1. Philadelphia CARe Meeting European Pricing Approaches Experience Rating May 7-8, 2007 Steve White Seattle

2. 1 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.

3. Loss Development Aggregate Excess vs Individual Large Loss

4. 3 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

5. Policy Limits

6. 5 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

7. Subscription Contracts Stacking and Participation

8. 7 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.

9. 8  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 Participation Participation

10. 9 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 Stacked Contracts

11. 10 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

12. 11 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 Participation Stacking

13. 12 25% Share 50% Share 100% Share Stacking and Participation Partial Participation without Stacking

14. 13 Stacking and Participation Partial 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

15. 14  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 Participation Summary

16. Loss Trending Calendar Year vs Accident Year

17. 16 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

18. 17 Index Clauses

19. 18 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

20. 19 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