How do you price a PMI product?
- Choose a base period over which to collect claims and exposure data
- Split data into homogeneous groups: age, gender, smoking status, claim size, reason for claim, underwriting decision etc.
- Calculate historical burning cost premium for each group
- Analyse the data e.g. to identify trends, seasonality, unusually heavy or light XP, changes in risk profile, large claims, IBNR
- Adjust and project forward to obtain future risk premiums, i.e. the expected claim amount over the period that policies covered by premium rates will be in force
- Allow for product features like excesses, limits and NCDs → affect claims experience, claims inflation, changes in PH behavior, changes in PH profile per benefit option.
- Need to load for commissions, expenses, the cost of reinsurance, profit, solvency margin and contingency margin. Investment income should also be taken into account.
How do you price a critical illness product?
Standalone RP = SA x i(x) x r(x)
Accelerated RP =SA x r(x) x[i(x)+q(x)*{1-k(x)}
Normal RP = SA x i(x)
Where r(x) is the survival period and q(x) is the mortality rate and k(x) is proportion of death due to non-CI
The risk premium is then inflated to office premium with expense and profit loadings.
How do you price a LTC product?
Step 1: Define the transition probabilities
Probability of transitioning from “Healthy” to “Disabled”: 0.02
Probability of transitioning from “Healthy” to “Dead”: 0.01
Probability of transitioning from “Disabled” to “Dead”: 0.05
Probability of remaining in the “Disabled” state: 0.95
Step 2: Define the costs associated with each state
Annual cost of being in the “Healthy” state: $0
Annual cost of being in the “Disabled” state: $50,000
Cost of transitioning to the “Dead” state: $0
Step 3: Define the discount rate
Annual discount rate: 3%
Step 4: Calculate the expected present value of costs for each state
* “Healthy” and “Dead” state: No costs associated with this state
* “Disabled” state:
Expected time spent in the “Disabled” state: 1 / (1 - 0.95) = 20 years
Present value of costs in the “Disabled” state: $50,000 × (1 - (1 + 0.03)^(-20)) / 0.03 = $639,987
Step 5: Calculate the expected present value of total costs
Probability of transitioning to the “Disabled” state: 0.02
Probability of transitioning to the “Dead” state: 0.01
Expected present value of total costs = 0.02 × $639,987 + 0.01 × $0 = $12,800
Step 6: Calculate the annual premium
Assume a policy term of 30 years
Annual premium = Expected present value of total costs / Annuity factor
Annuity factor = (1 - (1 + 0.03)^(-30)) / 0.03 = 19.6004
Annual premium = $12,800 / 19.6004 = $653
How do you price a group product?
RP = ZxA+(1-Z)xE+L
Z is the credibility factor between 0 and 1
A is the risk premium based on the group’s past experience data
E is the insurer’s book premium for the group
L is an expense / profit loading
How to reprice PMI product?
Here is a summary of the key points for calculating premium rates for a private medical insurance (PMI) product:
Claims Incidence Rate:
- Collect claims data and split into homogeneous groups by age, gender, smoking status, claim size, reason, underwriting decision, and occupation
- Calculate claim incidence rates for each group as claims divided by policyholders exposed to risk
- Project future incidence rates considering changes in mix of business, policy conditions, treatments covered, economic conditions, and benefits provided
Claim Amounts:
- Collect claims data and split into groups by underwriting status, exclusions, and reason for claim
- Calculate average claim amount for each group as total claim amount paid divided by number of claims
- Project average claim amounts considering medical inflation, changes in treatment costs and protocols, and hospital charging structures
Burning Cost Premium:
- For each risk group and procedure class, calculate burning cost premium as average cost of procedure multiplied by incidence rate, summed across all procedures
- This is the premium needed to cover claims costs
Renewal Rates:
- Calculate historical renewal rates as number of renewals divided by policies up for renewal, split by distribution channel, occupation, policy duration, and territory
- Project renewal rates considering premium inflation, economic outlook, competition, and changes in state PMI provision
Expenses:
- Analyze all expenses (renewal, acquisition, claims, termination) split by gender, distribution channel, occupation
- Express expenses as % of premium, % of average claim, or per policy
- Project expense loadings for inflation to the middle of the premium rate period
- Consider initial expenses recouped over time based on renewals, commission spread over renewals, and per policy expenses based on new business and renewals
Office Premium:
- Add projected expense loadings to the risk premium for each group
- Aim to maximize profit per policy, new business, and renewals
- Ensure competitiveness in the market
- Consider impact of reinsurance
- Include margins above best estimate assumptions to protect from risk
- Comply with regulations
The key is to thoroughly analyze historical data, make reasonable projections considering various change factors, and price premiums to balance profit, competitiveness, and risk protection. Let me know if you need any clarification or have additional questions!
