CLARK – Basics of Reinsurance Pricing; 2000 Exam: 5.5 points
(This article covers many basic reinsurance items that
appear in other articles)
What is the major difference between
reinsurance and primary as sited in Clark?
Reinsurance tailored more closely to buyer; no
such thing as average reinsured or average
reinsurance price
What is the “pricing paradox” for
reinsurance, according to Clark
If you can precisely price a given contract, the
ceding company will not want to buy it, i.e. if
the historical experience is stable enough to
provide data to make a precise expected loss
estimate, then the reinsured would be willing
to retain that risk.
List and briefly describe four types of
proportional treaties
1. Quota share – reinsurer receives a flat
percent of premium, and pays same % of
losses, including ALAE, pays ceding
commission (to reflect difference in
underwriting expenses)
2. Surplus share – reinsured may limit
exposure on any one risk to a given
amount
3. Fixed quota share on excess
4. Variable quota share on excess
For last two, underlying business is excess of
loss, but reinsurer takes a proportional share
of ceding company’s book.
List 6 steps that should be included in
pricing analysis for proportional treaties
1. Compile the historical experience on the
treaty
2. Exclude catastrophe and shock losses
3. Adjust experience to ultimate level and
project to future period
4. Select the expected non-catastrophe loss
ratio for the treaty
5. Load the expected non-catastrophe loss
ratio for catastrophes
6. Estimate the combined ratio given ceding
commission and other expenses
List four approaches to catastrophe
loading mentioned by Clark
1. Average cat loads based on the ceding
company’s projected distribution of
premium by state
2. If there is an occurrence limit on the treaty,
estimate the average number of times it is
likely to be exhausted in a year
3. “Spread” historical catastrophe losses over
a longer period
4. Use the expected cat amount from a cat
simulation model
Page 1 of 10
CLARK – Basics of Reinsurance Pricing; 2000 Exam: 5.5 points
List and briefly describe three special
features of proportional treaties
1. Sliding scale commission – percent of
premium paid by the reinsurer to the
ceding company which slides with the
actual loss experience, subject to minimum
and maximum amounts
2. Profit commission – subtracts actual loss
ratio, ceding commission, and a “margin”
for expenses from the treaty premium and
returns a percent of this additional
commission
3. Loss corridors – ceding company will
reassume a portion of the reinsurer’s
liability if the loss ratio exceeds a certain
amount.
Define loss corridor
Loss corridors – ceding company will
reassume a portion of the reinsurer’s liability if
the loss ratio exceeds a certain amount.
What is a “carryforward” provision
Allows that if the past loss ratios have been
above the loss ratio corresponding to the
minimum commission, the excess loss amount
can be included with the current year’s loss in
the estimate of the current year’s commission.
List two approaches to pricing the impact of
carryforward provisions, and the problems
with each approach
1. Include any carryforward from past years
and estimate the impact on the current
year only. Problem: ignores potential for
carryforward beyond current year
2. Look at the “long run” of the contract. The
variance of the average loss ratio for a
block of years should be significantly less
than the variance of the loss ratio for a
single year. Problems: method for reducing
variance is not obvious.
Define a property per-risk excess treaty
and contrast with per occurrence property
excess treaty.
Provides a limit of coverage in excess of the
ceding company’s retention. More narrow than
“per occurrence” property excess treaty, which
applies to multiple risks to provide catastrophe
protection.
For property per-risk excess treaty, what is
treaty premium set at?
Percent of a subject base premium, called
“gross net earned premium income” (GNEPI)
for losses occurring policies or “gross net
written premium income” (GNWPI) for risks
attaching policies. This premium is net of any
other reinsurance inuring to benefit of per risk
treaty but gross of per risk treaty being priced.
Page 2 of 10
CLARK – Basics of Reinsurance Pricing; 2000 Exam: 5.5 points
1. What is meant by losses occurring
and risks attaching?
2. Which is appropriate for each, written
premium or earned premium?
3. How do you calculate the net loss ratio
for each (p. 3, NEAS p 7)
Losses occurring – coverage is provided for
losses incurred (under ceding company’s
policies) during the treaty coverage period.
Earned premium is appropriate. Loss ratio =
Acc year losses / earned premiums
Risks attaching – coverage is provided for
losses incurred (under ceding company’s
policies) which were written during the treaty
coverage period. Written premium is
appropriate. Loss ratio = policy year losses /
written premium
What is the basic idea of experience
rating? What is it sometimes called?
Historical experience, adjusted properly, is the
best predictor of future expectations. Referred
to as “burn cost” model.
List five steps of experience rating. List
some complications that arise in each for
casualty.
