Clark Flashcards
Describe the 2 main methods by which reinsurance can be applied
- Facultative reinsurance
Reinsurance designed and purchased separately for each individual risk of ceding company - Treaty reinsurance
Single reinsurance contract allows reinsurer to cover multiple risks of ceding company
Describe the 2 main types of Treaty Reinsurance
- Proportional
Reinsurer assumes same % of losses an premium - Non-proportional
Reinsurer assumes losses in XS of retention limits.
Also known as XOL reinsurance.
Describe the 2 main types of Proportional Treaty Reinsurance
- Quota Share
% is same across all risks
Reinsurer will also pay ceding comm to ceding company to reflect larger UW expenses incurred - Surplus Share
% varies by risk
When ceding company wants to retain low risk policies & only cede high risk policies
Explain how losses are split between retained and ceded for Surplus Share reinsurance
Tot surplus lines = Retained line * # of lines purchased
If risk below retained line, keeps in full
If insured value above retained line, reinsurer assumes % of loss, ALAE & premium of:
max(0%, min(SurplusLines, InsValue - RetainedLine)/InsValue)
Describe the 3 types of Non-proportional reinsurance treaties
- Per Risk XL
Reinsurer assumes losses between retention and limit for each risk
Protects ceding company against large individual claims - Per Occurrence XL
Reinsurer assumes losses between retention and limit for each occurrence across multiple risks.
Commonly used as CAT reinsurance - Aggregate XL
Reinsurer assumes losses between retention and limit for aggregate tot losses for a given time period (usually 1y)
Offers frequency protection primarily.
Briefly explain the pricing paradox
If you can precisely price a given contract, ceding company will not want to buy it.
If historical is stable enough to provide data to make a precise expected losses estimate, then reinsured will be willing to retain that risk.
Describe the difference between risk attaching and losses occurring bases.
Risk attaching:
All policies beginning or renewing during reinsurance contract are covered regardless of when losses occur or are reported.
Losses on PY basis
WP
Losses occurring:
All claims occurring during reinsurance contract period are covered regardless of policy inception or when losses are reported.
Losses on AY basis
EP
Describe the 2 main methods for pricing reinsurance
- Experience rating
Use adjusted historical experience of either reinsurance contract or ceding company to calculate E(Loss) of prospective reinsurance contract.
Primary approach used to price proportional reinsurance. - Exposure rating
Use current risk profile and estimated loss distribution to calculate E(Loss) of prospective reinsurance contract.
Often used in combination with experience rating to price non-proportional reinsurance.
List adjustments made in experience rating of reinsurance contract
- On-level premium
- Trend exposures and premiums
- Develop losses at ultimate
- Trend losses
- Replace cat losses with cat loading
- Load expenses
Define subject premium
Non-proportional treaties have rate expressed as % of ceding company’s premium potentially subject to treaty.
Define burn cost
Rate based solely on experience rating (aka experience rate)
Define burning cost
Unadjusted ratio of past ceded losses to past subject premium.
List and advantage and a disadvantage of experience rating for reinsurance contract
+: use ceding company’s actual experience
-: experience is volatile and maybe outdated
List an advantage and a disadvantage of exposure rating for reinsurance contract
+: uses ceding company current mix of business
-: Loss distribution used may not be good fit for risks being priced
Describe the steps to price proportional treaty using experience rating
- Compile historical experience on treaty (5 or more years)
- Exclude CAT and LL
- Develop and trend losses, on-level and trend premiums and exposures.
- Select expected non-cat loss ratio for treaty
- Load for CATs
- Estimate other expenses & CR
- Decide whether CR is acceptable or not
If CR is not acceptable, list 3 adjustments reinsurer can suggest
- Lowering ceding commission
- Introducing occurrence limits
- Introducing adjustable features: sliding scale commissions, loss corridors, etc.
Describe Sliding Scale Commissions
When commission paid by reinsurer to ceding company varies with actual loss ratio on treaty, subject to max and min commission.
Provisional commission is paid at start of treaty and adjusted up or down later based on actual loss experience of treaty and scale.
