Reinsurance Pricing

Question 1

The key differences between Reinsurance Pricing and Direct Pricing (4)

Answer 1

• the VOLUME and NATURE OF DATA available for analysis.
• There are few Standard Contracts.
• The INDIVIDUAL NATURE of most pricing exercise.
• Reinsurers price STOCHASTICALLY

Question 2

Similarities in Direct Pricing and Reinsurance Pricing

Answer 2

Both find the expected loss cost, then load for various loadings.

Question 3

Reinsurance Loadings (3)

Answer 3

1. Expense

2. Profit/ROE 3.Commission and Brokerage

Question 4

RI Expense loadings:

Answer 4

• RI will load for own expenses , similar to direct insurer.

- This includes allowances for: operational expenses, admin expenses and cost of Reinsurer’s own reinsurance.

Question 5

RI Profit/ROE loadings:

Answer 5

• RI will build profit loading into reinsurance price.
• This can be derived from:
  a) a profit target expressed as % gross/net premium.
  b) a return on capital target.
  c) a target loss or CR

Question 6

RI Commission and Brokerage loading:

Answer 6

• Loading will depend on: line of biz, type of reinsurance, broker and territory.
• It is priced as a percentage load to the net of brokerage reinsurance costs.

Question 7

Why do QS usually involve higher reinsurance premium than XoL?

Answer 7

• The cedant is passing a proportion of every premium to the RI, whereas XoL the cedant only pays a premium to reflect the expected large claims.
• The % of brokerage tends to be low (1-3%) for QS.
• For other covers brokerage is 10% -20%.
• Surplus premiums will be cheaper than QS since insurer will not cede smaller risks.

Question 8

Differences in Direct Pricing and Reinsurance Pricing

Answer 8

• The amount and type of data available to assess EXPECTED LOSS COST and the DISTRIBUTION of loss cost.
• The cedant is arguably as knowledgeable as the Reinsurer.
• More of a negotiation process.
• The approach will depend on LOB. e.g property catastrophes

Question 9

Types of Property Catastrophes models (3)

Answer 9

RMS, AIR & EQECAT

Question 10

Consideration when using CAT models.

Answer 10

• Which models are more robust for which period and locations.
• Assumptions behind models and updates.
• Input data requirements
• Type of output

Question 11

Sources of uncertainty in CAT models

Answer 11

• Uncertainty about which event will happen.

- Uncertainty about the exact amount of insured loss

Question 12

Pricing Property CAT models (approach)

Answer 12

• Reinsurer uses OEP and AEP Files in a stochastic frequency /severity model to simulate catastrophe loss experience in an annual period.
• Calculate Reinsurance recoveries by applying Reinsurance contract terms to simulated losses.
• Derive distribution of recoveries, along with expected annual recoveries and volatility measures used in risk loading e.g standard deviation or 90th percentile.

Question 13

Two approaches to Pricing Property Casualty NON PROPORTIONAL

Answer 13

• exposure rating- based on amount of risk (exposure). Reinsurer use a benchmark e.g ILF & First loss scales.
• experience rating

Question 14

Exposure Rating using ILFs ( casualty)

Answer 14

-Cedant provides list of risks/limit profile (assumption on where in band limits/Excess lie required under limit profile. Also must consider they interact)
- RI only assess the expected loss cost NOT volatility/distribution.
-Calculate expected losses for reinsurance layer LR excess ER
-Formula
=(ILF( LR+ER)-ILF(ER))/(ILF( L+E)-ILF(E))
-Calculate the expected losses for ceded risks: loss ratio times premium charged. (Assumption loss ratio and gross premium are consistent)
-For each risk calculate the expected Reinsurance losses and sum to give undiscounted expected loss cost.
-Discount taking into consideration the recoveries based on RI experience or historical large loss experience of cedant or both.
-Assumptions- no limit on recoveries ;no reinstatement premium; 100% share written
-Practical Consideration: Pricing is driven by min rate requirements, expenses and cost rather than expected loss cost (maybe zero)

Question 15

Two approaches of Experience based Rating

Answer 15

• Burning cost
• Stochastic freqeuncy / severity model
• choice depends on loading for profit, volume of data and time/resources.

