[[Actuarial Notes Wiki|Wiki]] / [[Exam 5 (CAS)]] / **Credibility** ## Definition ==Credibility== Credibility is a measure of the statistical reliability of experience data, used to determine how much weight to assign to observed data versus expected or complement data when making predictions. ## Fundamental Concept ### Credibility Formula ``` Estimate = Z × Actual Experience + (1-Z) × Expected Experience Where: Z = Credibility factor (0 ≤ Z ≤ 1) 1-Z = Complement of credibility ``` ## Factors Affecting Credibility ### Volume of Data - More exposures → Higher credibility - Larger claim counts → More reliable - Longer experience periods → Better estimates ### Stability of Data - Consistent loss patterns → Higher credibility - Homogeneous risks → More reliable - Absence of catastrophes → Better predictability ### Quality of Data - Accurate reporting → Higher credibility - Complete information → More reliable - Timely updates → Better estimates ## Credibility Standards ### Full Credibility Criteria for Z = 1.00 (100% credibility): - Sufficient data volume - Statistical confidence level met - Typically 1,082 claims for frequency - Higher requirements for severity ### Partial Credibility For data sets below full credibility: - Square root rule: Z = √(n/n_full) - Limited fluctuation credibility - Greatest accuracy credibility ## Applications ### Ratemaking **Rate Level Indications** ``` Final Rate Change = Z × Indicated Change + (1-Z) × Complement Example: Indicated change: +15% Credibility: 60% Complement (Prior): 0% Final: 0.60 × 15% + 0.40 × 0% = 9% ``` **Classification Ratemaking** - Class relativities - Territory factors - Individual risk rating ### Reserving - Case reserve adequacy - IBNR estimates - Ultimate loss projections ### Experience Rating - Individual risk pricing - Retrospective rating - Large deductible programs ## Methods ### Classical Credibility - Limited fluctuation - Full credibility standard - Square root rule for partial ### Bühlmann Credibility - Greatest accuracy approach - Based on variance components - More sophisticated theory ### Practical Considerations - Actuarial judgment important - Regulatory requirements - Business constraints ## Example Calculation ``` Workers Comp Class Analysis: Claims: 75 Full credibility standard: 1,082 claims Z = √(75/1,082) = √0.0693 = 0.263 or 26.3% Indicated class relativitivity: 1.25 Manual relativitivity: 1.00 Credibility-weighted: = 0.263 × 1.25 + (1-0.263) × 1.00 = 0.329 + 0.737 = 1.066 Selected relativitivity: 1.07 (rounded) ``` ## Complement Selection Common choices for complement: 1. **Industry data** - Similar risks from broader market 2. **Prior indication** - Previous rate level 3. **Manual rates** - Current rate structure 4. **Zero** - No adjustment (use indicated only) Selection depends on: - Availability of data - Regulatory requirements - Business judgment - Market conditions ## Regulatory Considerations Many states require: - Credibility procedures documented - Standards justified - Complement explained - Results reasonable ## Related Concepts - [[Homogeneity]] - [[Overall Rate Level Indication]] - [[Classification Ratemaking]] - [[Experience Rating]] - [[Bühlmann Credibility]] ## References - Werner & Modlin, Chapter 10 - Mahler & Dean, "Credibility" - CAS Ratemaking Principles