E(Comm_range) = Comm_high + slide*(LR_high - AvgLR)
Define Expected Technical Ratio
ETR = ELR + Expected Comm Ratio
Briefly explain how sliding scale commissions can create CF advantage
Any difference between provisional commission and expected commission would give a CF advantage to either reinsurer or ceding company.
Expected > Provision = Adv to reinsurer
Expected < Provision = Adv to insurer
Briefly describe Carryforward Provision
Sliding Scale Commissions may also have carryforward provision, which means actual LR > LR corresponding with min commission.
Carryforward provision = LR prior - LR mincomm
Provision is added to LR in next year for determination of next year’s commissions.
Why do we use carry forward provision
In the long run, this helps smooth results.
Describe the 2 approaches to estimate impact of carry forward provisions.
- Decrease LR in each bracket of sliding scale by carry forward amount.
- Model sliding scale based on long-run expected impact of contract.
Expands method 1 to span of several years instead of just 1.
Serves to reduce aggregate variance by factor of # of years in block.
Identify a disadvantage of method 1 to estimate impact of carry forward provision
This assumes any past carry forward amounts only apply to current year’s LR.
Identify a disadvantage of method 2 to estimate impact of carry forward provision
Ignores fact that contract may non-renew, giving reinsured no carry forward benefit.
If comm deficit can be carried forward, but credits cannot, potential for non-renewal is exacerbated.
Briefly describe the impact of positive carry forward provision on next year’s commission (all else being equal)
If carry forward > 0, E(Comm) for next year will decrease, all else being equal.
Calculate Profit Commission
Profit commissions return some of reinsurer’s profit to ceding company as additional commissions.
Also based on actual LR and increases commission with low result.
Reins Profit = 1 - Actual Treaty LR - Ceding Comm - Reins Expense Margin
% Profit Comm = Reins Profit * % returned
$ Profit Comm = Actual Ceded P * % Profit Comm
Calculate LR Net of Loss Corridors
Loss corridors allow ceding company to reassume some liability if LR > certain amount.
Avg LR Net of corridor = min(AvgLR, Layer_min + max(AvgLR, Layer_max) - Layer_min, 0)*(1-corr) + max(AvgLR - Layer_max,0))
Describe the impact of Loss Corridor on reinsurer ELR
Loss Corridor decreases reinsurer ELR.
Calculate experience rating loss cost for Prop per risk XL treaty
- Gather historical data (ideally 10y since larger losses)
- On-level subject premiums and trend premium & exposures
- Trend losses & determine amount in reinsurance layer
- Apply LDFs to developped layer losses
- Calculate LR for each historical year and take average
- Load expenses
Describe the 2 ways ALAE can be handled
- Included with loss
Sum up trended loss & trended ALAE and treat it as a single amount when comparing to limit and retention
Covered = max(0, min(limit, Loss+ALAE - retention)) - Pro-rate with loss
Calculate portion of trended loss covered by treaty
Assume same % of trended ALAE will also be covered
Loss covered = max(0, min(limit, loss - retention))
ALAE covered = (loss covered/loss) * ALAE
Calculate exposure rating loss cost for Prop per risk XL treaty
Done using exposure curves P(p): expected loss capped at % p of IV divided by expected unlimited loss.
P(p) = E(X;pIV) / E(X) = 1 - XS ratio (p)
Exposure factor = P(ret+lim / IV) - P(ret / IV)
State an advantage of exposure rating
Current risk profile is modelled not what was written years earlier + very helpful when data is sparse.
Can we use the same exposure curves for different risk sizes.
Ideally not.
Ow assume scale independence: prob of $10K loss on $100K risk = prob of $100K loss on $1M risk)
Scale independence is not realistic in practice, particularly for commercial insurance.
Discuss 3 issues on Property per Risk Treaties
- Free cover
Arises when there is no loss experience in highest portion of layer. Experience away would give away any XS coverage for which there is no loss experience. - Credibility for experience rating
Lack of credibility will reduce appropriateness of experience-rated indicated loss costs. - Inuring reinsurance
When XS treaty applies on top of another, need to adjust.
