1 / 40

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 Theory. Importance to Practicing Actuaries Credibility Methods Formula and Variance Real Life Mortality Example

Download Presentation

Practical Applications of Credibility Theory

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Practical Applications of Credibility Theory Tom Rhodes, FSA, MAAA, FCA AVP & Actuarial Director MIB Solutions February 16, 2007

  2. 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)

  3. 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.

  4. 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

  5. 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

  6. 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

  7. 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)

  8. 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

  9. 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.

  10. 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

  11. Real Life Mortality ExampleNS Preferred Class Structure of 2 (NS PCS 2)Limited Fluctuation Method

  12. Real Life Mortality ExampleNS Preferred Class Structure of 2 (NS PCS 2) Bühlmann Empirical Bayesian Method

  13. Elements of Credibility Theory • Prior A/E Ratios • Company A/E Ratios • Estimate A/E Ratios

  14. 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

  15. 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

  16. 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

  17. 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

  18. 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

  19. Credibility Theory Lapse Application Many lapses, ‘Z’ is high Company Experience Rules

  20. 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

  21. Term Lapse for NS PCS 2Limited Fluctuation Method

  22. Term Lapse for NS PCS 2 Bühlmann Empirical Bayesian Method

  23. 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

  24. 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

  25. 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

  26. 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

  27. Selecting industry basic table (UCS method) • For each mortality segment • Apply the UCS method for mortality segment • Select the appropriate RR table

  28. 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

  29. 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

  30. 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

  31. 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

  32. 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’

  33. 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

  34. 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

  35. 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

  36. 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

  37. 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!

  38. Questions? trhodes@mib.com 917-400-0213

More Related