Question 16

Experience Rating using Burning Cost

Answer 16

• Trend the claims data (inflation)
• Apply reinsurance contract terms to give the loss to the layer
• Aggregate by year of loss (loss occuring) or underwriting year (risk attaching) to give triangles of paid/incurred losses
• Develop to ultimate using benchmarks if necessary (when data is sparse at high excess layers. E.g RAA and ISO)
• Adjust exposure (often premium or vehicle year ) for past rate and exposure changes.(RI will need data on historical rate changes )
• Divide losses by exposure to get burning cost

Question 17

Experience Rating using frequency /severity model

Answer 17

• Trend individual losses
• For open claims either ignore or determine development factors ( especially liability lines). Alternatively, use stochastic model for development.
• The development factor should only allow for IBNER. IBNER development can be derived by arranging historical loss development into development triangles.
• Determine IBNR development factors using the large loss count development.
• Estimate the ultimate large claims count for each historical year.
• Adjust exposure change (similar to BC)
• Fit frequency distribution to final adjusted claim counts.
• Combine frequency and severity distributions to model cedant large losses and hence Reinsurance recoveries.

Question 18

Practical issues when RI Pricing

Answer 18

• Discounting- pricing should be based on discounted values. The choice should reflect the investment returns of assets held and capital. For liability pricing is sensitive to discount rates- long term assets.
• Inflation rate choice - factors: size of loss (small claims have lower inflation rates), group up losses / excess layer, drivers of inflation e.g court award inflation, increased propensity to claim & territory
• Shock loss treatment - * remove, analyse without it, and add loading. * spread the loss over a period of time
• Census point - reporting threshold for large loss data. A high census point means Reinsurer will not see many claims.
• Mix of cedant business- analyse segment differently if possible

Question 19

Key considerations when pricing Property Casualty PROPORTIONAL

Answer 19

Risk premium is not key. The key items are:

• Assessing the likely overall LOSS RATIO.
• Determine the level of CEDING COMMISSION or PROFIT COMMISSION while retaining profit.

Question 20

Assessing Loss ratio of Proportional RI. Type of Data.

Answer 20

• Gather (at least 10 years) triangulated premium and incurred data for each lob on an underwriting year basis.
• Gather information on rate changes split as the data triangles.
• Estimates of premium income to be written and rate changes.
• Information on changes in mix of business, policy terms.
• Information on CAT exposure.

Question 21

Assessing Loss ratio of Proportional RI. Approach QS

Answer 21

• Project triangulated data to the ultimate settled position for each historical year.
• Calculate loss ratios.
• Apply trends to loss ratios to put them on level to reflect premium rates.
• Average the adjusted loss ratios to give estimate of expected loss ratio (use lognormal distribution to fit if from statistical distribution)

Question 22

Determine the level of CEDING COMMISSION or PROFIT COMMISSION for QS. Approach

Answer 22

1. Assuming no profit /ceding commission.
   - Check 100 -loss ratio - ceding commission leaves enough to cover expenses and profits.
   - Assess probability of making loss to adjust ceding commission
2. Assuming ceding commission varies or there is profit commission.
   - Use loss ratio distribution to calculate the distribution of the reinsurer’s position.
   - RI will have requirement
   a) a probability of making a loss of no more than x%
   b) a probability of making a loss of y% or no more than z%
   c) combination of both
   - RI can adjust ceding commission or profit commission scales until requirements are met.

