- 105 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about 'Practical Applications of Credibility Theory' - valencia-cruz

Download Now**An Image/Link below is provided (as is) to download presentation**

Download Now

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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

### Practical Applications of Credibility Theory

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

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
- 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

- 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 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

- 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 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 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

- 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

- 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 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

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

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

Elements of Credibility Theory

- Prior A/E Ratios
- Company A/E Ratios
- Estimate A/E Ratios

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 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 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

- 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

- 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

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

- 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

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

- 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 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)

- 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 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 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 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

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

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’

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 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 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 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

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!

Download Presentation

Connecting to Server..