Reinsurance Pricing

Question 1

one major difference between primary insurance and reinsurance

Answer 1

is that reinsurance is generally customized to each individual buyer

Question 2

2 main methods by which reinsurance can be applied

Answer 2

1. facultative reinsurance – designed and purchased separately for each individual risk of ceding company
2. treaty reinsurance – allows a reinsurer to cover multiple risks of ceding company; priced based on risks in aggregate

Question 3

2 main types of treaty reinsurance

Answer 3

1. proportional – assumes given % of losses and premium
   - quota share - % ceded is same across all risks
   - surplus share - % ceded varies by risk
2. non-proportional – assumes losses in excess of ceding company’s retention limits (XL reinsurance)
   - Per risk XL – assumes losses between a retention and limit for each risk; offers protection against large individual claims
   - Per occurrence XL – assumes losses between retention and limit for each occurrence across multiple risks; offers protection against CATs
   - Aggregate XL – assumes losses between retention and limit for aggregate total of losses for given time period; offers frequency protection

Question 4

policies can be provided upon 1 of several bases

Answer 4

1. risks attaching – all policies that begin or renew during contract period are covered regardless of when losses occur or are reported; think of losses typically on PY basis and relate them to WP
2. losses occurring – all claims that occur during contract period are covered regardless of when policies were incepted or losses are reported; think of losses typically on AY basis and relate them to EP
   - there are other types of bases as well: claims made, policies issued, in-force

Question 5

2 methods to price reinsurance policies

Answer 5

1. experience rating – use adjusted historical experience of either the reinsurance contract or ceding company to calculate premium for prospective reinsurance contract
   - primary approach used to price proportional reinsurance
2. exposure rating – use current risk profile and estimated loss distributions to calculate premium for prospective reinsurance contract
   - often used in combination with experience rating to price non-proportional

Question 6

adjustments in experience rating pricing for reinsurance are similar to pricing insurance policies

Answer 6

On level premiums

Trend exposures and premiums

Develop losses to ultimate

Trend losses

Replace actual CAT losses with CAT load

Load for expenses

Question 7

QS

Answer 7

reinsurer assumes a flat % of premium and pays that same % of loss and alae

-reinsurer will also pay a ceding commission to ceding company to reflect that ceding company will have much larger UW expenses

Question 8

ceding company may wish to purchase a SS treaty

Answer 8

if want to retain low risk policies and cede higher risk policies

• for any risks with insured value below retained line, ceding company keeps risks in full
• for risks with insured values above retained line, reinsurer will assume a % of loss, alae, and premium on those risks of max[0, min(surplus lines, IV - retained line)]/IV

Question 9

6 steps in experience rating to price a proportional treaty for property coverage

Answer 9

1. compile historical experience on treaty
2. exclude cat and shock loss
3. develop and trend losses, on-level and trend premiums and exposures
4. select expected non-cat LR for treaty
5. load expected non-cat LR for CAT
6. estimate other expenses and combined ratio

Question 10

Sliding Scale Commission

Answer 10

• common feature in reinsurance policies is called sliding scale commission
• commission paid by reinsurer to ceding company varies with actual LR on treaty, subject to max and min commission
• in balanced sliding scale plan, commission at expected LR = expected commission
• not always the case, so it is best to calculate expected commission as probability weighted average of commission at each LR

Question 11

sliding scale commissions may also have a carryforward provision

Answer 11

-this means if actual LR exceeds LR for min commission, then amount of LR in excess of LR for min commission is added to LR in subsequent year for purposes of determining next year’s commission

Question 12

there are 2 approaches to pricing carryforward provisions

Answer 12

1. assume that any past carryforward amounts only apply to current year’s LR
   - can assume this by subtracting carried over LR amount from LRs in current year’s sliding scale
   - problem with this approach is that it ignores potential for future carryforward
2. look at expected ultimate commission ratio for block of years together
   - problem with this is that it isn’t obvious how to reduce variance of aggregate loss distribution when you combine the years and it ignores that contract might not renewed