1. Gather data (subject premium and
historical losses for as many years as
possible). Complication: For GL and Auto
Liab, underlying policy limit should also be
listed. For auto split limit losses, other
modifications needed. For WC, need
losses fully undiscounted
2. Adjust subject premium to future level
using rate, price and exposure inflation
factors as outlined in the section on
proportional treaties. Complication:
adjustment factors will vary for each line
3. Apply loss inflation factors to the
historical large losses and determine the
amount included in the layer being
analyzed. Use ISO. Capped losses and
underlying policy limit may understate final
results (look up possible approaches)
4. Apply excess development factors to the
summed losses for each period. Apply
RAA Loss dev study for industry
benchmark
5. Dividing the trended and developed layer
losses by the adjusted subject premium
produces loss costs by year. Loss cost
may be adjusted for time value of money,
expenses, risk load.
What advantage does exposure rating have  Current risk profile is modeled and not what
was written in prior years. Developed for
over experience rating for property per
homeowners, used for commercial property.
risk excess treaties as per Clark?
Page 3 of 10
CLARK – Basics of Reinsurance Pricing; 2000 Exam: 5.5 points
What is the formula for exposure rating?
Given a list of percent of Insured Values and
corresponding exposure factors:
% of IV
Exposure factor (exposure curve P)
0%
0%
10%
37%
20%
49%…
100%
93%
P ((Retention + limit)/Insured value) –
P(Retention/Insured Value)
P = exposure curve, = losses capped at a
given percent (p) of the insured value (IV)
relative to total value of the loss.
Example: for $400k excess 100k, formula is
P (400+100)/500) – P (100/500) =
P (100%) – P(20%) = 93% - 49%
Give the formula for Exposure rating
exposure factor including umbrella policies
UL = Umbrella liability
AP = attachment point
Lim = treaty limit
PL = ceding company policy limit
EF = [E(x;min(UL+PL,UL+AP+lim)E(x;min(UL+PL;UL+AP)] /
[E(x;UL+PL)-E(x;UL)],
Give the formula for Exposure rating
exposure factor including umbrella policies
with drop down
Φ(y) = aggregate excess change factor at
point y
EF = [E(x;min(UL+PL,UL+AP+lim)-
What other issues are mentioned in the
Clark article specifically for Property per
Risk Treaties?
1) Free Cover – experience rating in which no
losses trend into the highest portion of the
layer being priced
2) Credibility - # claims expected during the
historical period. If not easily calculable,
dollars of expected loss based on
exposure rating may be used. Often
significant credibility given to experience
rating
3) Inuring Reinsurance – if actuary has
exposure curves varying by size of insured
value, the curve should be selected based
on the insured value before the surplus
share is applied, but the exposure factor
should apply to the subject premium after
the surplus share is applied.
Where E(X;n) is the increased limit factor
E(x;min(UL+PL;UL+AP)] (1-Φ(y)) +E(x;lim+AP)E(x;AP) Φ(y)]
/ [(E(x;UL+PL)-E(x;UL))(1- Φ(y))+E(x;PL)( Φ(y)],
Where E(X;n) is the increased limit factor
Page 4 of 10
CLARK – Basics of Reinsurance Pricing; 2000 Exam: 5.5 points
One of the issues mentioned for property
per risk treaties is the “free cover”
problem. Define “free cover”. What is an
approach to the “free cover” problem?
Free cover: when the losses don’t reach the
excess layer, experience rating does not have
losses for rate. Use the experience rating as a
basis for the lowest portion of the layer and
then use the relativities in the exposure rating
to project the higher layer
List three categories that Casualty per
Occurrence Excess Treaties are often
separated into.
1. Working layer – lower layer attachment
that is expected to be penetrated
2. Exposed Excess – excess layer which
attaches below some of the policy limits on
the underlying business
3. Clash covers – or high layer attachment
excess – will be penetrated due to multiple
policies in a single occurrence (cat) or
when extra-contractual obligations (EXO)
or rulings awarding damages in excess of
policy limits (XPL) are determined in a
settlement
While RAA statistics may be considered a
benchmark Clark mentions some cautions
to be aware of when using the data.
1) Retrocessional business is included in the
data, and may have several levels of
reporting lags.
2) Mix of attachment points and limits is not
cleanly broken out.
3) Asbestos and Environmental may or may
not be excluded – some long tem claims.
4) Treatment of Tabular Discount may not be
consistent among all companies.
Name three of the four considerations
Clark mentions as subjective with respect
to the Catastrophe Model.
 1) WC losses may be included within the
cover
2) The insuring reinsurance terms may not be
calculable by the model
3) Even if earthquake coverage is not sold,
there may still be exposure due to a fire
following the earthquake
4) Other coverage terms, such replacement
instead of ACV may be critical
What does exposure rating approach for
casualty per occurrence excess treaties
use?
