C2. Basics of reinsurance pricing Flashcards
Types of reinsurance bases and data
- Risks attaching
- definition: covers all insurance policies that begin/renew during the reinsurance contract period (no matter when losses occur or are reported)
- data:
- premiums covered: written
- losses covered: policy year
- avg loss date: 1 yr after effective date
issue : potential for reinsurer to pay multiple times on same event
- Loss occurring
- definition: covers all insurance losses that occur during the reinsurance contract period (no matter when policies incept or when losses are reported)
- data:
- premiums covered: earned
- losses covered: accident year
- avg loss date: 6 mth after effective date
Problem/solution for an reinsurer if the insurer changes the base from risks attaching to losses occurring
If risks attaching for YYYY and losses occurring for YYYY+1:
-policies written during YYYY that have losses occurring during YYYY+1 would be covered twice (each treaty pays once)
Solution:
-interlocking clause to assign the losses of policies inforce during YYYY+1 that were written during YYYY to a specific treaty (either the risks attaching or the losses occurring)
Methods for pricing reinsurance treaties
- Experience rating (proportional):
- traditional model: use adjusted historical experience to calculate prospective premium
- burn cost model - Exposure rating (non poportional):
- use current risk profile and estimated exposure curve to calculate prospective premium for prospective reinsurace contract. can price high layer not penetrated by experience
Free cover problem/solution in experience rating of non proportional treaties
Free cover problem:
-when there is no loss experience in the highest layers, experience rating will “give away” any coverage excess of the highest loss in the experience
Solution:
- use experience rating for the lower layers that have loss experience
- then use exposure rating for the highest layers => exposure rating prices layers even if not penetrated during experience
4 ways to calculate cat loading despite insufficient historical data in experience rating
- based on ceding company’s rate filing
- based on expected number of times the occurrence limit is exhausted
- if cat=1-in-5 and limit=25M => loading=5M - based on historical data but spread over a long period of time
- ex: loading=(sum cat losses 10 yrs)/10 - based on expected losses of a cat model
2 ways to deal with underlying policy limits when trending losses in experience rating
- issue for casualty excess treaty and trendind of losses that are capped at policy limits
Policy limit generally increases over time as policyholder chooses higher policy limit each year due to inflation. So using those losse to preduct future losses may understate the future loss potentiel
- cap trended losses at historical limits ( aka ignore the problem) :
- ignores limits tend to increase over time
- Disadvantage: understates futur loss potential - do not cap trended losses:
- assumes limits increase at the same rate as the severity trend
- need to increase historical premiums to reflect those implied higher limits
- Disadvantage: difficult to quantify the required increase in historical premiums ( need to adjuste subject premium to refelct hiGher limits )
2 options for XS LDFs when developing excess trended losses in experience rating
- use the ceding company data to derive the XS LDFs
- use the Reinsurance Association of America (RAA) data to derive the XS LDFs, but with the considerations:
- report lag can vary by company
- mix of retentions and limits may not be cleanly broken out
- asbetos and environmental claims may be in data but not subject to treaty
- tabular discounts may be inconsistent in data for work comp
Why the upward drift of policy retentions and limits may distort the trending of losses for umbrella policies
If trending historical excess losses:
- trended XS loss = histo XS loss*(1+trend)
- upward drift of retentions => historical retention was lower than current retention => less losses should pierce current retention => overstates trended XS losses
If trending historical subject losses:
-trended XS loss = (AP + histo XS loss)*(1+trend) - AP
historical AP = 2000 and loss of umbrella = 4000
historical total loss = 6000
if new AP = 3000
than would consider a total loss = 7000
Why the change of policy deductibles may distort exposure rating
- if deductibles increase, losses below deductible are unknown for longer
- they will pierce the deductibles, but more later
- thus difficult to determine the appropriate exposure rate at given time - If deductible increase the subject prm decreases and the expected excess losses may not change significantly so the old exposure rate would be to low
- if deductible decrease, losses below the original deductible may be unknown so information is missing about the loss distribution. This makes it challenging to derive a new exposure curve for the lower deductible
Methods for pricing carryforward provisions
- The easy-peasy method:
- substract any past carry forward to the current year sliding scale LR ranges
- Disadvantage: ignores potential for carryforwards in future - The not so easy-peasy method:
- model the expected ultimate commission ratio for a block of years
- Disadvantages: difficult to determine the reduction in variance of agg dist due to higher # of years, ignores the contrat might not renew in future
Finite risk covers
A finite risk cover is a property cat treaty that has:
- lower maximum losses than a traditional per occurrence XL ( ** low risk treaties)
- multiple year features
- loss-sensitive features (ex: loss corridor, profit commission, swing plan, carryforward provision)
Complications for pricing finite risk covers
- carryforward provisions
- changes in profit commission by year
- expenses
- reinstatement premium
- cancellation provisions
Measures of credibility for experience rating in non proportional treaties
- expected # of claims or expected $ of losses during historical period (use expected instead of actual, otherwise it would assign more credibility to worse than average years) => higher is more credible
- variance of projected loss costs = (expected $ loss)/(expected # claims) during historical period => lower is more stable and therefore more credible
Problems of exposure rating with (1+e) factor to load ALAE when ALAE is actually included with loss
- overstates expected ALAE in higher layers
- (1+e) factor assumes that ALAE varies directly with capped loss
- however when loss increases, ALAE as a % of loss normally tend to decrease - ignores exposure to higher layers that are only penetrated due to ALAE
- if retention=1.1M and underlying limit=1M, then (1+e) factor assumes no exposure (since it is applied on capped loss=0)
- however if ALAE is 0.5M, then there would be exposure of capped loss=0.4M
Layers for non proportional treaties
- working layer:
- lower layer
- expected to be hit multiple times / year
- experience rating: stable results - exposed excess:
- higher layer but lower than some underlying policy limits
- less frequent, may not be hit at all in some years
- experience rating: may still be used - clash cover:
- higher layer that is higher than any individual underlying policy limit
- may only be hit due to multiple policies being impacted by the same event
- experience rating: only large carriers
- exceptions to be hit by a single policy:- extra contractual obligations
- ALAE are included in treaty (therefore in excess of the policy limit)
- court rulings awarding damages in excess of the policy limit
