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

Pricing Techniques: Practical Track2June 2-3, 2003 Treaty Pricing Experience and Exposure Rating Cessions Rated Treaties Treaty Features Modeling and Simulation

Pricing Techniques: Practical Track3June 2-3, 2003 Selecting the Rating Layer Handling CAT and Shock Losses Data Mix Adjustments Biased Analysis Experience Rating

Pricing Techniques: Practical Track4June 2-3, 2003 Experience Rating Layer Attachment Competing tendencies => Maximize # of claims (lower attachment point) => Minimize extrapolation to treaty layer (higher attachment point)

Pricing Techniques: Practical Track5June 2-3, 2003 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.

Pricing Techniques: Practical Track6June 2-3, 2003 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.

Pricing Techniques: Practical Track7June 2-3, 2003 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

Pricing Techniques: Practical Track8June 2-3, 2003 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

Pricing Techniques: Practical Track9June 2-3, 2003 GL Severity Mix Adjustment GL MixAverage Exposure ELF Mix Adjusted Index Table ATable C %30%8.30% %35%8.85% %40%9.40% %45%9.95% % 10.50%1.0000

Pricing Techniques: Practical Track10June 2-3, 2003 GL BURN Adjusted for Change in Mix On-Level Subject Premium Ultimate Loss BurnMix Adjusted index Adjusted Burn , % % , % % , % % , % % ,0001, % % AVG 8.17%9.25% 3 YR 9.00%9.48%

Pricing Techniques: Practical Track11June 2-3, 2003 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.

Pricing Techniques: Practical Track12June 2-3, 2003 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

Pricing Techniques: Practical Track13June 2-3, 2003 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

Pricing Techniques: Practical Track14June 2-3, 2003 Average Premium Change vs Rate Change Change in Average Premium does not necessarily equal change in rate! Extra Heavy TrucksMedium TrucksTotal Year#Average Premium # $5,000400$2,500$3, $4,500200$2,250$3, % +12.5%

Pricing Techniques: Practical Track15June 2-3, 2003 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

Pricing Techniques: Practical Track16June 2-3, 2003 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

Pricing Techniques: Practical Track17June 2-3, 2003 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

Pricing Techniques: Practical Track18June 2-3, 2003 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

Pricing Techniques: Practical Track19June 2-3, 2003 Cessions-Rating by SIR Example Policy Limit = $5M Layer = $4M x $1M ILF LimitILF 1M1.00 2M1.20 5M1.50 6M1.55 Cession Rate [ no SIR ] = ( )/(1.50) = 33% Cession Rate [$1M SIR] = ( )/( ) = 64%

Pricing Techniques: Practical Track20June 2-3, 2003 Use Consistent ILFs for Cessions-Rating Inconsistent ILFs can lead to pricing inversions  Example LimitILF Difference 1M1.0 2M M M M3.8.7 Problem: 1M x 4M is more expensive than 1M x 3M

Pricing Techniques: Practical Track21June 2-3, 2003 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

Pricing Techniques: Practical Track22June 2-3, 2003 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 ( ) = $240 Frequent calculation is 100 x (1 -.1) x 2.5 = $225

Pricing Techniques: Practical Track23June 2-3, 2003 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

Pricing Techniques: Practical Track24June 2-3, 2003 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.

Pricing Techniques: Practical Track25June 2-3, 2003 Treaty Features Losses LR Corridors LR Caps Annual Aggregate Deductibles Premiums Reinstatements Swing Rating Commissions Profit Commission Sliding Scale Commission

Pricing Techniques: Practical Track26June 2-3, 2003 LR Corridor Example Start of Corridor60% End of Corridor70% ProbCedants LRTreaty LR 20%55% 20%60% 20%65%60% 20%70%60% 20%75%65% Avg65%60%

Pricing Techniques: Practical Track27June 2-3, 2003 LR Cap Example LR Cap70% ProbCedants LRTreaty LR 20%55% 20%60% 20%65% 20%70% 20%75%70% Avg65%64%

Pricing Techniques: Practical Track28June 2-3, 2003 Annual Aggregate Deductible Example AAD500k ProbCedants LossTreaty Loss 20% % % % %1, Avg600200

Pricing Techniques: Practical Track29June 2-3, 2003 Swing Rated Premium Example Loss Loading Factor1.25 Max rate15% of Subject Prem Min rate 5% of Subject Prem Burn(% of SP)Swing Rate(% of SP) 0.0%5.0% 4.0%5.0% 8.0%10.0% 12.0%15.0% 16.0%15.0%

Pricing Techniques: Practical Track30June 2-3, 2003 Reinstatement Premium Example Up-front Ceded Premium 250k Layer 1m xs 1m 1 Reinstatementat 100% Individual Loss Ceded LossReinstatement Premium 1, , ,0001,0000 1,20000 Maximum Ceded Loss = 2,000 Maximum Total Premium = 500

Pricing Techniques: Practical Track31June 2-3, 2003 Sliding Scale Commission Example Commission =25%at LR =50% Slide 1:2 to 20%at LR =60% ProbLRCommission 20%45%25.0% 20%50%25.0% 20%55%22.5% 20%60%20.0% 20%65%20.0% Avg55%22.5%

Pricing Techniques: Practical Track32June 2-3, 2003 Profit Commission Example PC Share50% Reinsurer Margin10% Provisional Comm30% ProbLRPC 20%45%7.5% 20%50%5.0% 20%55%2.5% 20%60%0% 20%65%0% Avg55%3.0%

Pricing Techniques: Practical Track33June 2-3, 2003 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

Pricing Techniques: Practical Track34June 2-3, 2003 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

Pricing Techniques: Practical Track35June 2-3, 2003 Simulation vs Formulas for 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.

Pricing Techniques: Practical Track36June 2-3, 2003 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 Actuaries should check answers Do back of envelope check Compare EV with formula based result Conduct sensitivity tests But what if model is wrong or assumptions are bad?

Pricing Techniques: Practical Track37June 2-3, 2003 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