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Practical Applications of Credibility Theory. Tom Rhodes, FSA, MAAA, FCA AVP & Actuarial Director MIB Solutions February 16, 2007. Practical Applications of Credibility Theory. Importance to Practicing Actuaries Credibility Methods Formula and Variance Real Life Mortality Example

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practical applications of credibility theory

Practical Applications of Credibility Theory

Tom Rhodes, FSA, MAAA, FCA

AVP & Actuarial Director MIB Solutions

February 16, 2007

practical applications of credibility theory1
Practical Applications of Credibility Theory
  • Importance to Practicing Actuaries
  • Credibility Methods
    • Formula and Variance
    • Real Life Mortality Example
    • Selection of Method
  • Elements of Credibility Theory
    • Prior A/E Ratios
    • Company A/E Ratios
    • Estimate A/E Ratios
  • Lapse Application
  • Mortality Applications (VM-20, pricing, risk mgmt)
importance of credibility theory
Importance of Credibility Theory
  • Company results vary substantially from the intercompany averages
  • Credibility Theory provides a statistically sound method of measuring variability of company results from intercompany results.
  • Credibility Theory provides company specific estimates of mortality and lapse based on company results, intercompany results and the measured variability.
importance of credibility theory1
Importance of Credibility Theory

Prospect of Principles-Based Reserving raises its importance among life and annuity actuaries

  • NAIC’s Life and Health Actuarial Task Force
    • New Valuation Law and Valuation Manual (VM)
    • VM-20 includes credibility practices in valuation of life insurance products
    • Companies set reserves based on own experience
  • Academy’s Credibility Practice Note highlights
    • Determine the level of reliance that can be placed on company experience
    • Determine assumptions for modeling company cash flows
credibility theory practices report
Credibility Theory Practices Report
  • The SOA’s Committee on Life Insurance Research, Financial Reporting and Product Development Sections sponsored a report on application and adoption of credibility theory for life insurance and annuities.
  • MIB Solutions team of Stuart Klugman, Tom Rhodes, Marianne Purushotham and Stacy Gill produced Credibility Theory Practices report: http://www.soa.org/research/life/research-credibility-theory-pract.aspx
credibility theory practices report theory practical methodology and more
Credibility Theory Practices ReportTheory, Practical Methodology and More!

Theory: Formulas developed for two established statistical credibility methods, Limited Fluctuation and Bühlmann Empirical Bayesian

Practical Methodology: For Limited Fluctuation and Bühlmann Empirical Bayesian, formulas for ‘Z’ applied to sample of small, medium and large companies:

  • Mortality and lapse results
  • Excel files implementing formulas included
  • Appendices document this Excel file implementation
  • Companies can perform Limited Fluctuation method in-house

Survey and Bibliography

Survey

Bibliography

credibility methods formula
Credibility MethodsFormula
  • Credibility formulas use a credibility factor ‘Z’ varies from 0 to 1.
  • The standard form of credibility formula:

Estimate A/E Ratio =

Z × (Company A/E Ratio) + (1-Z) x (Prior A/E Ratio)

Addresses Academy Practice Note Highlights

    • Determine the level of reliance that can be placed on company experience (Z)
    • Determine modeling assumptions for company cash flows (Estimate A/E Ratio)
credibility methods variance
Credibility Methods Variance
  • Total Variance = Process Variance + Variance of Hypothetical Means
  • Limited Fluctuation uses Process Variance
  • Bühlmann Empirical Bayesian uses both Process Variance + Variance of Hypothetical Means
real life mortality example
Real Life Mortality Example
  • Experience is from ten companies that participated in the SOA 2004-05 experience study
  • Companies were selected in order to give a mixture of large, medium and small size companies.
  • To maintain strict confidentiality of individual company information, only a portion of each company’s mortality and lapse data was used.
real life mortality example1
Real Life Mortality Example
  • The variability of the Company A/E Ratios around the Prior A/E Ratio of the inter-company study is evident
  • In general, Credibility Factor ‘Z’ increases with increasing number of deaths.
  • Difference between estimate A/E ratios and company A/E ratios varies substantially among different companies
slide14
Real Life Mortality ExampleNS Preferred Class Structure of 2 (NS PCS 2) Bühlmann Empirical Bayesian Method
elements of credibility theory
Elements of Credibility Theory
  • Prior A/E Ratios
  • Company A/E Ratios
  • Estimate A/E Ratios
prior a e ratio in credibility theory methods
Prior A/E Ratio in Credibility Theory Methods