Uses a severity distribution, based on industry
statistics, to estimate layer of losses.
Distribution is used to calculate ILF, and ELF
(excess loss factors) for WC.
Page 5 of 10
CLARK – Basics of Reinsurance Pricing; 2000 Exam: 5.5 points
Show ISO’s truncated pareto formula for
ILF and ELF for casualty per occurrence
excess treaties and list two limitations.
ILF = E[x;U]/E[x;L}
ELF = (E[x] – E[x;L])/E[x]
Where E[x;L] = PS ((1-P)/(Q-1)) [(B+QT)(B+L)((B+T)/(B+L))^Q]
For Q<>1, L>T
1. Only applies for losses above the truncation
point T
2. Excess factors for higher layers become
very dependent on the Q parameter
What else are severity curves used for?
Proportional treaties on excess business.
T/F Exposure rates should be based on
factors including risk load
False. Should be excluding risk load.
What happens to ISO’s truncated pareto
formula for ILF and ELF when B=0 and Q
goes to 1?
It becomes log-logistic distribution
E[x;L] = PS + (1-P) T (1-ln(T/L))
In casualty excess exposure rating, once a
severity dist is selected, an exposure factor
can be calculated. Give the formula
Exposure factor =
(E[x;min(PL,AP+Lim)] – E[x;min(PL;AP)] ) /
E[x;PL]
where PL = ceding company policy limit
AP = treaty attachment point
Lim = treaty limit
WC severity dists are most used from
NCCI curves. Show the inverse power
curve that easily approximates ELFs from
these curves.
ELFL = (E[x] – E[x;L])/E[x]
= aL-b
parameters a and b are estimable from
selected excess factors.
Exposure factor for WC formula
ELFAP – ELFAP+Limit
List 6 special problems on casualty excess
treaties
1. Credibility
2. Free cover
3. Including umbrella policies – for experience
rating, selecting appropriate trend factor; for
exposure rating, formula leaves out
possibility of “drop down” feature of
umbrella policy
4. Handling ALAE included with loss –
problem for exposure rating because ALAE
may exceed percent of capped losses in
some cases
5. Loss sensitive features
6. WC experience rating
Page 6 of 10
CLARK – Basics of Reinsurance Pricing; 2000 Exam: 5.5 points
List four aggregate distribution models
1. Empirical distribution – use actual data
2. Single distribution model (lognormal)
3. Recursive calculation of aggregate
distribution
4. Other collective risk models
Contrast the single distribution model with
the collective risk model (MEMORIZE!)
The single distribution approach assumes that
the aggregate of all losses to the treaty
follows a known CDF form. In contrast, in a
“collective risk” model, there is explicit
modeling of frequency and severity
distributions.
List an advantage and two disadvantages
in using the single distribution model
Advantage – relatively simple to use, even
when source data is limited.
Disadvantages:
1. No allowance for the loss free scenario
2. No easy way to reflect the impact of
changing per occurrence limits on the
aggregate losses.
In what type of scenarios is the recursive
formula a very convenient tool for
calculating aggregate distributions?
For low frequency scenarios. It uses Poisson
distribution, which is easy to use.
List an advantage and two disadvantages
of using the recursive calculation of
aggregate distribution
Advantage – simple to work with, provides an
accurate handling of low frequency scenarios
Disadvantages:
1. For higher expected frequencies, the
calculation is inconvenient because all the
probabilities up to the desired level must
be calculated
2. Only a single severity distribution can be
used in the analysis
The collective risk model is generally the
best way to price stop loss treaties (treaties
which cover losses in excess of a set loss
amount or loss ratio. List four cautions from
Clark in using these
1. Complexity of calculations can lead to a
“black box” mentality
2. Most models assume that each
occurrence is independent of the others
and that the frequency and severity
distributions are independent of each
other.
3. Some collective risk models use numerical
methods with a large error term for low
frequency scenarios
4. Aggregate distribution reflects the process
variance of losses but does not reflect full
parameter variance.
Page 7 of 10
CLARK – Basics of Reinsurance Pricing; 2000 Exam: 5.5 points
What does a property catastrophe cover
provide?
Provides protection for a catastrophic event,
such as a hurricane or earthquake.
When a cat cover limit is reached or
partially used up, list two types of limit
reinstatement.
1. Pro-rata as to amount – if half the limit is
exhausted, it can be reinstate for premium
proportional to the amount reinstated
2. Pro-rata as to time – premium would be
further reduced to reflect only the amount
of time left in the policy period. (seldom)
What are three methods for pricing cat
covers?
