15 - Pricing Flashcards
Describe the key assumptions that are crucial to actuarial work in the field of pricing, contribution setting and valuations, as outlined in the syllabus objectives.
The crucial assumptions include, but are not limited to:
* Morbidity
* Mortality
* Persistency
* Claim amount
* Expenses
* Inflation
* Investment return
* Profit requirements
What are the two main approaches used for pricing individual and group benefit arrangements?
The two main approaches are experience-rated and book-rated.
Explain the concept of experience rating in pricing.
Experience rating is a practice where the premium depends wholly or partially on the past experience of the insured. Past experience of the insured group is used as the basis for pricing, whereas experience-rated refers to incorporating some element of experience specific to an individual or group to determine their premium/contribution rate.
How is a book-rated approach typically used for pricing?
A book-rated approach is usually used for pricing health and care benefits where some individual PMI policies may have no-claims discounts (NCDs), which are a specific type of experience rating. Furthermore, experience rating as an approach has become the more common approach when pricing for groups given the balance required between competitive premiums and anti-selection.
In the formula for the risk premium (RP) for a group, RP = Z × A + (1 – Z) × E, what do Z, A, and E represent?
- Z is the credibility factor for this group (0 ≤ Z ≤ 1).
- A is the insurer’s standard risk premium, or book rate, for PMI benefits for the group.
- E is the equivalent risk premium charged based on the past experience of the group.
What factors does the value of the credibility factor (Z) depend on?
The value of Z will depend mostly on the size and the number of years of data available. However, other factors may be involved if the past data affect the reliability with which future experience of a group can be predicted from its past data, or if they affect the relevance of the data to predicting future experience.
Outline the two main pricing methods in the context of healthcare insurance.
The two main pricing methods are the:
* Formula approach - Often used for long-term insurance contracts.
* Cashflow approach - Also used for long-term insurance products, with the main difference between pricing life and health insurance products being in the modelling of the benefit cashflows.
Briefly describe the high-level approach for pricing individual policies.
The high-level approach involves:
1. Choosing the pricing basis and approach, which includes understanding the product and benefit design.
1. Collecting and checking data, making sure to correct any errors.
1. Splitting the data into homogenous groups based on the underlying relevant risk cells.
1. Calculating a burning cost, or the cost of the underlying risk benefit.
1. Analysing the data and the results.
1. Making adjustments to the base values so that they are complete and relevant, representative of the expected period being priced.
1. Determining and calculate the assumptions needed.
1. Projecting forward the expected base cost of the risk benefit being priced.
1. Adjusting the base cost for other loadings such as profit, expenses, including administration, claims, operational and marketing, tax, investment return, and cost of capital (CoC).
1. Considering other considerations which may include competition, cross-subsidies, options, guaranteed and discounts, unique product features, regulation, and market trends.
What is a crucial distinction between pricing for an individual and the process of generating a quote or reviewing the premium for an individual or group?
There is an important distinction between pricing at a product level and the process of generating a quote or reviewing the premium for an individual or a group. The pricing of a product involves building a pricing model. The final output of a pricing model is a premium/contribution table.
What are some sources of uncertainty that necessitate margins in pricing?
Where uncertainty is prevalent in future outcomes, it is prudent to build in margins to ensure, as far as possible, that the insurer’s promises are met. This is especially the case in health and care insurance. The volume of relevant statistics is not nearly as credible as in life insurance; claim outcomes are often more subjective, or less clear-cut, and more influenced by factors outside the control of the insurer, for example, social and economic circumstances.
What are the two main elements that the concern regarding margins depends critically on?
The concern regarding margins depends critically on:
* The degree of risk associated with each parameter used.
* The financial significance of the risk from each parameter.
What are the three approaches to applying margins to the expected values?
The three approaches are:
* Applying margins to the expected values.
* Using a stochastic approach.
* Assuming a higher discount rate.
Outline the key steps involved in pricing for PMI.
The key steps for most modelling exercises involved in deriving a risk premium for PMI are as follows:
* Choose a base period over which to collect claims and exposure data.
* Collect data, checking the accuracy and appropriateness of the data.
* Split the data into homogeneous groups.
* Calculate a historical burning cost premium for each group.
* Analyse the data, and project forward, to identify future trends.
* Adjust and project forward to obtain future risk premiums, which is the expected claim amount over the period that policies covered by the premium rates will be in force.
Define the Burning Cost Premium (BCP) and provide its formula.
A common starting point in the calculation of the risk premium is the BCP. The BCP is the true past risk premium of an actual portfolio of data, meaning the actual cost of claims incurred per policy or per unit of exposure.