Credibility method for PCS 2 NS

  • Sample company experience was compared to expected basis 100% of 2001 VBT
    • Admittedly NOT a preferred class table
  • Intercompany study adjusts
    • From 100% of 2001 VBT expected basis goes down to 65.6% of 2001 VBT
  • 65.6% of 2001 VBT is the ‘Prior A/E Ratio’ used in credibility formula
prior a e ratio in credibility theory methods1
Prior A/E Ratio in Credibility Theory Methods
  • Fixed Table as Prior A/E Ratio
    • Limited Fluctuation Method
    • Could use fixed table as Prior A/E Ratio
      • For example 100% 2001 VBT
    • Intercompany experience does not modify fixed table
    • Choice of fixed table can drive results, actuarial judgment is necessary
      • For example 65% of 2001 VBT for preferred
prior a e ratio actuarial judgment needed
Prior A/E RatioActuarial Judgment Needed

The selection of the Prior A/E Ratio affects estimate resulting from credibility method

Prior 65.6% , Company 112.4% , Estimate 70.4%

If one varies the Prior A/E assumption, one varies the Estimate A/E

The selection of the Prior A/E Ratio assumption requires actuarial judgment

practical sources of prior a e ratios
Practical Sources of Prior A/E Ratios
  • Fixed table (RR table, pricing assumption as % of standard table)
  • Pivot tables from SOA Experience Reports
    • Important to select appropriate mortality segment to correspond with assumption
  • Subsets of industry studies for product/underwriting class/peer group
company a e ratios
Company A/E Ratios
  • In individual company experience study
    • Select mortality segment consistent with mortality segment of Prior A/E Ratio
    • Use policy by policy experience results
  • Mandatory company studies under both NAIC Model Regulation 815 and proposed Valuation Law/Valuation Manual
    • Statistical agent for Life needs to be named, comparable to statistical agent for P&C
credibility theory

Credibility Theory

Lapse Application

Many lapses, ‘Z’ is high

Company Experience Rules

application of credibility methods to lapse
Application of Credibility Methods to Lapse
  • Used term policies in the NS PCS 2 for the 7 companies studied for mortality sample
  • Recent LIMRA study is basis for expected lapse
  • Actual experience of 7 companies produces mean used for Prior A/E Ratio
credibility theory and vm 20
Credibility Theory and VM-20
  • NAIC’s Life and Health Actuarial Task Force
    • New Valuation Law and Valuation Manual (VM)
    • VM-20 covers valuation of life insurance products
      • Credibility theory not used for less than 30 deaths
      • Credibility theory used for 30 or greater deaths in credibility set of mortality segments
vm 20 for 30 or greater deaths in credibility set of mortality segments
VM-20: For 30 or greater deaths in credibility set of mortality segments

Determine prudent estimate mortality by:

  • Selecting credibility method
  • Selecting industry basic table (UCS method)
  • Determine mortality from experience studies and credibility method
  • Determine margin
  • Use credibility mortality plus margin to select industry basic table with higher mortality
selecting credibility method
Selecting credibility method
  • Either the Limited Fluctuation method or the Bühlmann Empirical Bayesian method are options.
  • Limited Fluctuation method
    • Requires only your company’s data
    • Can use Excel tables from MIB Solutions report
    • Can be done in-house
  • Bühlmann Empirical Bayesian method
    • May give higher ‘Z’ than Limited Fluctuation method
    • Requires data from multiple companies
    • Can only be done by statistical agent
  • For this example, use Limited Fluctuation Method
vm 20 for 30 or greater deaths in credibility set of mortality segments1
VM-20: For 30 or greater deaths in credibility set of mortality segments

Determine prudent estimate mortality by:

  • Selecting credibility method
  • Selecting industry basic table (UCS method)
  • Determine mortality from experience studies and credibility method
  • Determine margin
  • Use credibility mortality plus margin to select industry basic table with higher mortality
selecting industry basic table ucs method
Selecting industry basic table (UCS method)
  • For each mortality segment
  • Apply the UCS method for mortality segment
  • Select the appropriate RR table
vm 20 for 30 or greater deaths in credibility set of mortality segments2
VM-20: For 30 or greater deaths in credibility set of mortality segments