Need to restate historical to be net of of inuring reinsurance.
Explain how to deal with Free Cover
Use experience rating for lower portion of layer and then use exposure rating relativities applied to lower layer experience loss cost to price higher portion of layer.
Describe 3 layers of Casualty per Occurrence XL Treaties
- Working layer
Lower layer expected to be hit, often multiple times per year.
A perfect working layer would produce stable enough results to be retained by ceding company. - Exposed Excess Layer
Sees losses less frequently and sometimes not at all during a given year.
Experience rating may still be used to price this layer. - Clash Cover layer
Usually only hit due to multiple policies involving a single occurrence (ex: cats)
Could also be hit by Extra Contractual Obligations (ECO) or rulings awarding damages in XS of policy limits.
Could be hit by single policy depending on how ALAE is included.
Describe the steps for experience rating a Casualty per occurrence XL Treaty
- Gather historical data
- On-level and trend premium and exposures
- Apply severity trend to losses and ALAE
- Sum trended losses by year and apply excess LDFs
- Divide trended and developped layer losses by adjusted subject premium to get loss costs by year.
Explain 2 methods to deal with policy limits in Casualy per occ XL treaties
- Apply historical policy limit to each trended loss
Ignores fact that limits tend to increase over time - Apply trend factor to historical loss without policy limit cap (& adjust subject premium to reflect premium that would have applied at higher limit)
Assumed limits increase with inflation
Which data should be used to derive excess LDFs
Ideally, ceding company data
Otherwise, industry data published by RAA, but caution:
1. Report lag can vary by company and may include several layers of lag
2. Mix of retention and limits is not clearly broken out (can distort LDFs)
3. Data may contain asbestos and environment claims (may distort patterns)
Use exposure rate to price Casualty per occ XL treaty
As with property exposure rating, we can use distribution related to claim severity based on industry statistics to estimate layer losses.
For WC, distribution is used to obtain ELFs = E(X) - E(X;L) / E(X)
Once exposure curve (sev distribution) is known, you can obtain exposure factor:
(ILF(AP+Lim) - ILF(AP)) / ILF(PL)
AP = Attachment Point
Then apply exposure factor to expected losses (net of inuring reinsurance).
How is the exposure rating formula different if ALAE pro-rata
Exposure factor = E(X;min((AP+Lim)/(1+e),PL) - E(X;min(PL,AP/(1+e)) / E(X;PL)
e is % ALAE
Discuss 2 issues with loading ALAE in casualty per occ XL treaties and how can we resolve
- Both methods assume ALAE varies directly with capped indemnity.
Not good assumption since you can have ALAE and no indemnity + large claims do not tend to have proportional ALAE
This tends to result in overestimating ALAE in higher layers - In formula with e, it can result in exposure factor of 0 applying to higher layer that could actually be hit since ALAE can exceed selected loading.
These issues can be resolved by modeling ALAE to loss relationship:
ELFs can be approx by aL^(-b)
a and b can be estimated from selected XS ratios found in NCCI retro manual.
In Casualty per occ XL treaties, which 3 distributions can be used to obtain E(X;L)
- Truncated Pareto
E(X;L) = pS + ((1-p)/(Q-1))((B+QT)-(B+L)(B+T)*Q/(B+L))
T is truncation point
p is prob of small loss
S is avg small severity - Log-Logistic (special case of Truncated Pareto with B=0 and Q=1)
E(X;L) = pS + (1-p)T(1-ln(T/L)) - Mixed Exponential
E(X;L) = sum of wjuj(1 - exp(-L/uj))
Identify 2 disadvantages of using Truncated Pareto in Casualty per occ XL treaties
- Only apply to losses > T
- Excess factors for higher layers become very dependent on Q
Briefly explain how umbrella policies are a problem for casualty excess treaties
Umbrella policies differ from standard excess insurance since they usually provide broader coverage not tied to underlying policy definitions.
If written above primary policies from ceding company, can be treated as single policy with higher limit.