What are important considerations when pricing products?
- Profitability
- Marketability
- Competitiveness
- Cost of capital
- Reinsurance
- Regulator
- Reviews
What are the different ways to price an option?
- Conventional method
- North-American method
- Stochastic process
Option pricing: conventional method
Assumptions:
* The premium for the option policy would be calculated using select mortality and morbidity assumptions
* 100% of eligible PH will take up option.
* Claims experience of ‘option-takers’ is expected to be ultimate claims experience.
* If PH provided with different option dates, choose option that results in largest losses to the insurer.
The cost of the option:
* EPV (option cost) = EPV(benefits)+EPV(expenses)-EPV(premiums).
* To determine the largest loss, calculate EV (option cost) under different dates.
* Cost of option should be charged for by extra premium payable until option is exercised/or at earlier claim .
Data needed
* Current premium basis assumptions for select and ultimate claims experience
Conventional method vs. North American method
- Conventional method
- Relies on fewer assumptions
- Requires less data
- Since 100% take up rate, covers cost of every possible impaired life exercising option → conservative approach.
- Conservative approach may lead to overstatement of expected option cost.
- North American method
- results are very sensitive to assumptions made
- If there is not good data backing assumptions, higher risk of undercharging
- If data is reliable then could lead to competitive premium
Option pricing: Stochasic model
- The core cost of options can be established through stochastic modelling
- The future experience is projected and the numbers taking up the various options and their subsequent claim propensities are investigated
- A large number of simulations will be tested, and the cost of the option will be calculated with a particular statistical degree of accuracy
- The model will have to subdivide the population of PHs into different risk categories (possibly with additional subgroups within these)
- The proportions ending up in each risk group could be modelled as stochastic variables
- Therefore need appropriate probability distributions for these
Considerations for guarantees pricing
- Resilience testing premium rates
- Premiums need to be assessed on a resilience basis to judge whether, in the absence of an ability to change the premium / benefit relationship, the premium charged will be sufficient to meet all outgoings with an agreed level of confidence.
- Similar to sensitivity testing.
- This will require an establishment of reserves in early years when the risk is lower and more certain.
- Adequacy of reserves in pricing
- Need to incorporate into the premium a loading to cover the additional cost of providing the guarantee (determined under the resilience test) including the cost of holding the guarantee reserves.
- If the true cost of guarantees appears in the premium → may encourage many to move to a reviewable contract where the same benefits will cost considerably less.
- Regulatory approval
- The local regulator will normally want to see evidence of the techniques employed and their output, to judge the adequacy of the premiums and reserves required.
Profit criteria: net present value (NPV)
- NPV = discounting the profit signature at the risk discount rate
- Assumptions
- Market is perfectly efficient capital market
- When two risky investments are compared, each is discounted at a risk discount rate appropriate to its riskiness
- Practical points
- It is subject to the law of diminishing return
- Otherwise a company that could sell one policy with a + NPV could sell an unlimited no. of policies and increase the value of the company without limit
- It says nothing about competition
- There is no point in designing a contract with a high NPV if it cannot be sold (this is also true for the other profit criteria)
- It is subject to the law of diminishing return
- How is NPV expressed?
- NPV by itself tells you little - except the sign tells us if the risk discount rate has been met.
- You can calculate the NPV of future profits/NPV of initial commission to get NPV per unit of initial commission. If this is 2 this shows for every R1 of commission paid (reflects effort to sell policy), insurer makes twice as much value.
- you can calculate NPV of future profits/NPV of premium income to get NPV as a percentage of premium. If this is 10%, for every R100 premiums sold, company earns NPV of R10 in future profits. The higher the %, the better for the insurer (this can be achieved by selling same amount of perms but for higher NPV).
Profit criteria: IRR
- This is defined as the rate of return at which the discounted value of the cashflows is zero.
- A company should prefer a contract with a higher internal rate of return. IRR does not always agree with NPV.
- NPV may be more reliable in some cases:
- May not be a unique IRR
- If there is more than one change of sign in the stream of profits in the profit signature - NPV can be related to useful indicators of the policy’s worth to the company, in terms of sales effort or market share
- No way to do this with IRR - IRR may not always exist if a policy makes profits from the outset (though this is rare)
- NPV always exists
- May not be a unique IRR
- Can also argue that the IRR is not telling you much that the NPV does not. NPV already tells us if the risk discount rate is met - not so important to know by how much.
