Seminar on Reinsurance – June 2-3, 2003 Pricing Techniques: Practical Track 2-3

1. Seminar on Reinsurance – June 2-3, 2003Pricing Techniques: Practical Track 2-3 Michael Coca Chief Actuary, PartnerRe

2. Pricing Techniques: Practical Track Treaty Pricing • Experience and Exposure Rating • Cessions Rated Treaties • Treaty Features • Modeling and Simulation

3. Pricing Techniques: Practical Track Experience Rating • Selecting the Rating Layer • Handling CAT and Shock Losses • Data Mix Adjustments • Biased Analysis

4. Pricing Techniques: Practical Track Experience Rating Layer Attachment • Competing tendencies => Maximize # of claims (lower attachment point) => Minimize extrapolation to treaty layer (higher attachment point)

5. Pricing Techniques: Practical Track Experience Rating Layer Limit • Don’t make the limit too big • Select a limit which does not require an adjustment for “Free Cover” • A small # of claims are no more credible if they are at the top of a layer than if they are at the bottom.

6. Pricing Techniques: Practical Track CAT Losses • Develop experience rating indications including and excluding CAT losses. • Compare the difference in indications to the expected CAT losses generated from a proprietary or vendor supplied cat model. • The experience data set probably doesn’t encompass any scenarios past the 1:50 or 1:100 year events.

7. Pricing Techniques: Practical Track Shock Losses • By definition, shock losses should be infrequent events • Don’t treat all large losses as shock losses. • Develop experience rating indications including and excluding shock losses. • When experience indications vary significantly • Amortize shock losses over a reasonable return period • Add the shock load to the experience indication that excludes shock losses

8. Pricing Techniques: Practical Track Data Mix Adjustment • Mix • Different severity classes • Blocks with historically different LRs and rate levels • Adjust for changes in mix • Index to bring historical experience to projected mix • Apparent trends can be revealed or eliminated

9. Pricing Techniques: Practical Track GL Severity Mix Adjustment

10. Pricing Techniques: Practical Track GL BURNAdjusted for Change in Mix

11. Pricing Techniques: Practical Track Biased Experience Rating? • Never do experience rating if: • Any large losses or poor years have been removed • The business that gave rise to the poor experience • is still being written. • Result is clearly biased • Insurance is always a profitable business when you get rid of the losses! • If it happened once, it can and will happen again. • A small fraction of claims often give rise to a large percentage of losses.

12. Pricing Techniques: Practical Track Partly Biased Experience Rating? • Partly biased experience rating • Losses and premiums for a bad class of business are removed from the data • The bad class is no longer being written • Result may still be partly biased • What defines the bad class other than its high LR? • Could remaining classes also run into trouble? • Select credibility value for remaining business

13. Pricing Techniques: Practical Track Rate Changes • Overt Rate Components • Base rates • Primary and secondary rating factors • Deductible discount and ILF factors • Schedule rating credits/debits • Package mods • Backdoor Rate Factors • Classification shifts • Mileage estimates

14. Pricing Techniques: Practical Track Average Premium Change vs Rate Change • Change in Average Premium does not necessarily equal change in rate!

15. Pricing Techniques: Practical Track Cessions-Rated Treaties • Idea is to Cede Only Exposed Premium • Risk by Risk Rating • Risk limits determine layer exposure • Per Risk premium allocated to treaty layer • Focus on Adequacy of Allocated Premium • Check adequacy of total premium • Validate allocation formulas • Update parameters

16. Pricing Techniques: Practical Track Clear-up Cessions-Rating Mysteries • No information provided on cessions factors or ILFs • Why? • There are no ILFs • The company is using “market” rates • What do you do? • Use agreed-on cessions factors

17. Pricing Techniques: Practical Track Cession Factors by SIR • As the SIR increases, XOL reinsurers should receive a greater percentage of the premium • They are providing coverage for a greater percentage of the total losses subject to the policy. • What do you do? • Use cession factors which vary with the SIR • Apply the cession factors to ground-up premium prior to the SIR credit

18. Pricing Techniques: Practical Track Avoid Base Rate -Total Rate Skewer • Base Rates up - Total rates flat • Why is this bad for reinsurers? • Base rates eating up more of the total premium • Less premium left for the XOL reinsurers • XOL reinsurers end up taking it on the chin. • What do you do? • Review adequacy of underlying premium and ILFS • Compute factors to give reinsurers a fair cut

19. Pricing Techniques: Practical Track Cessions-Rating by SIR Example • Policy Limit = $5M • Layer = $4M x $1M • ILF • LimitILF • 1M 1.00 • 2M 1.20 • 5M 1.50 • 6M 1.55 • Cession Rate [ no SIR ] = (1.50-1.00)/(1.50) = 33% • Cession Rate [$1M SIR] = (1.55-1.20)/(1.55-1.00) = 64%