Question 13

Profit Commission

Answer 13

• returns some of reinsurer’s profit to ceding company as additional commission
• similar to sliding scale commission that is based on actual LR and increases commission with low loss result

Question 14

Loss Corridors

Answer 14

-allow ceding company to reassume some liability if LR exceeds certain amount

Question 15

property per risk XL treaty provides

Answer 15

reinsurance coverage above a retention and up to limit for each risk

-treaty premium is set as % of ceding company’s subject premium base which will either be:

Gross net EP income for policies on loss occurring basis

Gross net WP income for policies on risks attaching basis

• net refers to net of any other inuring reinsurance (reinsurance that applies before this treaty)
• gross refers to property per risk XL treaty being priced

Question 16

Experience Rating for Property Per Risk XL

-steps for experience rating:

Answer 16

1. gather historical subject premium and loss data, ideally 10yrs; losses should include any that could pierce layer after trend
2. on level subject premiums and trend premiums and exposures
3. trend losses for severity, determine trended amount in layer, and sum them for each year
4. apply excess LDFs to develop excess losses; ideally derive LDFs from ceding company data; trend losses for frequency if needed
5. divide trended and developed loses by adjusting subject premium to get loss costs from each historical year; take average of years to get expected loss cost; loss costs by year should be fairly random around average; load loss costs for reinsurer profit and expenses

Question 17

Free Cover

Answer 17

• one issue that arises in using experience rating for excess of loss treaties is when there is no loss experience in highest portion of layer
• experience rating would give away any excess coverage for which there is no loss experience -> concept is called free cover
• for example, if you are pricing 750k XS of 250k and highest trended ground up loss is 500k, then experience rating would indicate that treaty should cost just as much as 250k XS 250k ie no charge for layer 500k XS of 500k
• one way to deal with this is to use experience rating for lower portion of layer and then use exposure rating relativities to price higher portion of layer

Question 18

2 measures of credibility to use for experience rating property per risk XL treaties

Answer 18

1. expected number of claims or expected dollars of loss during historical period; use expected claims since actual claims would assign more credibility to worse than average years
2. use variance of historical projected loss costs; more stable LRs, more credibility that should be assigned to experience
   - Clark says amount of credibility assigned is subjective

Question 19

Inuring Reinsurance

Answer 19

• in case excess treaty applies on top of another reinsurance such as surplus share, some adjustments need to be made to price for treaty
• for experience rating, need to restate historical experience to be net of inuring reinsurance
• exposure rating can be applied directly to adjusted risk profile that is adjusted for inuring reinsurance
• if exposure curves vary by risk size, select curve based on gross insured value but apply exposure factors to expected losses net of inuring reinsurance

Question 20

casualty per occurrence XL treaties are usually separated into 3 layers

Answer 20

1. working layer – lower layer that is expected to be hit
2. exposed layer – higher layer but attaches below some underlying policy limits; layer is hit less frequently and may not be hit at all in some years
3. clash covers – high layer that is usually only hit due to multiple policies involving a single occurrence; could also be hit by extra contractual obligations or rulings awarding damages in excess of policy limits; layer could also be hit by a single policy is alae is included in treaty
   - paper focuses specifically on GL, AL, and WC casualty excess of loss treaties

Question 21

Experience Rating for Casualty Per Occurrence XL

-steps for experience rating:

Answer 21

1. gather historical premium and loss data; capture alae separate from loss
   - for GL and auto, capture underlying policy limit
   - for WC, obtain case reserves excluding any tabular discounts
2. on-level and trend premiums and exposures
3. apply severity trend to individual historical losses and alae
   - deal with policy limits by either:
   - capping trended losses at historical policy limits; this ignores that limits tend to increase over time
   - don’t cap, assuming policy limits drift up at same rate as loss trend; need to also increase premiums to reflect higher limits and quantify amount of this adjustment can be difficult
4. sum trended losses by year and apply excess LDFs
5. divide trended and developed layer losses by adjusted subject premium to get loss costs by year; take average and select final expected loss cost; load for time value of money, expenses, and risk load