Question 23

Pricing Surplus share contracts

Answer 23

• The experience will be dependent in the way large losses are distributed
• The pricing is similar to QS, except Reinsurer will want to ensure no adverse selection from cedant in terms of types and amounts being ceded.
• Assess probability of making loss to adjust ceding /profit commission

Method 2

• It will depend on RI expected ratio and distribution.
• Collect as many years as possible of past data (paid, incurred and premiums).
• Adjust the data to allow for rate changes, past and future inflation, changes in terms and conditions, IBNR, etc … … so that the data is fully developed and on-level reflecting the period of cover being priced.
• allow for reinsurer’s expenses (including brokerage and retrocession) and profit requirements

Question 24

Pricing Stop Loss Reinsurance.

Answer 24

• Excess/Limits are expressed as loss ratios and responds to Aggregated results in a year (rather than an individual loss)
• Loss ratio view adjusted to assess volatility and likelihood of large losses.
• Alternatively, separately model for better volatility a)attritional losses (using historial experience and adjusted), b)large losses (using frequency-severity) and c)catastrophe (vendor model) losses

considerations:

• Terms of particular stop loss contract
• Inuring reinsurance covers
• Risk transfer criteria (meeting regulatory minima)
• Retained amount of recoverable layer by cedant

Question 25

Complications and/or unusual elements of Reinsurance arrangements when pricing.

Answer 25

1. Loss ratio caps
   - puts max limit on cover which prevents loss ratio exceeding certain limit e.g 300%
   - Pricing: Set price without limit. Determine what limit corresponds to the loss ratio using unlimited price. Reset price with maximum limit. Repeat till premium stabilized.
   - Check the likelihood of cap being breached on an unlimited price. If low, assume unlimited price.
2. Aggregate deductibles
   - The first £x of losses that would be recovered is not.
   - Allow for it by reducing losses to the layer for each year/simulation by £x.
3. Indexation clause / stability clause (fully indexed, severe indexation, francise indexation)
   - aim is to maintain real value of limit/retention.
   - common to injury claims.
4. Reinstatements limited and/or paid
   - Reinsurers will limit cover.
   - For BC, maximum limit is applied to each loss.
   - For F/S ,the same is done in each simulation of loss experience and recoveries.
   - For exposure methods, reinsurers will create tables of discount based on benchmarks.
5. Swing rates
   - premium depends on loss experience
   - Two forms:
   - “minimum plus”-min plus factor times actual losses.
   - “deposit + adjustment”
   - Pricing: Start with aggregate Distribution. Check that terms of the swing meet RI profit criteria. If not vary the terms to find acceptable combination.

Question 26

OEP

Answer 26

Occurrence exceedance probability. It considers the largest individual event loss in a year exceeds a particular threshold.

Question 27

AEP

Answer 27

Aggregate exceedance occupancy. It considers the probability that aggregate losses from all loss events in s year exceeds a particular threshold.

Question 28

Critical Assumptions Rating XoL using exposure curve.

Answer 28

• Band midpoint- e.g use average if sum insured is evenly distributed.
• Loss ratio-use the same Vs different loss ratios to the band.
• midpoint and inflation assumptions
• Applying same inflation to all claims- different claims are affected differently by inflation
• Will same curve apply to all limits or different. Also factor in heterogeneous
• Presence of aggregate features e.g deductibles, max reinstatements will require adjusting.
• Is it possible to split data into homogeneous groups (limited by data)
• Use linear interpolation to obtain intermediate points in curve or parametric curve points

Question 29

Indexation clause. Reinsurer approach

Answer 29

• The reinsurer can allow exactly for indexation in a burning cost calculation, but this can become very complex with multiple indices.
• The reinsurer can approximate, allowance by estimating the average delay to settlement/ payment (whichever appropriate).
• By making an assumption about the average future rate of earnings inflation the average effect of indexation can be calculated.
• This can be used to calculate to what on average the limit and retention should be indexed, and thus to price a layer with this limit and retention.
• The reinsurer can do this just for injury claims and price the non-injury claims, separately. Or the reinsurer can estimate the proportion of the claims that the reinsurer believes will be injury and can use this to weight between the unindexed and indexed layer prices