Reserving - basics Flashcards
Accurate estimate of unpaid claims are important to:
- Internal management: estimates are used to make business decisions in pricing and UW as well as strategic and financial decisions
- inaccurately high could lead to decisions such as raising rates, tightening UW guidelines. Exiting LOB or territory, or purchasing add. reinsurance - Investors: estimates impact profitability of insurer and thus returns paid to investors
- inaccurately high would lower insurer’s profit, making it appear worse investment to potential investors - Regulators: estimates are used to monitor solvency of insurer
- inaccurately high resulting in lower profit might cause regulator to restrict insurer’s ability to write new business
Assumptions of Chain Ladder
2 main assumptions
- Development of future claims will be similar to development in prior periods
- Claims observed for an immature period tell you something about claims yet to be observed
Other assumptions:
- consistent claims processing
- stable mix of types of claims
- stable policy limits and deductibles
- stable reinsurance limits
Chain Ladder works best when
- no material changes in insurer’s operations
- presence or absence of large claims doesn’t greatly distort data
- sufficient volume of credible data
- LOB has high freq low severity with stable and timely reporting
Impacts of changes on CL estimates:
Speedups in settlement rates
Speedups in settlement rates
- Paid: overestimate because applying historical LDFs based on slower settlement rates to higher paid amounts
- Reported: no effect because moving money from ending case reserve bucket to cumulative paid loss but total reported remains unchanged
Impacts of changes on CL estimates:
Increase in case reserve adequacy
Increase in case reserve adequacy
- Paid: unaffected because would no impact paid triangle
- Reported: overestimate because applying historical LDFs based on lower case reserve adequacy to higher reported amounts
Impacts of changes on CL estimates:
Changes in LRs, frequency, or severity
Changes in LRs, frequency, or severity
-changing LR does not imply change to either paid or reported loss development -> LDFs are same for each year even though numbers are higher for deteriorating LR assuming prem is constant
Impacts of changes on CL estimates:
Exposure Growth
Exposure Growth
- no impact if no change to average accident date within each period
- avg accident date will usually be later more recent AYs than in older AYs for growing BOB
- this means claims in more recent AYs will have had less time to develop so applying historical LDFs would cause you to underestimate Ultimate losses -> true for paid and reported
- way to deal with this is to use quarterly or monthly triangles since avg accident date will be more stable
Impacts of changes on CL estimates:
Changing product mix
Changing product mix
- when you having changing MOB, both paid and reported development patterns can be impacted if segments of business that are changing have different development patterns
- if both segments are grow @ same rate, combined development is fine
- underestimate ultimates using combined LDFs if segment that is growing at larger rate is longer tailed (aka larger LDFs)
Expected Claims Method and Assumptions
-estimates ultimate as ratio * exposure base
Ult claims=ELR*EP
Ult claims=EPP*EE
Assumptions
- ultimate claims for exposure period can be better estimated based on a priori estimate than using experience observed to date for that exposure period
- AKA claims reported to date for that exposure period tell you no useful info about your ultimate claims for that exposure period
- reasonable expected claims ratio can be obtained
Expected Claims Method:
Works best for
Works best for
- when entering new LOB aka insufficient data to obtain historical LDFs
- when operational or environmental changes make historical data irrelevant for projecting ultimate claims
- when estimating ultimates @ early maturities for long-tailed LOBs where early CDFs are highly leveraged
- when data is unavailable
Expected Claims Method
Advantages/Disadvantages
Adv = providing stable estimate of ultimate
Dis = unresponsive to recent experience
Expected Claims Method
2 challenges
2 challenges
- determining appropriate exposure base
- estimating claims relative to that exposure base
Calculating the expected claims ratio
can calc based on historical data
-intentionally exclude any data for that exposure period for which we are estimating ultimate claims
Steps:
- develop claims to ultimate for each year -> CL
- calc ultimate claim ratio for each year of historical experience
- adjust historical claim ratios to be on same rate, tort reform, loss trend, premium trend, and exposure trend levels as they year you are estimating claims
- selected expected claims ratio based on adj historical claims ratios
- if no pattern, select straight average
Impact of changes on EC estimates:
Speedups in settlement rates
Speedups in settlement rates
- unaffected to extent ECR is not impacted by this change
- if speedup started in most recent AY, estimate produced will be unaffected and accurate
- if started in earlier year, error will be in same direction as CL but to lesser extent if using CL to get ECR
- ECR only potentially impacted if calc based on paid data
Impact of changes on EC estimates:
Increase in case reserve adequacy
Increase in case reserve adequacy
- unaffected to extent ECR is not impacted by this change
- if strengthening started in most recent AY, estimate produced will be unaffected and accurate
- if started in earlier year, error will be in same direction as CL but to lesser extent if using CL to get ECR
- ECR only potentially impacted if calc based on reported data
Impact of changes on EC estimates:
Changes in LRs, frequency, or severity
Changes in LRs, frequency, or severity
-does not react to any changes in most recent AY because not responsive to these changes -> accurate in these situations
Impact of changes on EC estimates:
Exposure Growth
Exposure Growth
- unaffected by exposure growth on its own
- not impacted if avg acc date change only started in most recent year
