CAS Ratemaking Seminar March 2004 WC5 Latest Developments

CAS Ratemaking Seminar March, 2004 WC-5 Latest Developments in Retrospective Rating Ideas for Future Development Ira Robbin, Ph. D Senior Pricing Actuary Partner RE

Ground Rules and Disclaimers n n n The purpose of this session is to promote actuarial discussion of possible improvements in NCCI Retro Rating Plans. Anti-trust guidelines will be scrupulously obeyed. No statements of Partner Re’s corporate position will be made or should be inferred.

Cautions n Examples are for illustrative purposes only. Do not use the results from any example in real-world applications.

Three Ideas n n n Refining ICRLL Filing an Advisory Agg Model Adding Terrorism and CAT Loadings n n Table M ELPF

ICRLL Review n n n Insurance Charge Reflecting Loss Limitation Logical modification of regular insurance charge calculation procedure Limited Loss Ratio Equations n n n Ratio Difference Value Difference Single Table M n Adjust Table M column (ELG)

ICRLL Ratio and Value Difference Expected Limited LR

Loss Group Adjustment n n n LUGS= Losses Used in Group Selection LUGS = E[L]*M S/H *Mk M S/H State/Hazard Group multiplier Mk per accident loss limit multiplier Mk = (1+. 8 LER)/(1 -LER) LER = ELPF/ELR

Impact of LG Adjustment n n Assume MS/H = 1. Then: LUGS > E[L] > E[LL] Larger $ Loss a. Smaller LG # a. Smaller Ins Charges

ICRLL vs “Correct” Solution n ICRLL uses theoretically correct value difference and ratio difference equations ICRLL approximates limited loss distribution by using distribution for a larger risk Correct solution: Limited Loss Table Ms n Table M for each per occ loss limit

Unlimited and Limited Loss Table Ms

Limited Loss Table Ms vs Table L

ICRLL Approx of Insurance Charge Values n Approximation good for intermediate r n n May over-reduce charges for small r n n n ICRLL use of larger risk gives smaller charges Per occ limitation should reduce charges Calibration of ICRLL rating values $ savings for small min should not change when a loss limit is introduced ICRLL may incorrectly show $ savings reductions May or may not reduce charges enough for large r

Understated Savings Example

Charges for Tiny Loss Limits n n Let the loss limit approach zero Charges should approach charges for the accident count distribution ICRLL charges approach those of a very large risk Conclusion: ICRLL has incorrect asymptotic behavior as loss limit decreases

Actual vs Theoretical Error n ICRLL theoretical potential error n n Low loss limits Low entry ratios High entry ratios ICRLL actual error? n n Needs further study! Tolerance for inaccuracy

For Greater Accuracy: n Promulgate Limited Loss Table Ms n n n Interpolate between Unlimited Table M and Count Table M n n Theoretically right Horribly impractical Has correct asymptotic behavior Use LER as interpolation weight? Still seems impractical File an Aggregate Model

The Model Solution n Solution considered in early 90 s n n Need Count and Severity Distributions n n n Rejected due to need for paper tables Concern about regulatory approval Prior to Internet and Windows 95 Should closely reproduce current Table M Not a trivial task, but not impossible Refine the model used to develop Table M Develop practical software File as advisory Table M software

Model Solution: Pros and Cons n n Theoretically correct and most accurate Practical n n n A Solution in Search of a Problem n n Modeling problems difficult, not impossible Internet or CD implementation feasible ICRLL generally accurate enough For greater accuracy, use consultants or in-house actuaries Too costly Difficulties with regulatory approval

CAT and Terrorism Loadings n n n Some actual CAT & Terrorism may be implicitly in Table M and ELPFs May also be part of flat load in ELPFs Current expectation of CAT &Terror not in Table M or ELPF n Property CAT models a. WC CAT potential is signficant

CAT and Terrorism: Property vs WC n n n Wind less a concern in WC Quake loss in WC varies with time of day Terrorism may be more of a concern in WC n n Attacks on people that may cause modest property damage Chemical and biological threats

Occ and Agg Terrorism Exposure n Single event explosion n n Large occ exposure Chemical or biological attack n n May not immediately generate WC losses Could eventually spawn large number of WC cases

Method for Loading ELPF? n One idea: n n n Compute ELF as per current method Weight with severe CAT distribution Example: n n Regular ELF = 10% CAT ELF = 50% CAT weight = 2% Final ELF =. 98*10%+. 02*50% = 10. 8%

How to Load Table M? n Model exposure by peril and size of risk n n n Number of locations Number of workers per location Distribution of # injured and severity of injuries for each CAT and Terror peril per location Generate simulated WC CAT and Terror losses and probabilities Model regular loss with current Table M Convolve

Modeling Issues n Source for parameters n n Model equations Validation of results n n n Property CAT models Experts and consultants Some validation for CAT models Minimal validation of Terrorism models High degree of difficulty

Practical Issues n Need to exclude actual CAT and Terror claims from regular data n n Ideal CAT & Terror weight n n n Claim coding needed to identify CAT &Terror By location: state and zip Size of risk and public profile Density and vulnerability of workers WC data doesn’t capture key factors Regulatory issues

Pros and Cons n n Ought to reflect known exposures in the Retro plan No way to determine right model or select parameters – no data Too costly and impractical No real need exists n n Market already charges vulnerable risks Models available from consultants

Conclusion n n Balance: accuracy vs practicality Uses of Retro parameters and tables n n n Roles of key players n n Large Deductible and Dividend plans XS of OCC and AAD pricing Dual role of NCCI Consultants Regulators Questions and Comments