1. Payback approach
2. Experience rating
3. Catastrophe models
What is the most common method for
pricing cat covers? How is this estimated?
How is it limited?
Payback approach – estimated as the limit
divided by the annual premium. It is limited in
that it does not consider such elements as the
growth in subject premium, reinstatement
provisions, or expenses.
What is another approach to pricing cat
covers?
Experience rating – historical cats can be
adjusted for loss inflation and changes in
exposure as a first order of approximation to
the exposure to the layer.
A catastrophe model will require several
types of information. List four
1.
2.
3.
4.
List four considerations that may need to
be included subjectively after results of a
catastrophe model is produced for a cat
cover.
1. WC losses may be included within the
cover.
2. Inuring reinsurance terms may not be
calculable
3. “Fire following” earthquake may be
included in ceded company’s losses
4. Other coverage terms (portion of
policyholders purchasing RCC instead of
ACV) may be critical
List two characteristics that are common to
most finite risk covers
1. Multiple year features
2. Loss sensitive features such as profit
commissions and additional premium
formulas
Measure of exposure
Terms of insurance policies
Geographical information
Details of inuring reinsurance
Page 8 of 10
CLARK – Basics of Reinsurance Pricing; 2000 Exam: 5.5 points
One type of loss sensitive program is the
“swing plan.” Describe this.
Actual losses to the layer are loaded for
expenses and the result is charged back to
the ceding company, subject to maximum and
minimum constraints.
Example:
Retro premium = actual layer losses x
(100/80)
Provision rate = 15%
Maximum premium = 30% x Subject premium
Minimum premium = 10% x Subject premium
List two issues with the “swing plan” and
solutions for each.
1. Maximum and minimum amounts are not
in balance. Solution: the loading,
maximum or minimum rates can be
adjusted to produce an acceptable loss
ratio
2. Provisional rate well below expected
ultimate swing plan premium rate.
Solution: difference is an added cash flow
advantage for the ceding company. It must
be included in the final pricing evaluation.
Clark mentions three approaches that take
timing and risk elements into account.
 1) Discounted Cash Flow Approach
2) Internal Rate of Return (IRR) on equity
flows
3) Target Return, Allocation of Surplus and
Risk Load
State the four methods mentioned in Clark
to allocate surplus to a product.
 1) Premium-surplus ratios – traditional
2) Variance or standard deviation – may be
readily available
3) Ruin Theory - focuses strictly on the
downside risk
4) Financial tests applied to statutory financial
statements – use of Risk Based Capital
formula
List the problems with variance of standard
deviation approach to allocating surplus
1. This may leave out parameter or model risk
2. Cases where variance decreases, but risk
does not. Example: use of annual aggregate
deductible (AAD). Reduces the variance of
losses within the AAD, but reinsurer is
concerned that losses will be greatly in
excess of premium instead.
Page 9 of 10
CLARK – Basics of Reinsurance Pricing; 2000 Exam: 5.5 points
List advantages of ruin theory for allocating
surplus (percentile set to an acceptable
probability of ruin)
1. Focuses strictly on the downside risk
2. Needed amount may be calculable directly
from an aggregate loss distribution model
3. Surplus is set such that the reinsurer’s loss
will exceed premium + surplus less than a
given percent of time.
List problems with ruin theory for allocating
surplus (percentile set to an acceptable
probability of ruin)
1. Combining the treaties together into total
book: Should standard apply for a single
treaty, all treaties for a given ceding
company, or some other grouping?
2. For property cat treaties, limit is much larger
than the annual premium.
3. Results on cat treaty are likely to be
strongly correlated with other property
treaties for the same ceding company and
with cat treaties with other cedents.
What are ECO, XPL, RAA
EXO – extra contractual obligations (see clash
covers, page 22)
XPL – Excess of policy limits (see clash
covers, page 22)
RAA – Reinsurance Association of America
Surplus share = Min[Insured Value – Retained portion], lines]/Insured Value
Profit commission = % returned * (1.0 – Actual LR – ceding commission – reinsurer’s margin)
Loss Corridors – ceding company assumes a portion above a certain amount
Free cover is when no losses trend into layer (use exposure rate with adjustment)
Umbrella Exposure Factor = (Emin(UL+PL, UL + AP + lim) – E(min(UL + PL, UL + AP)
E(UL +PL) – E(UL)
Exposure Factor including ALE under exposure rating (e = ALE as % of loss capped at PL:
EF = (E(x;min(PL, AP + lim))/(1+e) – E(x;min(PL, AP/(1+e))) )
E(x;PL)
PL applies to loss only and AP and lim apply to ALAE plus loss capped at PL
Page 10 of 10