* Formula: BCP = Total Claims / Total exposed to risk
* Alternatively: BCP = Average claim amount × Claims incidence rate
What are some factors that might necessitate adjusting the subdivided BCPs to allow for changes in the insurer’s practice or relevance of past data?
The subdivided BCPs may need adjustment due to:
* Policy acceptance: This is the basis on which proposals are accepted, underwritten, or have waiting periods applied.
* Policy coverage: These are the risks covered under the contracts in question relative to the period ahead.
* Marketing and method of distribution: This involves the influence of the selling process on the nature of risks insured or policyholders covered.
* Delays in claims settlement: These relate to the internal practices that may affect the timing of claims settlements.
Explain the significance of splitting data into homogeneous groups for pricing.
Data should be split into risk cells, where the total available data should be subdivided into homogenous subsets. This will:
* Enable greater understanding of the risk profile of each policyholder class and procedure/benefit.
* Help ensure that dangers of cross-subsidies are avoided, which means that profitability will not be dependent on a particular cross-section of policyholders and so the insurer will be less exposed to changes in the business mix.
What are some key considerations when projecting the base value for pricing?
When projecting the base value, it’s important to consider:
* Changes in policyholder profile by benefit option, considering the selective impact of membership movements, for example, older, less healthy policyholders selecting more comprehensive benefit options.
* Claims inflation.
* Trends, for example, changes in claim frequency or utilisation of healthcare services.
* Other changes in cover.
What are the key components involved in the projection for the allowance for inflation in PMI product pricing?
The allowance for inflation should consider the impact on:
* Professional fees and medical treatment, including hospital fees and medical allowances.
* The cost of pharmaceuticals and medical equipment, which may include exchange rate fluctuations in the case where pharmaceuticals and medical equipment are imported.
* The cost of claims, which could include fees paid to external claims administrators responsible for administering claims.
Describe how the risk class of policyholders is typically taken into account when pricing.
The total risk premium for the particular class of policyholders is found by summing the individual risk premiums for each benefit / procedure, as follows:
Risk premium (age, gender) = Σ(i_k × AC_k), where i_k is the incidence rate for benefit / procedure class k, and AC_k is the average claim cost for benefit / procedure class k. These are specific to each policyholder class, determined by age and gender.
What is the purpose of adjusting the risk premium for other loadings?
Insurers adopt many different ways of loading the risk premium for commissions, expenses, the cost of reinsurance, and other margins. Those who start by calculating pure risk premiums will load these premiums, either by applying a simple overall percentage addition or by allowing for expenses in a more detailed way, having regard to their fixed or variable nature.
Explain the concept of “allowance for investment income” in pricing.
The premium formula should recognise, either explicitly or implicitly, that the insurer can expect to earn some investment income on both the premiums received during the period from receipt of premium through to final settlement of claims as well as the reserves held. The investment income estimate should consider the distribution of the insurer’s assets between various asset classes. However, PMI claims are likely to be short-tailed, therefore assumption regarding investment income is not likely to be critical.
What is the significance of “contingency margins” in premium pricing?
A contingency margin can be introduced to allow for uncertainty in projected claims costs. This may be the case when pricing a new benefit or if an insurer is new to the market. It may also be appropriate during times of uncertainty, for example, during a pandemic where the effect on the underlying morbidity, PMI claims and well as access to healthcare services are very uncertain.
Briefly describe “NCDs, excesses, and guarantees” as other considerations in pricing.
The risk premium calculation will be adjusted for excesses, the presence of an NCD rating structure, if one exists, and any other product features that may impact the incidence rate or average claim cost.
What are “cross-subsidies” and why is it important to be aware of them in pricing?
Cross-subsidies refer to the entity concerned that on a medical scheme, of their entire portfolio and there may well be reasons for cross-subsidies between product lines or benefit classes, particularly on expenses. It is important because launching a new product or having enough policies on books to increase or maintain market share might necessitate cross-subsidy.
Differentiate between “individual-level rating factors” and “group-level rating factors”.
Individual-level rating factors are rating factors that apply to the individuals of the group and are therefore similar to the rating factors that would be used for individual business. For example, the individual-level rating factors for a CI policy might be age, gender, smoker status, and occupation.
Group-level rating factors also apply to the group itself, for example, industry and location, size of group, employer’s attitude to their employees’ health, etc..
Explain the concept of “experience rating” in the context of group PMI pricing.
