Ratemaking Flashcards
Fundamental Insurance Equation
Premium = Losses + LAE + UW Expenses + Profit
3 Main considerations in deciding time aggregation
- Accurately matching premium/exposure to losses
- Using most recent data available
- Minimizing the cost of data collection
Advantage and Disadvantage of Calendar Year aggregation
Advantage: Results are final, no development
Disadvantage: Poor match of premium/exposure to losses
Advantage and Disadvantage of CAY aggregation
Advantage: Better match of premium/exposure to losses
Disadvantage: Future loss development must be estimated
Advantage and Disadvantage of Accident Year aggregation
Advantage: Truer match of premium/exposure to losses
Disadvantage: Premium/exposure need to be developed and estimated
Advantage and Disadvantage of Policy Year aggregation
Advantage: True match of Premium/exposure to losses
Disadvantage: PY data takes longer to develop than AY
Advantage and Disadvantage of Report Year aggregation
Advantage: For claims made, number of claims are known at the end of the year.
Disadvantage: Not useful in estimating IBNR.
LAE Ratio
LAE/Losses
Operating Expense Ratio
UW Expense Ratio + LAE/EP
4 Principles of P&C insurance ratemaking
- A rate is an estimate of expected value of future costs.
- A rate provides for all costs associated with the transfer of risk.
- A rate provides for the costs associated with individual risk transfer.
- A rate is reasonable and not excessive, inadequate, or unfairly discriminatory if it is an actuarially sound estimate of the expected value of all future costs.
Options in adjusting data for shock losses
- Cap losses at basic limits
- Cap losses and apply excess loss loading
- Remove ground-up shock losses and apply a shock loss loading
Advantage and Disadvantage of Extensions of Exposures calculation
Advantage: It is the most accurate method
Disadvantage: It is hard to get the detailed data and is hard to compute.
Advantage and 2 Disadvantages of Parallelogram method
Advantage: It is quicker to calculate.
Disadvantage:
1. It assumes policies are written evenly throughout the historical period.
2. Direct effects of changes are often calculated at the aggregate level, but that may not be appropriate if effects vary by class.
Current trend factor when using WP to forecast EP
Current Trend Factor = Latest Average WP at Current / Historical Average EP at Current
Rule between average written date of earned premium and average earned date of earned premium
Average written date of EP is half a policy term earlier than the average earned date of EP
2 step trend periods for using average WP forecasting EP
Step 1: Average written date of EP to average written date of WP
Step 2: Average written date of WP to Average written date in the future period
4 Steps in Estimating Ultimates
- Exploratory analysis of the data: Identify key characteristics and anomalies
- Apply appropriate techniques to estimate ultimates
- Evaluate the conflicting results of the different techniques
- Monitor projections of actual vs. expected development
5 Types of Diagnostic Triangles and what they show
- Closed claim counts divided by reported claim counts: shows speedup or slowdown in closing claims.
- Closed without pay claim counts divided by closed claim counts: shows if higher or lower percentage of claims are being closed without pay.
- Average paid on closed claims: This will reflect both severity trends and speedups/slowdowns in the closing of small claims relative to large claims.
- Average case reserves: This will reflect severity trends, speedup/slowdowns in closing of claims, and case adequacy.
- Paid losses divided by reported losses: shows speedup/slowdown in closing of claims, and changes in case adequacy.
When selecting age-to-age factors, actuaries look at the following 5 characteristics
- Smooth progression of age-to-age factors across columns
- Stability of age-to-age factors for the same column
- Credibility of experience
- Changes in patterns
- Applicability of historical experience
Potential Issues with fixed expense ratios when using premium-based projection method
- One time changes can cause historical expense ratios to be different than the expected future ratios.
- Premium trends can also impact expense ratios.
- This method can create inequitable rates across states for multi state insurers when countrywide fixed expenses are allocated to state level.
Variable PLR formula
Variable PLR = 1 - Variable Expense % - Target UW Profit %
Total PLR formula
Total PLR = 1 - Total Expense % - Target UW Profit %
Pure Premium Method for rate indication
Indicated average rate = (PP including LAE + fixed expense per exposure)/(1-V-Q)
Loss Ratio method for Rate Indication
Indicated Rate Change = (Loss ratio including LAE + Fixed expense Ratio)/(1-V-Q) - 1
Differences between PP and LR methods
LR method relies on the loss ratio, which requires on-leveling and trending of the premium. For a new company or a new product where there is no current premium cannot use this method.
PP method relies on pure premium, which requires exposure to be well defined and estimated. If exposure estimate is based on historical exposures, they need to be developed and trended.
Coverage Trigger Description for Occurrence and Claims Made
- Occurrence policies cover claims that occur during the effective policy period regardless of when the claim is reported to the insurer. Coverage trigger is the occurrence of the accident.
