Individual Claims
    • Subject to Judgment/Availability of Auditors
    • May Underestimate Severe or IBNR/Reopened Claims
curve fitting methods description
Curve Fitting Methods Description
  • Exponential Decay
    • Constant Rate of Factor Decay
  • McClenahan’s Method
    • Constant Monthly Incremental Paid Decay
  • Skurnick’s Method
    • Simplify Using Annual Decay
  • Sherman’s Method
    • Use “Inverse Power” Curves
  • England-Verrall Method
    • Smooth & Extrapolate Incremental Data
curve fitting methods description1
Curve Fitting Methods Description
  • Advantages:
    • Straightforward & Intuitive
    • Extrapolate Beyond End of Data
    • Various Levels of Sophistication
  • Disadvantages:
    • May Underestimate Tail for Long-Tail Lines
    • Sub-Optimal If Pattern Not Consistent
    • Sometimes No Closed Form Solution
lifespan methods description
Lifespan Methods Description
  • Static Mortality Method
    • Frequency / Severity Using Mortality Rates
  • Trended Mortality Method
    • Greatest Impact on “Distant” Years
  • Sherman-Diss Method
    • Separate Impact of Inflation & Mortality
  • Corro’s Method
    • Modeling of “Pension” Claims
lifespan methods description1
Lifespan Methods Description
  • Advantages:
    • Extrapolate “Very-Long” Tail
    • Can Include “Increasing” Factors
    • Detailed Assumptions/Some Non-Subjective
  • Disadvantages:
    • More Complex
    • Need “Very Old” Data to Parameterize
    • Need Specific Mortality Rates
miscellaneous methods description
Miscellaneous Methods Description
  • Restating Historical Experience via a Claims Audit
    • Adjust for Changes
miscellaneous methods description1
Miscellaneous Methods Description
  • Advantages:
    • Improves “Other” Methods
    • Adjustments Readily Understood
    • Add Claim Professional Judgment
  • Disadvantages:
    • Difficult to Reconstruct Old Claim Files
    • Auditor Must Ignore Prior Development
    • Auditor Must Evaluate at Multiple Points