If ceding company does not write underlying policy, it becomes more difficult to price treaty.
Define umbrella insurance
Liability coverage in excess of other policies where coverage is limited or non-existent.
Calculate exposure factor for umbrella policy without drop-down coverage
Trended Umbrella Loss = (Loss + Underlying Limit)*TrendFactor - Underlying Limit
Ignores new trended losses piercing umbrella policy.
Exposure Factor = (E(X;min(UL+PL,UL+AP+Lim))-E(X;min(UL+PL,UL+AP))) / (E(X;UL+PL)-E(X;UL))
Define drop-down coverage
If underlying policy agg limits exhausted, umbrella will drop-down to provide primary coverage.
Calculate exposure factor for umbrella policy drop-down coverage.
Exposure Factor = (E(X;UL+min(PL, AP+Lim))-E(X;UL+min(PL, AP))(1-phi)+(E(X;min(PL,AP+Lim))-E(X;min(PL,AP))phi) / ((E(X;UL+PL)-E(X;UL))(1-phi)+phi*E(X;PL))
phi is the agg excess charge (analogous to table M charge)
Describe 2 loss-sensitive features
- Annual Aggregate Deductibles (AAD)
Enables ceding company to retain losses in working layer, subject to specified limit.
XS treaty then covers aggregate losses in layer.
Excess charge = integral of (y-AAD)*g(y)/E(y) - Swing Plans
Type of retro rating, can be applied to single treaty or block of treaty years combined.
Retro P = (Actual Layer Loses)*100/ELR
ELR is before accounting for max/min
Briefly explain why swing plans are not balanced and how to correct for this (3)
Because load is 100/ELR.
To correct for this, you can:
1. Change expense load
2. Change max rate G
3. Change min rate H
Briefly explain how discount is an issue for WC treaty experience rating
Tabular discounts may distort experience rating.
To unravel discount, individual claim costs need to be projected into treaty layer.
This require demographic info and cost info.
List 4 ways to construct aggregate distribution models
- Empirical distribution
- Single distribution
- Recursive calculations
- Other Collective Risk Models
Explain the empirical distribution method to construct aggregate distribution models. Give 1 advantage and 2 disadvantages.
Use historical experience
+: Easy to calculate
-: Does not account for all possible outcomes (not reliable if limited data)
-: Volatility may be understated if volume or mix has changed significantly over time or if smoothing development technique is used (ex: B-F)
Explain the single distribution method to construct aggregate distribution models. Given 1 advantage and 2 disadvantages.
Assume agg losses follow known distribution, such as lognormal.
Distribution can be fit to historical data and then prob and expected losses within each range of agg losses can be calculated using distribution formulas.
+: Easy to use even with limited source data
-: No allowance for loss-free scenario (undefined at l=0)
-: No easy way to reflect impact of changing per-occ limits.
Explain the recursive calculations method to construct aggregate distribution models. Give 1 advantage and 2 disadvantages.
Panjer’s recursive algorithm formula generates agg loss distribution given equally-spaced discrete severity distribution with spacing h and claim counts N distribution that satisfies f(n) = (na+b)*f(n-1)/n
+: Easy to work with
-: Calculation is painful for higher frequency
-: Can only use 1 severity distribution
Explain the Other Collective Risk Models method to construct aggregate distribution models. Give 1 advantage and 2 disadvantages.
