Clark - Basic of Reinsurance Pricing

Question 1

When property proportional treaties are priced, the expected non-cat loss ratio should be loaded for cat. However, there will typically be insufficient credibility in historical experience. What are the four approaches he suggests to address this issue?

Answer 1

1. use an average cat loading based on ceding company’s rating filing
2. use an estimate of average number of times the occurrence limit is exhausted
   e. g. Limit = 25M, expectation of cat is 1 in 5 yrs=> cat load =5M
3. Spread cat loss over a long period of time (e.g. 10 years)
4. use expected cat. loss from a catastrophe model

Question 2

What is a “balanced plan”?

Answer 2

A balance plan is one in which the ultimate commission is a function of expected loss ratio. The expected sliding scale commission should equal to the sliding scale commission at expected loss ratio.

Question 3

What is the correct method to interpret potential profitability of a sliding scale reinsurance agreement from reinsurer’s prospective?

Answer 3

Potential profitability should be assessed by developing a probability distribution of loss ratios within intervals. For each interval, compute sliding scale commission. Then determine expected commission ratio.

Question 4

casualty excess treaty
According to Clark, a problem arises when trended losses are capped at policy limits when using experience rating to price a casualty excess treaty.

Briefly state the problem, and list two possible approaches for addressing this problem and a disadvantage for each approach.

Answer 4

Policy limit generally increases over time as policyholder chooses higher policy limit each year.

i. Cap trended losses at historical cap level.
- historical cap level does not reflect the cap level policyholder will choose in the future

ii. Do not cap trended losses and assume that policy limit increases at the same rate as inflation
- adjust prem to show what prem would have been at the higher loss limit is difficult

Question 5

How should surplus share treaty be reflected when experience rating per-risk excess treaty if surplus inures the per-risk treaty (ie. surplus applys before per-risk)

Answer 5

loss * % retained after the surplus treaty

apply the surplus treaty, then experience rate the remaining amount.

Question 6

List and briefly describe two reasons why exposure rating can be distorted when deductible levels change.

Answer 6

1. when ded. increases, primary rates decreases and since the expected excess losses don’t change, exposure rate charge has to increase to offset primary price decrease.
2. as ded increase, it is diff. to determine the appropriate exposure factor b/c group up losses below ded that haven’t pierced it are unknown.

Question 7

Explain what a carryforward provision is and why it is used

Answer 7

A carryforward allows the losses over the max. LR to be carried over to the next yr for that yr’s calculation of commission.
Gives insurers incentive to control losses even if their loss ratio passes the max threshold.

Question 8

Explain two approaches used in pricing impact of a carryforward

Answer 8

1. Calculate the impact on current yr only (ignore that it can continue to be carried forward in more and more yrs)
2. look at longer term impact by modeling a block of yrs rather than just one yr
   (ignores the fact that the contract may not renew the following year, potentially leaving the reinsured with no carryforward benefits)

Question 9

Problem of “Free cover”, and how can it be priced?

Answer 9

Free Cover: when no historical losses trend into the highest portion of the layer

One approach: use experience rating on lower portion, and apply relativities based on exposure rating to project higher layer

Question 10

Property Per Risk Excess Treaty:
What assumption need to be made when using the same exposure curve for multiple insured values?

When is this assumption appropriate and not appropriate?

Answer 10

the likelihood of loss as a % of insured value is the same across all insured values.

To show this, calculate Pure Premium/Insured Value and check if this ratio is consistent across all insured value ranges. (use mid range point is Insured value is given in a range)

Not idea for commercial book, can be used for homeowners.
Reason:
-HO risks are very homogeneous, even over a large size of home range.
-commercial risks are very heterogeneous in terms of both construction type and occupancy, therefore it is difficult to tell is 10% loss is as likely to a 1m property as to a 10m one.

Question 11

what premium data and claims data should be used for the following types of proportional treaties

1. loss occurring
2. risk attaching

Answer 11

loss occurring: EP and AY, avg accident data = 6 month from effective date
risk attaching: WP and loss from the policies, avg accident date is 1 yr from affective date

Question 12

Property Per Risk Excess Treaty:

what is limits profile, what must be verified about the limits profile or distortion will result.

