Siewert Flashcards
List 3 advantages of high deductible programs.
- Achieves price flexibility while passing additional risk to larger insureds
- Reduces residual market charges and premium taxes
- Gives cash flow advantages to insured (insurer pays claim first and must seek reimbursement from insured)
- Provides incentive for insureds to control losses while protecting them from large losses
- Allows self-insurance without subjecting insureds to demanding state requirements
Briefly explain how to estimate the overall reserve wile reflecting differing mixes of deductibles and limits
After selecting appropriate development factors, apply them at the account level using each account’s deductibles and limits.
Then aggregate estimated ultimate over all accounts.
List the 4 development approaches explored by Siewert to estimate XS reserves
- Loss ratio approach
- Implied development approach
- Direct development approach
- BF approach
Name 2 situations where loss ratio approach should be used
- No data is available
- For immature years where data is sparse
Briefly explain how to calculate the full coverage loss ratio when using loss ratio approach
Use company experience by state, reflecting individual account’s premium distribution.
Supplement company experience with industry experience if credibility is a problem.
Note: loss experience should be developed to ultimate, brought on level and trended to the appropriate exposure period for calculating loss ratios.
Calculate per-occurrence excess losses when using loss ratio approach.
Per-occ XS Losses = Premium * ELR * Per-occ charge
= PEX
X = per-occ charge = XS ratio
Calculate per-aggregate excess losses when using loss ratio approach.
Agg Loss Charge = Per-Agg XS losses = Prem * ELR * (1-XS ratio) * per-agg charge
= PE(1-X)*phi
One approach to get phi is using NCCI Table M
Note: phi applies applies to losses below deductible (ones retained by insured).
List 3 advantages of loss ratio approach.
- Can be used when no data is available or when data is immature
- Loss ratio estimates can be consistently tied to pricing programs
- Relies on a more credible pool of company and industry experience
List 2 disadvantages of loss ratio approach
- Ignores actual emerging experience (not as useful for mature years)
- May not properly reflect account characteristics, since development may emerge differently due to the exposures written
Explain the Implied Development Method to estimate XS reserves
- Develop full coverage losses to ultimate
- Develop deductible losses to ultimate by applying development factors reflecting various inflation indexed limits
- Determine ultimate excess losses by subtracting limited ultimate losses from full coverage ultimate losses
Ult(XS) = Ult(Unlim) - Ult(Lim)
Rsv(XS) = Ult(XS) - (Loss(Unlim) - Loss(Lim))
Note: unlimited loss tail factors should be consistent (higher) with limited tail factors (we do not want to develop limited losses beyond unlimited losses)
Describe 2 ways to determine the index value when determining development factors and why indexing.
Indexing keeps the proportion of deductible/XS losses constant around the limit from YtoY. Otherwise, a constant deductible implies increasing XS losses.
Possible ways:
1. Fit a line to average severities over a long-term history
2. Use an index that reflects movement in annual severity changes
List 3 advantages of implied development approach
- Provides an estimate of XS losses at early maturities even when XS losses have not emerged.
- Development factors for limited losses are more stable than those determined for XS losses.
- Estimating deductible losses helps determine the asset value represented by service revenue.
Name a disadvantage of implied development approach
It does not explicitly recognize excess loss development.
Calculate XS reserves using the Direct Development approach.
Given limited and full coverage LDFs, there are XSLDFs that balance limited and XS development with full coverage development.
Ult(XS) = Loss(XS) * XSLDF
Name an advantage of the direct development approach.
It explicitly recognizes excess loss development.
List 2 disadvantages of the direct development approach.
- XSLDFs tend to be overly leveraged and extremely volatile.
- If XS losses have not yet emerged, we cannot estimate IBNR (nothing to apply factors to!)
calculate XS ultimate using the BF approach (credibility-weighted method)
E(Loss(XS)) = PEX
Z_BF = 1/XSLDF
Ult(XS) = Z(Loss(XS)XSLDF) + (1-Z)PE*X
Which is a weighting between loss ratio approach and direct development approach.
List 3 advantages of the BF approach
- We can determine liabilities either directly or indirectly
- Gives us the ability to tie into pricing estimates for recent years where XS losses have yet to emerge
- Provides more stable estimates over time
Name a disadvantage of the BF approach
It ignores actual experience to the extent of the complement of credibility (may need to find weights that are more responsive to the actual experience).
Explain how to calculate tail factors to be used in the development method.
- Fit the inverse power curve on unlimited age-to-age factors to project unlimited ultimate losses.
- Select a time (ult age) at which the projection should stop (since inverse power curve continues forever)
- Once ultimate age is chosen for unlimited losses, fit the curve to each deductible limit and extend that to a common maturity.
