C.2. Basics of reinsurance pricing

Question 1

Types of proportional reinsurance

Answer 1

• Quota share: The percent of premium and loss ceded is the same across all risk.
• Surplus share: The percent of premium and loss ceded varies by risk.

Question 2

Types of non-proportional reinsurance

Answer 2

• Per risk XL: The reinsurer assumes losses between a retention and a limit for each risk. This protects the ceding company against large individual claims.
• Per occurence XL: The reinsurer assumes losses between a retention and a limit for each occurence across multiple risks. This is commonly used as catastrophe reinsurance.
• Aggregate XL: The reinsurer assumes losses between a retention and a limit for the aggregate total of losses from the ceding company in a given time period (usually 1 year). This offers frequency protection primarily.

Question 3

Bases of reinsurance

Answer 3

• Risks attaching: All policies of the ceding company that begin or renew during the reinsurance contract period are covered, regardless of when their losses occur or are reported. You would think of the losses typically on a policy year basis, and you would usually relate them to written premium.
• Losses Occurring: All claims that occur during the reinsurance contract period are covered, regardless of when the policies were incepted or when the losses are reported. You would think of the losses typically on an accident year basis, and you would usually relate them to earned premium.

Question 4

Definition of burning cost

Answer 4

Question 5

Reinsurer share on a surplus share treaty

Answer 5

Question 6

Steps on pricing proportional reinsurance

Answer 6

1. Compile historical experience on the treaty
2. Exclude catastrophe and shock (unusually large individual) losses
3. Develop and trend losses, on-level and trend premiums and exposures
4. Select the expected non-cat loss ratio for the treaty
5. Load the expected non-cat loss ratio for catastrophes
6. Estimate the other expenses and combined ratio

Question 7

Calculating expected sliding scale comission

Answer 7

Question 8

Expected technical ratio formula

Answer 8

Expected technical ratio = Expected Loss Ratio + Expected Commission ratio

Question 9

Carryforward provision definition

Answer 9

The amount of the actual loss ratio in excess of the loss ratio for the minimum sliding scale commission is added to the loss ratio in the subsequent year for the purposes of determining next year’s sliding scale commission.

Question 10

2 approaches to pricing carryforward provisions

Answer 10

1. Assume that any past carryforward amounts only apply to the current year’s loss ratio. You can apply this by subtracting the carried over loss ratio amount from the loss ratios in the current year’s sliding scale. The problem with this approach is that it ignores the potential for future carryforward.
2. Look at the expected ultimate commission for a block of years together. The problems with this approach are that it isn’t obvious how to reduce the variance of the aggregate loss distribution when you combine the years, and it ignores that the contract might now renewed.

Question 11

Profit commission calculation

Answer 11

Reinsurer profit = 100% - Actual treaty loss ratio - Ceding commission - Reinsurer expense margin

Profit commission = Reinsurer profit x Percent returned

Question 12

Loss corridor definition

Answer 12

Loss corridors allow the ceding company to reassume some liability if the loss ratio excees a certain amount. For example, the loss corridor might be 75% of the layer between an 80% and 90% loss ratio.

Question 13

Steps for experience rating a property per risk XL treaty

Answer 13

1. Gather historical subject premium and loss data. Losses should include any that could piece the layer after trend.
2. On-level and trend subject premium or exposures.
3. Trend losses for severity, determine the trended amount in the layer, and sum them for each year. Add in ALAE if it is pro-rata with loss.
4. Apply excess LDFs to develop the excess losses. Ideally, derive the LDFs from the ceding company data. Also trend losses for frequency if needed.
5. Divide the trended and developed losses by adjusted subject premium to gete loss costs from each historical year. Take an average of years to get the expected loss cost. Lost costs by year should be fairly random around the average. Load loss costs for reinsurer profit & expenses.

Question 14

Exposure curve formulas

Answer 14

Question 15

Why exposure curve percent of insured value may exceed 100%

Answer 15

If the limits profile doesn’t include coverages like additional living expenses for homeowners or business interruption for commercial.