Some form of experience rating is usually incorporated in group PMI pricing at a level below that which a strict statistical approach would demand. This may be due to commercial pressures and market practice. Note that this differs from individual PMI pricing which is normally priced on a collective basis, where the premium is associated with all other lives in the same risk cell without reference to individual claims experience.
What are some factors that can alter the applicability of past experience when calculating premiums for a group?
Factors that can alter the applicability of past experience include:
* Demographics
* Location
* Work practices
* Cover required
In the context of pricing for cash plans, what is the expected benefit typically calculated for?
For health cash plans, premiums for health cash plans are determined by first calculating the expected claims for each of the benefits, typically an incidence rate multiplied by the average benefit paid. The expected benefit will take account of any excesses, coinsurance, factors that apply.
Describe the general approach to pricing for accidental death and total permanent disability (TPD) products.
The rating method for short-term accidental death and TPD insurance is based on calculating the expected claims for the accidental death and disability benefits, which is the incidence rate multiplied by the sum assured. Where products are sold to groups, an average rate is often agreed to for a particular group.
What is the fundamental approach to pricing for critical illness (CI) insurance?
The approach for CI is much simpler than the approach for indemnity cover, as the benefit is a lump sum rather than a claim cost. The premium would be determined based on multiplying the CI incidence rates by the expected sum assured and this may need to be done for each benefit type and summed together. Loadings would be added to determine the final premium.
Define the overall CI incidence rate ($i_x^c$) in terms of the incidence rates for different causes of critical illness.
The overall CI incidence rate ($i_x^c$) is the sum of the incidence rates for different causes, such as heart disease ($i_x^{hd}$), stroke ($i_x^{s}$), cancers ($i_x^{ca}$), and other causes ($i_x^{o}$). So, $i_x^c = i_x^{hd} + i_x^{s} + i_x^{ca} + i_x^{o}$.
Explain the concept of “accelerated CI insurance rates”.
A relatively simple approximation for risk premium rates for an accelerated CI policy, namely one where the benefit is paid out on the earlier of death or CI, can be derived as: $i_x^a + (1 - i_x^a)q_x$, where $i_x^a$ is the CI incidence rate, $k_x$ is the proportion of deaths due to CI, and $q_x$ is the mortality rate. Note: The source uses $i_x$ for CI incidence rate in this formula and doesn’t define $k_x$ explicitly in this section, but it implies the CI incidence rate out of those who are alive and healthy. A more consistent notation from other parts of the text would use $i_x^c$ for the CI incidence rate. Assuming the intention is that $i_x^a$ represents the CI incidence rate for a healthy life, the formula calculates the probability of claiming due to CI or death, considering those who don’t claim CI might then die within the year.
How is the stand-alone CI insurance incidence rate typically expressed?
The stand-alone CI cost is similarly expressed as a rate: $i_x^c \times {\text{probability of surviving the survival period}}$.
What are some key factors affecting health options, particularly those with a ‘select life’ feature?
Some factors affecting health options include:
* The term of the policy with the option. The longer the term, the longer the policyholder will have the option, and the more likely it is that, at some time, their health will deteriorate, thus making the option appear worthwhile.
* The number of times the policyholder gets the chance to exercise the option. For example, this may be every 5 years, on every policy anniversary, or at any time whatsoever.
* Conditions attaching to exercising the option.
* The encouragement given to policyholders to exercise the option.
* The extra cost to the policyholder who exercises the option.
* Selective withdrawals.
What are the two main methods commonly used for valuing a mortality/morbidity option?
There are two main methods in common use, namely the ‘North American’ method and the ‘conventional’ method. The main distinction between the two methods is the amount of data available at the time of pricing. When there is sufficient data to use the North American method, then this approach may be preferred. In both methods, the option price will be calculated and added to the total premium for all policyholders.
Briefly describe the “North American method” for valuing a mortality / morbidity option.
The North American method aims to calculate which policyholders will exercise the option, and what those policyholders’ experience is expected to be once the option is exercised. This method requires two additional items in the pricing basis:
* A double, or triple, decrement table for lives who have not yet exercised the option, with decrements of death / disability and exercising the option represented by dependent rates of decrement at age x of $(al)_x^j$ and $(ao)_x^j$ respectively, displayed in a double decrement table (as $(ad)_x^j$ and $(aq)_x^j$ numbers of decrements out of $(al)_x^j$ lives).
* A mortality / morbidity table for lives who have exercised the option, represented by mortality / morbidity rates $q_i^j$.
What are the key assumptions underlying the “conventional method” for valuing a mortality / morbidity option?