Name 2 advantages of the Siewert’s tail factor procedure
- It is consistent for each limit
- It produces uniformly decreasing tail factors
Name one problem with Siewert’s tail factor procedure.
Bias exist due to extending each limit to the same maturity (lower limits should fully develop much sooner than higher limits).
Calculate Limited Severity Relativity
R_L = Severity Limited to L ar age t / Unlimited Severity at age t
Name 2 relationships of severity relationships
- Should decrease as age increases
Because more losses are capped at the per-occurrence limit as age increases - Should be higher for larger limit
Because a higher limit means less of the loss is capped, so relativity is higher
Calculate XSLDF from limited and unlimited development factors.
Limited LDF = Unlimited LDF * Sev Relativity at t2/Sev Relativity at t1
XSLDF = Unlimited LDF * (1-Sev Relativity at t2)/(1-Sev Relativity at t1)
Calculate unlimited LDF from Limited LDF and XSLDF
LDF(t1-t2) = Sev Rel at t1 * Limited LDF(t1-t2) + (1-Sev Rel at t1)*XSLDF(ti-t2)
Name a solution when limited development is greater than unlimited development.
Distributional approach:
Fit a model (e.g. Weibull) to severities in order to calculate consistent severity relativities and LDFs.
This makes it easy to interpolate among limits and years.
Parameters vary over time by development period.
Parameters can be estimated by minimizing chi-square between actual and fitted severity relativity’s at deductible size.
Constrain parameters so that model produces the actual unlimited severity at maturity.
Name 2 advantages of the distributional model
- Helps tie the relativities to the severities and provides consistent loss development factors.
- Allows for interpolation among limits and years.
List 2 approches to estimate per-aggregate XS losses
- Collective risk modeling
- NCCI Table M
Explain collective risk modeling to estimate per-aggregate XS losses
Implies modeling frequency & severity separately to determine loss development factors.
Siewert uses Weibull to model severity and Poisson to model claim counts.
Due to volatility of XS agg limits, Siewerts recommends using the BF method to determine final estimate of ultimate agg XoL.
Complete the sentence:
Development for losses excess of aggregate limits _____ with smaller deductibles than larger ones.
Decreases more rapidly over time with smaller deductibles than larger ones.
This makes sense because most of the later development occurs in the layers of loss above per-poco deductible, which is not covered by aggregate.
Only losses below per-occ deductible contribute to aggregate limit.
Explain how to use NCCI Table M to estimate per-aggregate XS losses
Relies on using the proper insurance charge table (more intuitive).
Adj Factor = (1+0.8X)/(1-X)
X = XS ratio = per-occ charge
The idea behind the adj factor is that increasing expected losses is equivalent to using a less dispersed loss ratio distribution, resulting in a smaller insurance charge.
Define service revenue
The amount paid by the insured to the insurer for handling claims below deductible.
Partition expected development around deductible limit
% Unpaid = 1 - 1/LDF = (LDF-1)/LDF
% Unpaid = R_L,t1(LDF_L - 1) + (1-R_L,ti)(XSLDF - 1) / LDF
Before the “+” is expected development below deductible
After the “+” is expected development above deductible
Calculate Ult(XS Agg) using BF method
Loss(XS Agg) = Loss(deductible) - Agg Limit
LDF(XS Agg) = E(Loss(XS Agg) at ult) / E(Loss(XS Agg) at t)
Ult(XS Agg) = Loss(XS Agg) + (1 - 1/LDF(Xs Agg))*E(Loss(XS Agg))
Calculate Service Revenue Asset
Ult(deductible net Agg) = Ult(deductible) - Ult(XS Agg)
Ult(recoverables) = Ult(Deductible Net Agg) * Loss Multiplier
Service Revenue Asset = Ult(recoverables) - Known recoveries
Describe 2 ways to handle allocated claims expense (ALAE) for high deductible programs.
- Account manages expense itself (ALAE not covered)
Development patterns reflect loss only - ALAE is treated as loss and subjected to applicable limits
Development patterns reflect Loss&ALAE
We assume expenses are equivalent to additional loss dollars
List 2 potential improvements to Siewert’s methods
- Obtain longer histories of experience
- Derive parameters that provide better fits to actual data
- Determine better tail factors
- Develop more advanced approaches to index loss limits
Provide an advantage and a disadvantage of using industry data to estimate ult(XS)
Advantage:
More stable at early maturities where excess losses are thin and XSLDFs are highly leveraged/volatile
Disadvantage:
Insurer might trust its loss experience more than industry average and want to reflect actual development
