seminar on reinsurance – june 2-3, 2003 pricing techniques: practical track 2-3

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

Michael Coca

Chief Actuary, PartnerRe

Pricing Techniques: Practical Track2 June 2-3, 2003

Treaty Pricing

Experience and Exposure Rating

Cessions Rated Treaties

Treaty Features

Modeling and Simulation


Selecting the Rating Layer

Handling CAT and Shock Losses

Data Mix Adjustments

Biased Analysis

Experience Rating


Experience Rating Layer Attachment

Competing tendencies

=> Maximize # of claims (lower attachment point)

=> Minimize extrapolation to treaty layer (higher attachment point)


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.


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.


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


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


GL Severity Mix Adjustment

GL Mix Average

Exposure

ELF

Mix

Adjusted

IndexTable A Table C

1998 70% 30% 8.30% 1.2651

1999 65% 35% 8.85% 1.1864

2000 60% 40% 9.40% 1.1170

2001 55% 45% 9.95% 1.0553

2002 50% 50% 10.50% 1.0000


GL BURNAdjusted for Change in Mix

On-Level Subject

Premium

Ultimate Loss

Burn MixAdjusted

index

Adjusted Burn

1998 10,000 800 8.00% 1.2651 10.12%

1999 10,000 650 6.50% 1.1864 7.71%

2000 10,000 800 8.00% 1.1170 8.93%

2001 10,000 900 9.00% 1.0553 9.50%

2002 10,000 1,000 10.00% 1.0000 10.00%

AVG 8.17% 9.25%

3 YR 9.00% 9.48%


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 experienceis 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.


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


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


Average Premium Change vs Rate Change

Change in Average Premium does not necessarily equal change in rate!

Extra Heavy Trucks Medium Trucks Total

Year # Average Premium

# Average Premium

Average Premium

2001 200 $5,000 400 $2,500 $3,333

2002 400 $4,500 200 $2,250 $3,750

-10% -10% +12.5%


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


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


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


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


Cessions-Rating by SIR Example Policy Limit = $5M

Layer = $4M x $1M

ILF

Limit ILF

1M 1.002M 1.205M 1.506M 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%


Use Consistent ILFs for Cessions-Rating

Inconsistent ILFs can lead to pricing inversions Example

Limit ILF Difference

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


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


Cessions-Rating with Deductible -ExamplePolicy 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


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


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.


Treaty Features Losses

LR CorridorsLR CapsAnnual Aggregate Deductibles

PremiumsReinstatementsSwing Rating

CommissionsProfit CommissionSliding Scale Commission


LR Corridor Example

Start of Corridor 60%

End of Corridor 70%

Prob Cedants LR Treaty LR

20% 55% 55%

20% 60% 60%

20% 65% 60%

20% 70% 60%

20% 75% 65%

Avg 65% 60%


LR Cap Example

LR Cap 70%

Prob Cedants LR Treaty LR

20% 55% 55%

20% 60% 60%

20% 65% 65%

20% 70% 70%

20% 75% 70%

Avg 65% 64%


Annual Aggregate Deductible Example

AAD 500k

Prob Cedants Loss Treaty Loss

20% 200 0

20% 300 0

20% 500 0

20% 800 300

20% 1,200 700

Avg 600 200


Swing Rated Premium ExampleLoss Loading Factor 1.25

Max rate 15% 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%


Reinstatement Premium Example Up-front Ceded

Premium 250k

Layer 1m xs 1m

1 Reinstatement at 100%

Individual

Loss

Ceded Loss Reinstatement

Premium

1,500 500 125

1,500 500 125

2,000 1,000 0

1,200 0 0

Maximum Ceded Loss = 2,000

Maximum Total Premium = 500


Sliding Scale Commission ExampleCommission =25% at LR =50%

Slide 1:2 to 20% at LR =60%

Prob LR Commission

20% 45% 25.0%

20% 50% 25.0%

20% 55% 22.5%

20% 60% 20.0%

20% 65% 20.0%

Avg 55% 22.5%


Profit Commission ExamplePC Share 50%

Reinsurer Margin 10%

Provisional Comm 30%

Prob LR PC

20% 45% 7.5%

20% 50% 5.0%

20% 55% 2.5%

20% 60% 0%

20% 65% 0%

Avg 55% 3.0%


Treaty Models

Loss Ratio Model vs Count-Severity Model

Loss Ratio ModelExample: 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


Model ParametersMean 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


Simulation vs Formulasfor Pricing Treaty Features

QS Treaties with LR Models Can often evaluate EV of feature using LEV formulasEvaluating Var often requires complicated formulas May be best to use simulation and check EV of simulation with formula calculation

XOL Treaties with Count-Severity ModelsCan use aggregate distribution approximation formulas), but application may get complicatedSimulation may be easier all-purpose approach.


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 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

seminar on reinsurance – june 2-3, 2003 pricing techniques: practical track 2-3

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