Philadelphia CARe MeetingPhiladelphia CARe Meeting

European Pricing ApproachesEuropean Pricing ApproachesExperience RatingExperience Rating

May 7-8, 2007May 7-8, 2007

Steve White

Seattle

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Experience Rating

The Experience Rating discussed here is largely for the rating of Excess of Loss contracts. Some of the discussion will be appropriate for other contract types.

Due to lack of exposure rating benchmarks, Experience rating is more heavily relied on outside of the US.

Disclaimer: the following comparisons between US and European methods are broad generalizations which vary greatly by user and company.

Loss DevelopmentLoss DevelopmentAggregate Excess vs Individual Aggregate Excess vs Individual Large LossLarge Loss

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Loss Development

US

Aggregate Excess

1. Trend Losses

2. Apply Excess Layer

3. Aggregate Losses to the Layer

4. Apply Loss Develop to the Aggregate Layer Losses

European

Individual Large Loss

1. Trend Losses

2. Apply Loss Development to Individual Losses (preferably stochastic)

3. Apply Excess Layer Terms (including layer indexing)

4. Aggregate Losses to the Layer

5. Include Load for IBNR

One reason for the preference of Individual Large Loss Development is the use of Index Clauses

Policy LimitsPolicy Limits

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Policy Limits

US

Capping of trended losses due to policy limits

Trending losses when original loss is larger than policy limit

Changes in policy limits (trend) over time

European

Often no limit or limit very large

Becoming more common

Lack of Policy Limits is one of the reasons that “unused exposure” is a bigger concern

Subscription ContractsSubscription Contracts Stacking and ParticipationStacking and Participation

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Subscription based Contracts (Stacking and Participation)

Each risk can be covered by a series of excess contracts (a Stack). The insurer may “participate” on some of the contracts. Their participation or share can vary from one contract to the next.

But since the contracts are covering the same risk, for reinsurance purposes the combined loss for the insurer’s shares of all contracts is counted as an occurrence.

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Participation allows you to correctly model the situation where a contract only covers a proportional share of the underlying loss.

It is most common in a subscription type market like Lloyds, but it is also useful for modeling some facultative business.

Example

Assume the following:– Primary writes a 25% participation on a $1M Contract– You reinsure a $200K xs $200K treaty layer

In order to expose the Reinsurance Cover:– There must be a loss to the primary contract greater than $800K ($200K / 25%) – The largest subject loss is $250K (25% of $1M), or $50K to the layer– Actually, you would take 25% of losses ceded to an $800K xs $800K

reinsurance layer. But since the primary policy is $1M, the exposed treaty layer is effectively 25% of $200k xs $800k.

Stacking and ParticipationParticipation

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Stacking is where an insurer issues multiple excess contracts covering the same underlying risk

Assume someone writes a series of policies covering the same risk, $100K x $100K (Yellow), $300K x $200K (Blue), $500K x $500K (Red) and $1M x $1M (Green)

If all are written at the same level of participation then effectively it is the same as a single $1.9M xs $100K (Purple) policy with the given participation

In practice, not all contracts are at the same participation and not all contracts are written (can be thought of as participation = 0%, this is sometimes called ventilation)

Subscription based Contracts (Stacking and Participation) Stacking

Individual Contracts

StackedContracts

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Now Assume there is a $500K x $500K reinsurance treaty covering these contracts

If the contracts are assumed to be independent, then the treaty would only cover the $500K x $500K layer on the $1M x $1M policy. No other policy would expose.

If the contracts are assumed to be stacked, then you would cover the $500K x $500K layer on the $1.9M x $100K policy.

There can be significantly greater exposure to the Reinsurance Contract under the stacked assumption

Subscription based Contracts (Stacking and Participation) Stacking

Reinsurance Layer

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Stacking is generally thought of as an International Issue, but…

Stacking can be used in the Facultative Markets and Large Commercial Property Risks

Stacking can be used to model Umbrella written over a company’s own underlying policies

Stacking is commonly used in combination with participation in a subscription market like Lloyds

Stacking and ParticipationStacking

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Layer: 300k xs 200k - no stacking

Limits Profile Rescaled RescaledPolicy SIR/ Treaty Limit TreatyLimit Retention Participation (Capped) Retention

100,000 100,000 100.0% 0 200,000300,000 200,000 100.0% 100,000 200,000500,000 500,000 50.0% 100,000 400,000

1,000,000 1,000,000 25.0% 200,000 800,000

"Our share" of the layer would be Participation x Capped Treaty Limit

25% Share

50% Share

100% Share

Stacking and ParticipationPartial Participation without Stacking

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Stacking and ParticipationPartial Participation with Stacking

25% Share (250k)

50% Share (150k)

100% Share (300k)

100% Share (100k)

50% Share (100k)

Assume an insurer writes a series of policies covering the same risk, $100K x $100K (Yellow), $300K x $200K (Blue), $500K x $500K (Red) and $1M x $1M (Green).

– Their participation on each is: $100K x $100K (100%), $300K x $200K (100%), $500K x $500K (50%),

$1M x $1M (25%)

– These policies are stacked

– You reinsure a $500K x $500K layer

In order to expose the Reinsurance Cover:

– There must be a loss greater than $600K ($100K / 100% + $300K / 100% + $100K / 50%)

– The largest subject loss is $900K ($100K * 100% + $300K * 100% + $500K * 50% + $1M * 25%), or $400K to the layer

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Because of the leverage effect of trending, the trending needs to be done “from ground up” (FGU).

If you believe that loss development varies by size of loss, then the development of the losses will also need to be done on a “from ground up” (FGU) basis.

Then apply the terms of the underlying contracts to determine the exposure to the reinsurance contract.

You CANNOT simply uses the losses to the policy in your experience rating analysis.

Actuaries frequently recognize the need to reflect Stacking and Participation in Exposure Rating but overlook the need to do so in Experience Rating.

Stacking and ParticipationSummary

Loss TrendingLoss TrendingCalendar Year vs Accident YearCalendar Year vs Accident Year

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Loss Trending

US

Accident Year

– Insurance Data (Bureau) reported on Accident Year

European

Calendar Year

– Must rely on Economic Indices for trending data (possibly with adjustments

– Index Clauses Index based on published data

– Index Clause adjustments made based on calendar yr payment

Data still grouped by Accident Year

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Index ClausesIndex Clauses

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Index Clauses

The excess layer adjusts with inflation (or some pre-agreed upon index)

Purpose Share the effect of inflation between the ceding company and the reinsurer

Types Straight or Simple Franchise Severe

Triggers Payment date Settlement date

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Unused Exposures

US

Tend to rely on adjusted exposure rating if considered at all

European

More concerned with unused exposure

Where exposure rating information not available, the unused exposure may be analyzed using curve fitting techniques on the data observed

Unused exposure is the part of a layer where there is no (limited) claims experience but there is still potential for exposure