Question 16

Consistent granularity of exposure curves for commercial

Answer 16

If there are multiple locations per policy, you need to make sure that the limits profile is based on data at the same level of granularity as what you are pricing (per risk or per location).

Question 17

Exposures curves and different risk sizes

Answer 17

Usually, exposure curves are constructed separately for different risk sizes, and all risks of a given size are assumed to be homogeneous. However, you may only have 1 exposure curve for different risk sizes. If this is the case, it implies that the probability of a $10k loss on a $100k risk is the same as the probability of a $100k loss on a $1M risk (i.e., scale independance). This assumption may not be realistic in practice, particularly for commercial insurance.

Question 18

Free cover definition and a solution

Answer 18

One issue that arises in using experience rating for excess of loss treaties is when there is no loss experience in the highest portion of a layer. Experience rating would “give away” any excess coverage for which there is no loss experience. This concept is called “free cover”.

One way to deal with this is to use experience rating for the lower portion of the layer, and then use exposure rating relativities to price the higher portion of the layer.

Question 19

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

Answer 19

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

Question 20

Adjusting pricing methodes for inuring reinsurance

Answer 20

For experience rating, you need to restate the historical experience to be net of the inuring reinsurance. Exposure rating can be applied directly to an adjusted risk profile that is adjusted for the inuring reinsurance. Also, if exposure curves vary by risk size, select the curve based on the gross insured value, but apply exposure factors to the expected losses net of the inuring reinsurance.

Question 21

Layers for casualty per occurence XL treaties

Answer 21

1. Working layer: A lower layer that is expected to be hit, often multiple times per year.
2. Exposed excess: A higher layer, but attaches below some underlying policy limits. This layer is hit less frequently, and may not be hit at all in some years.
3. Clash covers: A high layer that is usually only hit due to multiple policies involving a single occurrence. It could also be hit by Extra Contractual Obligations (ECO) or rulings awarding damages in excess of policy limits (XPL). This layer could also be hit by a single policy if ALAE is included in the treaty.

Question 22

Steps for experience rating a casualty per occurence XL treaty

Answer 22

1. Gather historical premium and loss data. Capture ALAE separate from loss. For GL and Auto, also capture the underlying policy limits. For WC, obtain the case reserves excluding any tabular discounts.
2. On-level and trend premiums and exposures.
3. Apply severity trend to individual historical losses and ALAE. ALAE can be either pro-rata with losses in the layer, or it can be combined with losses.
4. Sum the trended losses by year and apply excess LDFs.
5. Divide the trended and developed layer losses by adjusted subject premium to get loss costs by year. Take an average and select a final expected loss cost. Load the loss cost for the time value of money, expenses, and a risk load.

Question 23

Dealing with policy limits when trending losses in experience rating casualty per occurrence XL treaties

Answer 23

You can deal with policy limits in 1 of 2 ways:

1. Cap trended losses at historical policy limits. This ignores that limits tend to increase over time.
2. Don’t cap trended losses, assuming that policy limits drift up at the same rate as the loss trend. If doing this, you need to also increase premiums to reflect the higher limits, and quantifying the amount of this adjustment can be difficult.

Question 24

Options for LDFs in experience rating casualty per occurence XL treaties

Answer 24

Ideally use the ceding company data to derive the LDFs. Another option is to use data published by the Reinsurance Association of America (RAA), but cautions need to be taken when using their data:

• Report lag can vary by company.
• The mix of attachment points and limits may not be cleanly broken out.
• The data may contain asbestos and environmental claims.
• For WC, the data may include inconsistent tabular discounts.

Question 25

2 ways ALAE can be handle in XL treaties

Answer 25

1. Included with loss: Sum up the loss and ALAE and treat it as a single amount when comparing to the limit and retention.
2. Pro-rata with loss: Calculate the portion of ground-up loss (net of any inuring reinsurance) covered by the treaty. The same percentage of ground-up ALAE (net of inuring reinsurance) will also be covered by the treaty.