Transcript Download Handout 5

May 7-8, 2007
European Pricing Approaches
Experience Rating
Philadelphia CARe Meeting
Steve White
Seattle
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.
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Loss Development
Aggregate Excess vs Individual
Large Loss
Loss Development
US
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
Aggregate Excess
1. Trend Losses
2. Apply Excess Layer
3. Aggregate Losses to the Layer
4. Apply Loss Develop to the
Aggregate Layer Losses
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Policy Limits
Policy Limits
US

European
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

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
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Subscription Contracts
Stacking and Participation
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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Stacking and Participation
Participation
 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.
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Subscription based Contracts
(Stacking and Participation) Stacking
Individual
Contracts
Stacked
Contracts
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)
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Subscription based Contracts (Stacking and Participation)
Stacking
Reinsurance Layer
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
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Stacking and Participation
Stacking
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
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Stacking and Participation
Partial Participation without Stacking
25%
Share
Layer: 300k xs 200k - no stacking
Limits Profile
Policy
Limit
Rescaled
Rescaled
SIR/
Treaty Limit
Treaty
Retention Participation (Capped)
Retention
100,000 100,000
300,000 200,000
500,000 500,000
1,000,000 1,000,000
100.0%
100.0%
50.0%
25.0%
0
100,000
100,000
200,000
200,000
200,000
400,000
800,000
50%
Share
100%
Share
"Our share" of the layer would be Participation x Capped
Treaty Limit
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Stacking and Participation
Partial Participation with Stacking


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
25%
Share
(250k)
50%
Share
(150k)
50% Share
(100k)
100%
Share
(300k)
100%
Share
(100k)
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Stacking and Participation
Summary
 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.
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Loss Trending
Calendar Year vs Accident Year
Loss Trending
US
European
 Accident Year
– Insurance Data (Bureau) reported
on Accident Year
 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 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
Unused exposure is the part of a layer where there is no (limited) claims
experience but there is still potential for exposure
US

European
Tend to rely on adjusted exposure
rating if considered at all

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
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