Determine prudent estimate mortality by:

  • Selecting credibility method
  • Selecting industry basic table (UCS method)
  • Determine mortality from experience studies and credibility method
  • Determine margin
  • Use credibility mortality plus margin to select industry basic table with higher mortality
determine mortality from experience studies and credibility method
Determine Mortality from Experience Studies and Credibility Method
  • Determine mortality segments
    • RR table for Prior A/E Ratio
    • Company A/E Ratio calculated using policy by policy results from experience study
  • Use MIB Solutions report
    • Needed formulas, Appendices serve as guide
    • Excel files provide template to do calculations
  • Apply actuarial judgment
determine mortality from experience studies and credibility method1
Determine Mortality from Experience Studies and Credibility Method

Apply Actuarial Judgment

  • Start with credibility model’s Estimate A/E Ratio
  • Credibility model produces an estimate of flat percentage of base mortality table
    • Flat percentages may be modified for higher older age Qx’s
    • Mortality curve varied by product characteristics ,e.g., term mortality after level period
  • Other actuarial judgment changes possible
vm 20 for 30 or greater deaths in credibility set of mortality segments3
VM-20: For 30 or greater deaths in credibility set of mortality segments

Determine prudent estimate mortality by:

  • Selecting credibility method
  • Selecting industry basic table (UCS method)
  • Determine mortality from experience studies and credibility method
  • Determine margin
  • Use credibility mortality plus margin to select industry basic table with higher mortality
margins
Margins

For credibility theory methods, margin considerations:

  • Reliability of Company Experience Studies
  • Reliability of Prior A/E Ratio (If a fixed table and not adjusted by intercompany study, future mortality improvement eventually makes it out of date)
  • Difference of Company and Estimate A/E Ratios:
  • Company E has 46.2% Company and 63.6% Estimate
  • Company F has 84.9% Company and 68.2% Estimate
  • Future mortality trends
  • Refer to SOA ‘s ‘Analysis of Methods for Determining Margins for Uncertainty under a Principles-Based Framework for Life Insurance and Annuity Products’
vm 20 for 30 or greater deaths in credibility set of mortality segments4
VM-20: For 30 or greater deaths in credibility set of mortality segments

Determine prudent estimate mortality by:

  • Selecting credibility method
  • Selecting industry basic table (UCS method)
  • Determine mortality from experience studies and credibility method
  • Determine margin
  • Use credibility mortality plus margin to select industry basic table with higher mortality
credibility theory other mortality applications
Credibility TheoryOther Mortality Applications
  • For evaluating pricing assumptions
    • Use your company’s pricing assumptions as percentage of expected table as Prior A/E Ratio
    • Use company experience study for Co A/E Ratio
    • Limited Fluctuation method and Excel files from MIB Solution’s report to produce Estimate A/E Ratio
    • Modify results using actuarial judgment
credibility theory other mortality applications1
Credibility TheoryOther Mortality Applications
  • For risk management application
    • Use your best guess as Prior A/E Ratio
    • Use company experience study for Co A/E Ratio
    • Limited Fluctuation method and Excel files from MIB Solution’s report to produce Estimate A/E Ratio
    • Modify results using actuarial judgment
practical applications of credibility theory2
Practical Applications of Credibility Theory
  • Important – Co A/E varies from Intercompany A/E
  • Credibility Methods applied with actuarial judgment
    • Prior A/E Ratios
    • Company A/E Ratios
    • Estimate A/E Ratios
  • Selection of Credibility Method
    • Limited Fluctuation can be done in-house by company using MIB Solutions’ Report
  • Lapse Application – Company results rule, insist on high quality company lapse experience studies
  • Mortality Application - VM-20, evaluating pricing assumptions, risk management studies
invitations
Invitations

I.MIB Solutions is seeking current SOA contributor to ILEC study to develop practical implementation techniques for Credibility Theory:

  • Use that company’s already submitted data
  • Co-author practical credibility techniques paper
  • Involvement will
    • Improve knowledge of credibility techniques
    • Provide roadmap for applying in your company

II. If you have questions on implementing credibility theory, call me for free advice!

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