Question 22

-if using data published by RAA be cautious of:

Answer 22

report lag can vary by company, mix of attachment points and limits may not be cleanly broken out, data may contain asbestos and environmental claims, data may include inconsistent tabular discounts

Question 23

alae is handled in 1 of 2 ways

Answer 23

1. included with loss – sum up loss and alae and treat as single amount when comparing to limit and retention
2. pro-rata with loss – calculate portion of ground up loss covered by treaty; same percentage of ground-up alae will also be covered

Question 24

Swing Plans

Answer 24

-another loss sensitive feature is Swing plan which is type of retro rating

Question 25

WC Treaty Experience Rating

Answer 25

• if loss experience is distorted by tabular discounts, can develop past claims based on claim and claimant info including paid to date amounts to determine future expected payments
• can look at paid loss triangles instead of case incurred loss triangles to develop losses to ultimate

Question 26

for experience rating excess treaties covering umbrella policies

Answer 26

if ceding company also writes underlying policies below the umbrella, best to consider underlying and umbrella policies as single policy by adding their premiums and losses together

• if ceding company does not write underlying policies, it becomes more difficult to price treaty
• main difficulty in experience rating excess policies on umbrellas is selecting an appropriate severity trend

Question 27

aggregate distribution models

Answer 27

1. empirical distribution – use historical experience
   - does not account for all possible outcomes and actual results may differ greatly from historical averages
2. single distribution models – assume aggregate losses follow known distribution
   - advantage of being simple to use even when source data is limited
   - no allowance for loss free scenario and no easy way to reflect impact of changing per occurrence limits on aggregate losses
3. recursive calculations – frequency is assumed to be Poisson, negative binomial, or binomial and severity is defined in discrete equally spaced amounts
   - advantage of being simple to work with and providing accurate handling of low frequency scenarios
   - inconvenient of higher expected frequencies due to # calculations and only single severity distribution can be used
4. other collective risk models – collective risk model is one in which frequency and severity are analyzed separately

Question 28

collective risk model is usually very good way to produce aggregate distributions but need to sue some caution for following:

Answer 28

a. complexity of calculations can lead to black box mentality
b. assumption of frequency and severity being independent and each occurrence being independent of others may not be true
c. some models use numerical methods that have large error term for low frequency scenarios
d. aggregate distributions will reflect process variance of losses but not parameter variance of models used

Question 29

property cat treaties

Answer 29

are per occurrence excess treaties covering events such as hurricanes and EQs

• typically applied net of any existing surplus share, per risk XL, and facultative reinsurance
• important feature = reinstatements

Question 30

reinstatements

Answer 30

• these allow ceding company to refill treaty limit a certain number of times during policy period
• reinstatements can be pro rata as to amount of limit being refilled or pro rata as to time left on treaty or both
• reinstatements pro rata to time are not very popular due to seasonality of cats

Question 31

standard approach for pricing property cat treaties

Answer 31

cat models

-cat models require exposure info, coverage info for policies, geographical info, and details of any inuring reinsurance

Question 32

historical method for pricing property cat treaties

Answer 32

payback approach was used but now it is often just used as reasonability check on model results

Question 33

one important consideration in cat treaties

Answer 33

basis of treaty since risks attaching treaties have potential for reinsurer to pay multiple times on same event

Question 34

finite risk covers

Answer 34

property cat covers with lower max losses compared to traditional treaties

Question 35

finite risk covers have 2 common characteristics

Answer 35

1. multiple year features
2. loss sensitive features (ie profit commissions)

Question 36

2 conditions for ceding company to consider these reinsurance for accounting purposes

Answer 36

1. reinsurer assumes significant insurance risk
2. it is reasonably possible that reinsurer may realize a significant loss
   - some complicating factors in pricing these treaties

Reinstatement provisions

Expenses

Carryforward provisions

Changes in premium and profit commissions by year of treaty

Cancellation provisions