- On the other hand IRR is a concept that may be generally easier to understand.
Profit criteria: DPP
- The DPP is the policy duration at which the profits that have emerged so far have PV zero. i.e. It is the time it takes for the company to recover its initial investment with interest at the risk discount rate.
- The DPP will not usually agree with the NPV (as it ignores completely all the CFs after the DPP).
- A company with limited capital might prefer to sell contracts with the shortest payback periods possible.
Marketability
- look at product design: remove features that increase risk of net CFs + add innovative features
- Distribution channel: may need to review assumptions used in pricing model or charge higher premium without losing marketability
- Consider company’s profit requirement
- Always need to consider assumed expenses involved before marketing product (acquisition costs e.g. comm, admin costs, contribution to fixed overheads)
Competitiveness
- competitor might have better prices due to optimistic pricing or better risk differentiation
- this might impact volumes, making them lower
- might impact our ability to use cross-subsidization in margins, but over time profits should be immune to changes in business mix
- ensure return on capital is always met so if in excess, opportunity to reduce premiums
Cost of capital
- Premium rates should explicitly include the cost of holding the supervisory reserves and required solvency capital in the profit calculations.
- SCR may be reduced by the use of suitable reinsurance arrangements.
- companies with enough capital might decide not to charge some policies with the cost of their SCR for competitive reasons.
- The charge is the investment cost arising from holding some of the underlying assets as “locked in” statutory capital rather than investing directly in business acquisition.
Reinsurance
- where financial benefits of reinsurance exceed expense increases, price premium net of reinsurance to improve competitiveness
- A large portion of the risk may be passed to the reinsurer by way of quota share → reinsurer have influence on premium tables or can revise reinsurance commission payable
Regulator
- The actuary may have to submit their basis to the supervisory authorities before the policies can be marketed.
- may be API restrictions in excess of a specified margin over CPI each year.
- might be required to e.g. community rating or the inability to differentiate between risk cells
- might be required to only invest in local assets which impacts investment returns
- Cost impact: Any regulatory restriction on commercial operations may impose a cost that needs to be reflected in the premium assumptions
Reviews
- Premium bases must be kept up to date through frequent experience monitoring.
- Test new business premium rates against any changes to the current basis / assumptions to ensure alignment.
- Any potential changes to premium rates, are evaluated based on financial impact of company
- Premium rate changes also consider expense and marketability.
How to determine price of government trying to get private insurers to offer low premium products?
- need to determine contribution rate that is low enough to attract new members but high enough to prevent buy-downs
- benefit design, including limits and target market demographics, will influence costs.
- collect historical data on covered benefits such as doctor visits, radiology, pathology, and medicine costs from existing plans, adjusting based on public information. Break down the data by age, region, sex, and family size to calculate average costs per policyholder per month. Adjust historical costs for the target market’s claiming behavior and future prices using tariffs or inflation statistics.
Factor in expenses like commissions (percentage of expected costs) and administration (fixed monthly cost). Add risk margins to account for uncertainty in the new product, and include profit margins based on shareholders’ return on capital objectives.
Consider investment income from surplus funds, which can improve profitability or lower premium rates. Set premium rates based on the expected policyholder profile and the company’s pricing approach, varying by age and other acceptable rating factors.
Conduct sensitivity analyses to test the impact of changes in key assumptions. Additionally, consider factors such as reinsurance terms and costs, tax, and the impact of government incentives on overall cost and policyholder premiums.
How are cash plans premiums calculated?
- Premiums are determined by first calculating the expected claims for each of the benefits
- Expected claims = incidence rate x avg benefit expected to be paid
- Expected claims is different to BCP because it is not an actual claim amount
- Expected benefit considers excesses or coinsurance factors (it will decrease expected benefit)
- Total is adjusted to take account of inertia i.e. people’s propensity to not claim even when they are entitled to.
What is intertia?
Inertia is people’s propensity not to claim even when they are entitled to.
This may happen because:
*Individuals focus on a specific benefit and forget about other cover provided
*Size of benefits in absolute terms tend to be small + “customer apathy” leads to valid payments not being claimed
What is credibility factor?
- Z represents the proportion of the final risk premium that is derived from past experience, the balance coming from the book rates.
- Factors to consider when determining Z: size of employee base, volumes of past data, significant changes in employee base, location or work practices or cover provided, market practice
- If Z>0 then premiums are experience rates.