- Claims-made policies cover claims that are reported to the insurer during the effective policy period, regardless of when the claim occurred. The coverage trigger is the reporting of the claim.
5 Principles of Claims Made Ratemaking - Principle 1
- A claims-made policy should always cost less than an occurrence policy as long as claim costs are increasing.
If claim costs are increasing, the further in the future that claims are settled, the more time that the claims will have to increase. Claims made policies have no report lag.
5 Principles of Claims Made Ratemaking - Principle 2
- If there is a sudden, unpredictable change in the underlying trends, the claims-made policy priced based on the prior trend will be closer to the correct price than an occurrence policy based on the prior trend.
Since occurrence policies cover claims reported in future years, there is more time for trends to impact the cost of those claims than for claims-made policies.
5 Principles of Claims Made Ratemaking - Principle 3
- If there is a sudden, unexpected shift in the reporting pattern, the cost of a mature claims-made policy will be affected very little, if at all, relative to the occurrence policy.
5 Principles of Claims Made Ratemaking - Principle 5
- The investment income earned from claims-made policies is substantially less than under occurrence policies.
Since claims-made policies have no report lag beyond the end of the policy term, there is less time than occurrence policies for the premium collected to be invested.
5 Principles of Claims Made Ratemaking - Principle 1
- A claims-made policy should always cost less than an occurrence policy as long as claim costs are increasing.
If claim costs are increasing, the further in the future that claims are settled, the more time that the claims will have to increase. Claims made policies have no report lag.
5 Principles of Claims Made Ratemaking - Principle 4
- Claims-made policies incur no liability for pure IBNR, so the risk of reserve inadequacy is greatly reduced.
Since claims-made policies only cover claims that are reported by the end of the policy term, they do not have any pure IBNR.
4 Criteria for evaluating rating variables
- Statistical criteria - statistical significance, homogeneity, credibility
- Operational Criteria - objective, inexpensive to administer, verifiable
- Social Criteria - affordability, causality, controllability, privacy
- Legal Criteria - compliance with applicable laws
Credibility Formula - square root rule
credibility = min(1, sqrt(exposure/full credibility standard))
Benefits of GLMs
- They properly adjust for exposure correlations between rating variables.
- They attempt to focus on the “signal” in the data (systematic effects) and ignore the “noise” (unsystematic effects)
- They provide statistical diagnostics (e.g. confidence intervals)
- They allow for the consideration of interactions between rating variables, known as response correlation.
2 Basic Spatial Smoothing approaches
- Distance-based
2. Adjacency-based
Categories of clustering routines
- Quantile methods: clusters will have equal numbers of observations or equal weights.
- Similarity methods: clusters are based on the closeness of estimated relativities.
3 reasons why determining the correct ILFs are important over the years
- As personal wealth grows, people need more coverage to protect their assets.
- Inflationary trends have more impact on ILFs.
- There have been more lawsuits and higher jury awards over time.
Assumptions to determine ILFs for each limit
- All UW expenses and profit are variable and don’t vary by limit. In practice, profit loads might be higher for higher limits since they are more volatile.
- Frequency and severity are independent.
- Frequency is the same for all limits.
ILF Formula
ILF(H) = LAS(H)/LAS(B)
Reasons why deductibles are popular
- They reduce the insured’s premium.
- They eliminate the insurer from handling small claims.
- They provide an incentive for the insured to avoid or mitigate losses.
- The help reduce the insurer’s CAT exposure.
Indicated Deductible relativity for a deductible D (relative to a base level of no deductible)
Indicated Rel = Excess Ratio = 1 - LER(D)
Small workers compensation insureds generally have worse loss experience than larger insureds because
- Small companies usually have less sophisticated safety programs.
- Small companies usually don’t have return-to-work programs for injured workers.
- Small companies are not as impacted by or do not qualify for experience rating, so they have less incentive to prevent or mitigate injuries.
Formula for loss constant C so that small risk loss ratio would equal the large risk loss ratio
small risk losses/(small risk premium + # of small policies * C) = Large Risk Loss Ratio
Formula for loss constant C so that the loss ratio for small and large risks became equal
Small Risk Losses / (Small risk premium + #of small policies * C) = Large Risk Losses/(Large Risk Premium + # of Large Policies * C)
ITV - Home indicated rate per 1K
(Expected Claim Frequency * Average Payment across all loss ranges) / (Coverage amount / 1000)
Two issues when properties are insured to less than the full replacement cost
- The insured will not be fully covered in the event of a total or near-total loss
- If the insurer assumes all homes are fully insured to their replacement cost when calculating rates, then the premium charged for the underinsured policies will not be adequate to cover the expected losses for those policies.
