CAS RM 2008 – The Hybrid Reinsurance Pricing Method

1. Solving the Puzzle: The Hybrid Reinsurance Pricing MethodJohn BuchananCAS Ratemaking Seminar – REI 4March 17, 2008 CAS RM 2008 – The Hybrid Reinsurance Pricing Method

2. Agenda • Traditional Methods Recap • Hybrid Method: Experience / Exposure • Reserving analogy • Fundamental assumptions • Basic steps of the paper • Case studies • Hybrid roll-ups • Testing default parameters Appendix • Other considerations in attempting to solve the puzzle • Underwriting cycle: soft market experience model bias

3. Traditional Methods Recap • Experience • Relevant parameter defaults/overrides for: • LDFs (excess layers) • Trends (severity, frequency, exposure) • Rate changes • LOB/Hazard Grp indicators • Adjust for historical changes in: • Policy limits • Exposure differences • Careful “as-if” • Exposure • Relevant parameters defaults/overrides for: • ILFs (or ELFs, PropSOLD) • Direct loss ratios (on-level) • ALAE loads • Policy profile (LOB, HzdGrp) • Limit/subLOB allocations • Adjust for expected changes in: • Rating year policy limits • Rating year exposures expected to be written

4. Hybrid Pricing Method Reserving Analogy From paper accepted by CAS Variance – John Buchanan / Mike Angelina THE HYBRID REINSURANCE PRICING METHOD: A PRACTITIONER’S GUIDE

5. Fundamental Assumptionsof the Hybrid Method • In theory, with perfect modeling and sufficient data the results under the Experience and Exposure methods will be identical. (never attainable) • In practice, • if the model and parameter selections for both Experience and Exposure methods are proper and relevant, • then the results from these methods will be similar, • except for credibility and random variations. • Lower layer experience helps predict higher less credible layers. • Frequency is a more stable indicator than total burn estimates.

6. Basic Steps of The Hybrid Method • Estimate Experience burns & counts • Estimate Exposure burns & counts • Calculate Experience/Exposure frequency ratio by attachment point • Review Hybrid frequency ratio patterns - Adjust experience or exposure models if needed and re-estimate burns • Similarly review excess severities and/or excess burns • Combine Hybrid frequency/severity results • Determine overall weight to give Hybrid

7. Step 4-Review Hybrid Frequency Ratios(Example #1 from Paper) Step 4 Important Selection 6.00 expos x 80.0%

8. Steps 1-7: Bringing it All Together Step 1 Step 3 Step 5 Step 4 Step 6 Step 2 Step 7

9. Exposure vs. Experience (Example #2 from REI-3 Case Study) • In this case study, there is an inconsistent relationship as move up the attachment points • While the low layer Experience is about half of Exposure, the upper layers are about equal to Exposure • Need more investigation to reconcile and help solve the puzzle

10. Adjusting Experience for historically higher policy limits(Example #2 from paper)

11. Adjusting Exposure for clash potential(Example #3 from Paper)

12. Benefits of Hybrid Method • One of main benefits is questioning Experience and Exposure Selections • To the extent credible results don’t line up, this provides pressure to the various default parameters • For example, there would be downward pressure on default exposure ILF curves or loss ratios if • Exposure consistently higher than experience, and • Credible experience and experience rating factors • A well constructed Hybrid method can sometimes be given 100% weight if credible • Can roll-up Hybrid results across accounts to evaluate pressure on industry defaults

13. Hybrid roll-ups: Test of Default Factors Well below 100%, pressure to reduce expos params or increase exper params…but credible??

14. Other Considerations in Attempting to Solve the PuzzleAppendix

15. Inspect Hybrid Ratios From forthcoming paper - THE HYBRID REINSURANCE PRICING METHOD: A PRACTITIONER’S GUIDE

16. Pressure Indicators: Inspect Burn ratios by Year

17. Assessing Credibility of Exposure Method • Assess confidence due to: • Exposure curve selected • Exposure profile • Source of hazard or sub-line information • Prediction of next years primary loss ratio • Percentage of non-modeled exposure, clash, etc. • Company strategy and ability to realize strategy • Possibly take questionnaire / scoring approach to mechanize (Patrik/Mashitz)

18. Assessing Credibility of Experience Method • Assess confidence due to: • Overall volume of claims • Volume of claims within layer (lucky or unlucky?) • Stability of year by year Experience results • “ layer to layer Hybrid ratios • Source of loss development, trend factors, historical rate changes and deviations • Changes in historical profile limits affecting claims • Appropriateness of any claims or divisions that may have been removed (or “as-if’d”) • Including additional large claim(s) if feel account “lucky” • Underwriter “as-if” scorecard – soft market • Experience score compared to exposure score to determine credibility weight

19. Classical Credibility Weighting Techniques • Select credibility weights using combination of: • Formulaic Approach • Expected # of Claims / Variability • Exposure ROL (or burn on line) • Questionnaire Approach • Apriori Neutral vs. Experience vs. Exposure • Patrik/Mashitz paper • Judgment • Need to check that burn patterns make sense • i.e. higher layer ROL < lower ROL • similar to Miccolis ILF consistency test

20. Classical Credibility Weighting o Credibility weights can be judgmentally or formula selected o Soft market pressure to give more weight to experience indication when lower (perhaps implicitly by underwriter or management override)

21. Underwriting Cycle • Hard market vs. Soft market • Calendar year vs. accident year • Accident year – posted vs. “true” after adjusting for reserves • Loss ratios, combined ratios, operating ratios • Forensic analysis of cycle • Numerator impacts (loss trends, new plateaus, shock losses) • Denominator impacts (rate changes, terms and conditions) • Relative magnitude of components • Losses • Rates • Reserve adequacy (no impact if able to review “true” AY results) • Which is larger impact, losses or rates? Perhaps vary by line • Hypothesis • Soft market bias towards Experience model results • Could be implicit by underwriters or management override

22. Underwriting Cycle - AY

23. Underwriting Cycle – AY vs. CY Information Gap