- if avg acc dates have changed for several years then ECR will be impacted if using CL to estimate, error produced will be in same direction as CL but to lesser extent (underestimated)
Impact of changes on EC estimates:
Changing product mix
Changing product mix
- impacted if segments that are changing have different ECRs
- impacted if segments that are changing have same ECRs but have different development patterns and this causes the estimate of ECR from historical data using CL to be inaccurate
Bornhuetter-Ferguson
credibility weighed average of CL and expected claims technique
- credibility weighting with Z=1/CDF
- as given year matures, CDF will lower which mean more credibility given to CL i.e. actual data
Benktander
- second iteration of BF technique where BF Ult is used instead of EC
- credibility weighted average of CL and BF
- Benktander gives more weight to CL and thus actual data
- if you continue to iterate, more and more weight given to CL and thus approaches CL estimate
Assumptions of B-F
- unreported claims will develop based on expected claims
- AKA claims reported to date for that exposure period tell you no useful info about your IBNR for that exposure period
- reasonable expected claim ratio can be obtained
B-F: works best for
- there are random fluctuations or large claims at early maturities
- entering a new LOB
- estimating ultimates @ early maturities for long-tailed LOBs where early CDFs are high leveraged
Advantages/disadvantages of B-F and Benktander
Adv=providing more stable estimates than CL and more responsive than EC
Benk Adv=even more responsibe than BF while being more stable than CL (but not as stable as BF)
B-F/Benk: 2 Challenges
- Estimating expected claims
- Estimating expected % unreported
Downward development
- possible to have CDFs<1 for reasons such as salvage, subro, or significant case reserve reductions
- %rptd < 1 so credibility interpretation will not be reasonable
- possible options
Continue to use
Limit CDFs to 1
Rely on different tech to select ultimates for that year
Impacts of changes on BF estimates:
Speedups in settlement rates
-since weighted averages of CL and EC, take on characteristics of them when changes to BOB
Speedups in settlement rates
- Paid: overestimate but error will not be as big in magnitude as it would be using CL since weight given to EC reduces amount of error
- Reported: no effect because CL and EC will be accurate based on reported claims data
Impacts of changes on BF estimates:
Increase in case reserve adequacy
Increase in case reserve adequacy
- Paid: no effect because CL and EC will be accurate based on paid claims data
- Reported: overestimate but error will not be as big in magnitude as it would be using CL since weight given to EC reduces amount of error
Impacts of changes on BF estimates:
Changes in LRs, frequency, or severity
Changes in LRs, frequency, or severity
-do not fully react to changes in CRs due to weighting to EC
Impacts of changes on BF estimates:
Exposure Growth
Exposure Growth
- unaffected on its own
- if avg acc date is changing, then affected in same direction as CL but not to same extent (underestimated)
Impacts of changes on BF estimates:
Changing product mix
Changing product mix
- impacted if segments that are changing have different ECRs (impacts EC tech)
- impacted if segments that are changing have different development patterns (impacts CL and possibly EC depending on how ECR is calc)
Cape Cod Method
- Stanard-Buhlmann
- similar to BF but ECR calc differently
- uses all AYs including year for which estimates are being made
- Denominator is also called used-up prem
- uses reported claims
Cape Cod Method
Assumptions
- unreported claims will develop based on expected claims but expected claims are derived using reported claims and EP
- claims reported to date for that exposure period do provide some info about your IBNR for that exposure period
Cape Cod Method
Advantages/Disadvantages
Advantages
- ECR estimated from hist data rather than being judgmentally selected & random
- random fluctuations at early maturities do no significantly distort estimates
Disadvantages
- can’t be used for new LOB since no data for ECR
- estimates are highly dependent on appropriate OLEP which can be difficult (true for ECR for BF if using hist data too)
- when data is thin or volatile, ECR will not be reliable and BF pay perform better
Impacts of changes on CC estimates
Speedups in settlement rates
Speedups in settlement rates
-Reported: accurate because reported claims are unaffected
Impacts of changes on CC estimates
Increase in case reserve adequacy
Increase in case reserve adequacy
-Reported: overestimate but error will smaller than CL but larger than BF
Impacts of changes on CC estimates
Changes in LRs, frequency, or severity
Changes in LRs, frequency, or severity
- more responsive to changing CLs than BF since calc ECR using more recent exposure period
- not fully responsive like CL
- increasing CRs, underestimate but not as much as BF
Impacts of changes on CC estimates
Exposure Growth
Exposure Growth
- unaffected on its own
- if avg acc date is changing, then affected in same direction as CL but not to same extent (underestimated)
Impacts of changes on CC estimates
Changing product mix
Changing product mix
- impacted if segments that are changing have different ECRs
- impacted if segments that are changing have different development patterns
seeing if there is speedup
look at disposal rate = cum closed/ult count
if disposal rate is increasing down the column, evidence of speedup
seeing ig there is strengthening of case reserves
look @ avg case reserves = (reported-paid)/open claim counts
look at annual % change in avg case
if changes increase down columns, could be evidence of increase in case
look @ avg cum paid = cumulative paid/cumulative closed
if avg paid is fairly steady (annual % change is constant down column), conclude case asequacy has increased
Characteristics of selecting DFs
- smooth progression of factors across columns
- stability of factors for same column
- credibility of experience
- applicability of historical experience