2 ITV Initiatives
- Guaranteed Replacement Cost coverage which would pay for a total loss regardless of the actual cost if the home was fully insured.
- Sophisticated estimation tools that estimate the replacement cost of each property
Coinsurance Penalty formula starting from the apportionment ratio
a = min(1, coverage amount / required coinsurance % * replacement cost)) I = min(a * loss amount, coverage amount) e = min(loss amount, coverage amount) - I
6 Desirable Qualities for a Complement of Credibility
- Accurate (should be close to target)
- Unbiased (should be on target on average)
- Statistically independent from base statistic
- Available
- Easy to compute
- Logical relationship to base statistic
Loss Costs of a larger group that includes the group being rated as a complement - evaluate on the 6 qualities for a complement of credibility
Accurate, available, easy to compute.
Could have logical connection to subject experience. Could be independent.
Could be biased.
Loss Costs of a larger related group as a complement - evaluate on the 6 qualities for a complement of credibility
Available, easy to compute, independent.
Possibly accurate. Could have logical relationship.
Usually biased.
Rate change from larger related group applied to present rates formula
Complement = Current Loss Cost of Subject Experience * (larger group indicated loss cost) / (larger group current average loss cost)
Harwayne’s Method - evaluate on the 6 qualities for a complement of credibility
Unbiased, accurate, mostly independent, available, logical relationship.
Harder to compute.
Trended Present Rates formula for pure premium method and loss ratio method
C = Current Rate * Loss Trend factor * Prior Indicated Loss Cost / Prior Implemented Loss Cost
C = (Loss Trend Factor) / (Premium Trend Factor) * Prior Indicated Rate Change Factor / Prior Implemented Rate Change Factor
Trended Present Rates - evaluate on the 6 qualities for a complement of credibility
Unbiased, available, easy to compute, logical relationship.
Could be accurate, could be independent.
Competitor’s rates - evaluate on the 6 qualities for a complement of credibility
Independent, easy to compute, logical relationship.
Biased, inaccurate, difficult to obtain.
Increased Limits Analysis formula
C = Losses capped at A * (ILF_(A+L) - ILF_A) /ILF_A
Increased Limits Analysis formula
C = Losses capped at A * (ILF_(A+L) - ILF_A) / ILF_A
Lower Limits Analysis Formula
C = Losses capped at d * (ILF_(A+L) - ILF_A) / ILF_d
Limits Analysis Formula
C = Expected Loss Ratio * Sum(d>A) Premium_d * (ILF_(min(d, A+L)) - ILF_A) / ILF_d
ISO CGL formula
Mod = Z * (AER - EER) / EER
Unique considerations for pricing large deductible policies
- Claims handling - must be determined whether the insurer or the insured will be responsible for adjusting claims below the deductible
- Deductible processing - If the insurer pays for all losses first and seeks reimbursement from the insured for losses below the deductible, there will be an extra cost for the insurer to bill and process these amounts. In addition, there is credit risk in case insureds cannot pay the amounts.
- Risk margin - losses above deductible are very difficult to estimate, so the profit margin may be increased.
Large Deductible Premium formula
Premium = (Expected Loss above deductible + expected ALAE + Fixed expenses + Deductible processing and credit risk charge) / (1 - V - Q)
Retrospective Rating Formula
R = (b + CA)T
b = e - (C - 1)E[A] + CI
capped between minimum and maximum premium
b = basic premium A = reported loss C = loss conversion factor T = tax multiplier e = total expenses I = net insurance charge CI = converted net insurance charge
Factors that influence an insured’s purchasing decisions
- Competitor’s prices
- Overall cost of the product
- Rate changes for existing customers
- Insured characteristics e.g. how sensitive to prices are they
- Customer satisfaction and brand loyalty
Fixed Expense Fee per exposure formula
Fixed Expense per exposure / (1 - V - Q)
Deriving a New Base Rate without Rating Factor Changes - formula
Proposed Base Rate = Current Base Rate * (Proposed average premium - proposed additive fee) / (current average premium - current additive fee)
Deriving New Base Rate with Rating Factor Changes - extension of exposures formula
Proposed Base Rate = Seed Base rate * (Proposed average premium - proposed additive fee) / (Average premium with seed base rate and new rates - proposed additive fee)
Deriving New Base Rate with Rating Factor Changes - approximated average rate differential formula
Proposed Base Rate = (Proposed average premium - proposed additive fee) / Proposed average rating factor
Deriving New Base Rate with Rating Factor Changes - approximated change in average rate differential formula
Proposed Base Rate = Current base rate * Off-Balance * (Proposed Average Premium - Proposed Additive Fee) / (Current Average Premium - Current Additive Fee)
Off balance formula
= 1 / weighted average change factor
Trended Present Rates Complement Trend period
Original target effective date from the last review to target effective date of next rate change