Explicitly recognize frequency and severity
Recursive calculation is an example of collective risk model
+: Very good way to produce aggregate distribution
-: Complexity of calculation can lead to black box mentality
-: Assume independence of occurrences and freq/sev
-: Can produce large error terms in low-free scenarios
-: agg distribution shows process variance but not parameter variance
For lognormal, calculate sigma^2, u, E(Y:L)
sigma^2 = s^2 = ln(CV^2 + 1)
u = ln(mean) - (s^2)/2
E(Y;L) = exp(u+s^2/2)Phi((lnL-u-s^2)/s) + L(1 - Phi((lnL-u)/s)
Which distribution satisfy the Panjer’s recursive formula requirement
- Poisson
a = 0
b = u
f(0) = exp(-u) - NB
a = 1-p
b = (a-1)(1-p)
p is prob of failure
f(0) = p^a - Binomial
a = p/(p-1)
b = (M+1)p/(1-p)
p if prob of success
M is # trials
f(0) = (1-p)^M
Explain how to use the Panjer’s recursive algorithm
A0 = p0
A1 = p1f1
pk = (a+b/k)pk-1
so A1 = (a+b)p0*f1 = (a+b)f1A0
A2 = p1f2 + p2f1^2 = (a+b)f2A0 + (a+b/2)f1A1
A3 = (a+b)f3A0 + (a+2b/3)f2A1 + (a+b/3)f1A2
…
Ak = sum of Ak-1fi(a+b/k)*i
if Poisson:
Ak = sum of uifiAk-i(1/k)
Mean = u(xf1+2xf2+3xf3+…)
Var = u(fix^2+f2(2x)^2+f3*(3x)^3+…)
Calculate E(S) and V(S)
E(S) = E(N)E(X)
V(S) = E(N)V(X) + V(N)E^2(X)
Calculate reinstatement premiums for CAT treaties.
Reinstatements allow ceding company to “refill” treaty limit a certain # of times during policy period.
Assume any reinstatements will be automatically applied after any loss covered by treaty:
Agg limit = (1+#reinst)*occ limit
Pro-rate to amount:
Reinst P = Annual P * Reinst provision * Actual Covered Losses/Occ Limit
Pro-rata to amount and time:
Reinst P pro-rate to amount * (months left / 12)
Briefly explain why pro-rata to amount and time is not very popular for cats treaty.
Due to seasonality of CATs.
Explain the payback approach to price cat treaties.
CAT models are now standard approach for pricing property cat treaties, but historically, payback approach was used.
Now often used as reasonability check on model results.
Payback period = Treaty Limit / Annual Premium
Rate on Line = Annual Premium / Treaty Limit
State 4 subjective considerations in pricing CAT treaty after model is run
- WC exposures can be substantial for eqk if WC is covered in treaty
- Inuring reinsurance terms may not be calculable by model
- Fire following eqk exposure may exist even if eqk are not covered directly.
- Coverage terms such as replacement cost vs actual cash value may significantly impact losses.
Discuss how risk attaching treaties have potential to pay multiple times for same event
An additional complication is the need to write contracts correctly such that reinsurer is not potentially twice liable for one loss.
This happens in risk attaching treaties if effective dates of underlying policy do not line up with effective dates of reinsurance treaty.
Underlying policy is covered by 2 different treaties since treaty renews in middle of policy term.
To avoid overpayment, many treaties include an interlocking clause to apportion losses that may be covered under more than one contract.
Define finite risk covers
Finite risk covers are property cat covers with lower max losses compared to traditional treaties.
They have 2 common characteristics:
1. Multiple year features
3y contract may allow for cancellation after 1 or 2 years if premiums exceed losses.
2. Loss-sensitive features
Profit comm, additional premium, etc.
State the 2 conditions for ceding company to consider finite risk covers as reinsurance for accounting purposes
- Reinsurer assumes significant insurance risk
- It is reasonably possible that reinsurer realize significant loss
List 4 complicating factors in pricing finite risk cover treaties
- Reinstatement provisions
- Expenses
- Carryforward provisions
- Changes in premium
- Profit comm by year
- Cancellation provisions
Calculate Final Price of Treaty
Prem = (Loss Cost*(1+ULAE%) + f)/(1-v)
Reinsurance premium need to cover reinsurer’s expected losses + which 3 other things?
- Timing of CFs (impact investment income which contributes to profitability)
- Risk load for risk exposure to reinsurer
- Profit provision for reinsurer
Briefly describe 2 advantages of using continuous approx model to price XS layer insurance contracts.
- Requires software to do calculation since impossible to do by hand (not easy to calculate)
- Distribution fit can be very sensitive to input data and may be unstable if estimated based on small dataset