Answer 12

Limits profile: when using exposure rating, the calculation is performed on a distribution of premium by different ranges of insured value, known as “limits profile”

Must verify the size of risk ranges are on a per location basis. If it is assembled using total insured value covering multiple locations, distortion will result.

Question 13

Property Per Risk Excess Treaty:
when using exposure rating for a treaty after inuring insurance, what is the basis for selection exposure curve, before or after surplus share

Answer 13

insured value before surplus share

Question 14

Casualty per occurrence excess treaties

What are the three categories, and how can experience rating be applied to them

Answer 14

1. Working layer
   low layer attachment, expected to be penetrated multiple times in each annual period
2. Exposed Excess
   Excess layer attaches below some of policy limits on the underlying business
   ie. there are policies for which a full limit loss will cause a loss to the treaty
   These losses will be less frequent, and there will be some years that treaty layer is not penetrated

3.Clash Cover
high layer attachment
typically a loss on a single policy will not penetrate the treaty layer
A clash cover will be penetrated due to multiple policies involved in a single occurrence

• A perfect working layer will produce stable results for experience rating
• Experience rating are still used when the experience approaches the “exposed excess: category
• for large ceding carriers, clash losses may be common enough that experience rating can provide guidance for the price

Question 15

Casualty per occurrence excess treaties:
what are the two limitations when using exposure rating and ALAE is included with loss and apply a 1+e factor in the formula

Answer 15

1. assume ALAE varies directly with capped loss
   in general, as size of loss increases, ALAE as a % of loss will tend to decrease. this assumption will tend to result in overstatement of expected amounts in higher layers
2. exposure factor of zero will be applied to higher layers which are indeed exposed
   if underlying PL = 1M and ALAE factor = 1.5. then a treaty attaching at 1.5M will not be considered exposed by this formula

Question 16

What are the four
Aggregate distribution model?

Which one is the best way to price treaties?

Answer 16

1. Empirical Distribution

2.Single Distribution Model
assumes aggregate of all losses to the treaty follows a known CDF

3. Recursive Calculation
4. Collective risk models:
   Frequency and severity are explicitly recognized

4 is the best way to price treateis

Question 17

Aggregate Distribution:

What are the advantages and disadvantages of Empirical distribution?

Answer 17

Advantage:

• easy to calculate
• can be used as reasonability check for other methods

Disadvantages:

• experience does not take into account all possible outcomes
• if the volume or mix of business has been changing, the volatility of future period may be different than the historical period
• if loss development is using BF or cape cod method, the historical periods may present an artificially smooth LR

Question 18

Aggregate Distribution:
What is a commonly use single distribution model?

What are the advantages and disadvantages of this commonly used model?

Answer 18

Commonly used: lognormal distribution

Advantages:

• simple to use, even when source data is limited
• a reasonable fit is provided even when freq and severity distributions are not known

Disadvantages:

• no allowance for loss free scenarios
• no easy way to reflect the impact of changing per occurrence limits on the aggregate loss

Question 19

Aggregate Distribution:

What are the advantages and disadvantages of recursive calculation

Answer 19

Advantages:

• simple to work with
• provides an accurate handle of low freq scenarios
• # of pts evaluated on the severity distribution can be expanded to approximate continues curves

Disadvantages:

• for higher expected frequency, calculation is inconvenient
• only a single severity distribution can be used

Question 20

Collective risk model is generally the best way to price treaties, what are some of the cautions?

Answer 20

1. Complexity of the model can lead to a “black box” mentality
   - basic statistics should be compared to the empirical data for reasonability
2. Most models assume that each occurrence is independent of others
   - may be false in some cases

Question 21

Property Cat Covers:
What are the two ways to calculate reinstatement?
which one is more commonly used & why?

Answer 21

1. Pro-rata as to amount
2. Pro-rata as to time

1 is more popular due to the seasonal nature of some types of catastrophes