The underlying assumptions of the conventional method are:
* All lives eligible to take up the option will do so.
* The mortality / morbidity experience of those who take up the option will be the ultimate experience that corresponds to the Select experience that would have been used as a basis if underwriting had been completed as normal when the option was exercised.
* The mortality / morbidity basis used is not usually assumed to change over time, so the only data required are the Select and Ultimate mortality / morbidity tables used in the original pricing basis.
What are some important additional considerations at the time of arriving at a final premium?
Some important additional considerations include:
* The profit criteria that might be used.
* Marketability.
* How competitors affect the final premium.
* The impact of reserving and the solvency capital requirement on the final premium.
* How reinsurance might impact the final premium.
* How the regulator might impact the final premium.
What are the three basic approaches considered for determining the profit criteria?
The three basic approaches considered are determining the profit criteria based on:
* Net present value
* Internal rate of return
* Discounted payback period
Define “net present value” in the context of profit testing for insurance products.
Discounting the profit signature at the risk discount rate produces a ‘net present value’. A positive net present value suggests that the product is expected to be profitable based on the chosen discount rate and assumptions.
What is the “internal rate of return” as a profit criterion?
The internal rate of return is the rate of return at which the discounted cashflows is zero. All other things being equal, an insurer should prefer a contract that has a higher internal rate of return.
Describe the “Discounted Payback Period” as a measure of profitability.
The discounted payback period is the policy duration that the insurer needs to recover its initial investment with interest at the risk discount rate. The discounted payback period will not usually be the preferred profit measure as it ignores completely all the cashflows after the discounted payback period.
What are some factors that influence marketability and should be considered in pricing?
Factors influencing marketability include:
* The design of the product, so as either to remove features that increase the riskiness of the net cashflows or to include features that will differentiate the product from those of competing insurers.
* The distribution channel to be used.
* The insurer’s profit requirement.
* Whether to proceed with marketing the product.
* The overall level of premiums charged compared with competitors, which will be a function of how optimistic or conservative the pricing basis is.
* The number and accuracy of rating factors involved.
Briefly explain the concept of “competitiveness” in the context of pricing insurance products.
A close watch will normally be kept on the pricing approach of competitors with similar products. Any significant discrepancies should be investigated, though there could be many reasons, for example, different target markets. While a competitor’s cheaper price may reduce the insurer’s market share, more importantly, if a competitor is using more detailed price differentiation and risk selection the better, lower risk, lives would be more likely to go to the competitor, for a lower premium. Consequently, the insurer’s averaged pricing assumptions are called into question.
What is the key difference between “risk factors” and “rating factors”?
Risk factors are factors where the underlying risk is either higher or lower, for example, those with chronic conditions are higher risk than those without chronic conditions.
Rating factors are factors which are used to distinguish between premium/contribution charged. The same factor may be both a risk factor and a rating factor in order to ensure premiums / contributions charged are commensurate with the underlying risk.
Why is it important to consider “reserving” and the “solvency capital requirement” (SCR) in pricing?
The actuary needs to incorporate into the premium a loading to cover the additional cost of providing the guarantee, for example, as determined through a resilience test, including the cost of holding the guarantee reserves. If the true cost of guarantees appears in the premium, this may encourage many to move to a reviewable contract, where the guarantee will cost considerably less. Incorporating the cost of reserves and reviewability will be discussed in Chapters 20 and 22. Remember that all of the supervisory reserve requirement (SCR), ties up capital in the business. The key point here is that the supervisory reserves, including all solvency capital requirements, should be fully incorporated into the pricing model.
What are some key aspects to consider regarding “regulatory approval” of premiums?
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. In South Africa, health regulations set out requirements for universal acceptance and community rating for PMI products.
What are the three main types of investigations and reviews relating to premium / contribution rates?
The three main types of investigations and reviews are:
* Monitoring the assumptions used for pricing new business.
* Monitoring the assumptions used for pricing reviewable premium business.
* Monitoring whether the reserves set up to cover losses from loss leaders are adequate.
Briefly describe the purpose of “resilience testing of premium rates”.
Premium rates 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 acceptable level of confidence. This is essentially the process of sensitivity testing.
What is the importance of “adequacy of reserves in pricing”?
The actuary needs to incorporate into the premium a loading to cover the additional cost of providing the guarantee, for example, as determined through a resilience test, including the cost of holding the guarantee reserves. If the true cost of guarantees appears in the premium, this may encourage many to move to a reviewable contract, where the guarantee will cost considerably less.