20. Pricing Techniques: Practical Track Use Consistent ILFs for Cessions-Rating • Inconsistent ILFs can lead to pricing inversions • Example • LimitILFDifference • 1M 1.0 • 2M 1.8 .8 • 3M 2.5 .7 • 4M 3.1 .6 • 5M 3.8 .7 • Problem: 1M x 4M is more expensive than 1M x 3M

21. Pricing Techniques: Practical Track Deductible Credits in Cessions-Rating • Premium Calculation on Policies with Deductibles and ILFs • Deductibles credits apply to the Basic Limits • Correct: Premium = Base Rate x (ILF – Ded Cr) • Incorrect: Premium = Base Rate x (1 - Ded Credit) x ILF

22. Pricing Techniques: Practical Track Cessions-Rating with Deductible -Example • Policy Limit = $500,000 • Basic Limit = $100,000 • Deductible = $1,000 • Basic Limit Policy Premium = $100 • Deductible credit = 10% • ILF = 2.5 • Premium for $500K policy = 100 x (2.5 - .1) = $240 • Frequent calculation is 100 x (1 - .1) x 2.5 = $225

23. Pricing Techniques: Practical Track Items to Consider in Determining the Credibility Of The Exposure Loss Cost Estimate • The accuracy of the estimate of RCF, the primary rate correction factor, and thus the accuracy of the primary expected loss cost or loss ratio • The accuracy of the predicted distribution of subject premium by line of business • For excess coverage, the accuracy of the predicted distribution of subject premium by increased limits table for liability, by state for workers compensation, or by type of insured for property, within a line of business • For excess coverage, the accuracy of the predicted distribution of subject premium by policy limit within increased limits table for liability, by hazard group for workers compensation, by amount insured for property • For excess coverage, the accuracy of the excess loss cost factors for coverage above the attachment point. • For excess coverage, the degree of potential exposure not contemplated by the excess loss cost factors

24. Pricing Techniques: Practical Track Items to Consider in Determining the Credibility of the Experience Loss Cost Estimate • The accuracy of the estimates of claims cost inflation • The accuracy of the estimates of loss development • The accuracy of the subject premium on level factors • The stability of the loss cost, or loss cost rate, over time • The possibility of changes in the underlying exposure over time • For excess coverage, the possibility of changes in the distribution of policy limits over time.

25. Pricing Techniques: Practical Track Treaty Features • Losses • LR Corridors • LR Caps • Annual Aggregate Deductibles • Premiums • Reinstatements • Swing Rating • Commissions • Profit Commission • Sliding Scale Commission

26. Pricing Techniques: Practical Track LR Corridor Example

27. Pricing Techniques: Practical Track LR Cap Example

28. Pricing Techniques: Practical Track Annual Aggregate Deductible Example

29. Pricing Techniques: Practical Track Swing Rated Premium Example

30. Pricing Techniques: Practical Track Reinstatement Premium Example Maximum Ceded Loss = 2,000 Maximum Total Premium = 500

31. Pricing Techniques: Practical Track Sliding Scale Commission Example

32. Pricing Techniques: Practical Track Profit Commission Example

33. Pricing Techniques: Practical Track Treaty Models • Loss Ratio Model vs Count-Severity Model • Loss Ratio Model • Example: assume LR is Gamma or Lognormal • Count-Severity Model • Model Number of Claims and Size of Claims • Example: assume Poisson Counts and Pareto Severity • QS can often be modeled with LR model • XOL often requires Count-Severity model

34. Pricing Techniques: Practical Track Model Parameters • Mean loss for high excess should usually be larger than historical • Often no loss in XS layer • List potential scenarios and review limits profile • Selected CV should usually be larger than historical • Have 5-10 years of history • Probably don’t have 100 year event in history • Adjust for trend • XS layers have leveraged trend – impact of trend is • to increase frequency of layer penetration

35. Pricing Techniques: Practical Track Simulation vs Formulasfor Pricing Treaty Features • QS Treaties with LR Models • Can often evaluate EV of feature using LEV formulas • Evaluating Var often requires complicated formulas • May be best to use simulation and check EV of simulation with formula calculation • XOL Treaties with Count-Severity Models • Can use aggregate distribution approximation formulas), but application may get complicated • Simulation may be easier all-purpose approach.

36. Pricing Techniques: Practical Track The Simulation Mind-Lock • Tendency to accept model without question • False belief # of iterations proves model is right • “5,000 iterations good – 10,000 better” thinking But what if model is wrong or assumptions are bad? • Actuaries should check answers Do back of envelope check • Compare EV with formula based result • Conduct sensitivity tests

37. Pricing Techniques: Practical Track Pricing Pitfalls • Look for any bias in the data • Adjust for mix • Watch the pricing for your layer • XS Layer factors, ILFs, Base Rates • Think before you use a model and after you get the results