F102 Summaries P5 Flashcards
different types of models
- profit test model
- new business model
- existing business model
- full model office
requirements of models
- the model must be valid, rigorous and adequately documented
- the model points must represent the business accurately
- the model must incorporate all the material features of the business
- the parameter values must be set appropriately
- different variables should behave realistically to each other
- the workings of the model must be easy to explain and understand
- results should be clearly displayed, verifiable and communicable to to intended recipients
- the model should not be overly complex
- the model should be capable of subsequent development and refinement
basic features of life insurance models
- involves projecting cashflows
- cost of setting up supervisory reserves and required solvency margins needs to be allowed for in order to calculate the profit flows
- proper allowance must be made for guarantees and options: it is likely that a stochastic modelling facility will be necessary for this.
- allow for interactions and correlations between variables - dynamic links
- internal time period (frequency) of cashflow projection must be short enough to produce reliable results
why would a stochastic approach to modelling be preferred
because
- we need to cost options and guarantees
- we would need to see the likely distribution of outcomes, not just a single estimate
- the interaction between variables can be explicitly included, enabling the effect of the interactions to be assessed
- we need to estimate a probability
effective use of deterministic modelling
deterministic models can be used
- with sensitivity testing in order to get an approximation to a stochastic result
- where the result obtained would be very similar to or more prudent than a stochastically produced result
- as a check on a stochastic model
what is the problem with stochastic models
stochastic models also suffer from high sensitivity the chosen parameter values, with the risk of spurious accuracy. so we should only use stochastic modelling when the variable can be reliably modelled by a well defined probability distribution
what is the financial economic approach
the financial economic approach assumes market consistent values for parameters.
details of the financial economic approach
the assumed investment return should be the risk free rate as the potential additional returns from the more risky assets should be exactly cancelled by their increased risk.
assets are valued at market value. market consistent values of the liabilities can be calculated as the current market values of the risk free assets that match the liability cashflows.
assessing the market values of other non-financial aspects of the liability, e.g. mortality, is more problematic. there may be some actual market valuations of liabilities available - e.g. for traded endowments.
the actuary advising a life company will require models to assist with
- product pricing
- assessing return on capital
- assessing capital requirements
- assessing the profitability of the existing business including the present value of future profits on the existing portfolio
- developing an appropriate investment strategy
- projecting the future supervisory solvency position
any other work involving financial projections
how do you price a product through modelling cashflows?
use single policy model on individual model points.
find price by finding a premium or charges that satisfies the company’s profit criteria.
commonly used profit criteria
these are usually based on single figure functions of the profit signature. three commonly used functions:
- net present value - this can be expressed in different ways
- internal rate of return
- discounted payback period
net present value is normally expressed in relative terms such as
- in proportion to initial sales cots
- in proportion to total discounted premium income
calculating NPV of a profit signature
the NPV of a profit signature is calculated by discounting it at the risk discount rate. economic theory implies that the npv is the best profit criterion to use. however, it is dependent on the risk discount rate being appropriate for the inherent risk.
internal rate of return
this s defined as the rate of return which the discounted value of the cashflow is zero. it suffers from some disadvantages in comparison with the npv as a profitability criterion.
- it might not exist
- it might not be unique
- it cannot be related to other indicators such as sales cost or premium income
disadvantage of IRR compared to npv
- it might not exist
- it might not be unique
- it cannot be related to other indicators such as sales cost or premium income
discounted payback period
this is defined as the policy duration at which the profits that have emerged so far have a present value of zero. it is a useful reference for companies eager to recoup their initial capital investment in as short a time as possible.
which profit criterion is most useful? NPV, IRR or DPP
the most widely used profitability criterion is npv. in addition the dpp may be a useful measure if capital is particularly scarce and this can assist in designing capital efficient products.
other pricing considerations
price must also be considered for
- marketability
- whether the company has sufficient capital to finance expected sales volumes
- whether the return on capital for the business as a whole is satisfactory
model office and new business models can be sued ot assess the last two points.
it is also essential that all prices are sensitivity tested at all stages of modelling.
assessing the profitability of existing business
the future profits from the existing business model can be discounted at an appropriate risk discount rate to give the expected pv of future profits. this, plus the shareholders share of the net assets, forms the embedded value of the company.
assessing solvency
solvency is measured by comparing the value of assets against the value of liabilities, on a supervisory or economic basis. if the supervisory basis is stronger then supervisory solvency becomes the predominant criterion.
projecting solvency
future solvency will need to be projected in order to measure the impact of future variations in experience not allowed for in the supervisory reserving basis.
the modelling of such future variations will need to be dynamic.
solvency projections may also allow for management actions (such as changes in bonus and investment policy) where appropriate.
the projection can be done on either a deterministic or stochastic basis and may be on an ongoing basis or consider just the existing portfolio
why does a life company need capital
- to withstand adverse, often unexpected, conditions
- to finance new business strain
- to allow a riskier investment strategy than strict matching would dictate
this capital is normally provided on a day to day basis by the company’s free assets but in effect the capital is being provided by with profits policyholders, by shareholders in a pty company or by both.
sensitivity testing in models
results from the models will need to be looked at in conjunction with sensitivity tests to show the vulnerability of the results to unexpected future experience.
outcomes will be analysed for sensitivity to variations in
- model point assumptions
- parameter values
sensitivity testing on a deterministic basis
sensitivity testing on a deterministic basis can be used to help determine the margins that may be necessary in a basis.
such margins in each parameter assumption can be a way of allowing for risk in a pricing model, as an alternative to risk margins in the risk discount rate.
sensitivity analysis can help to determine the variance of profit or of the return on capital, for any business being modelled.
alternatively, stochastic simulation techniques can be used to assess profit variance.
how to set assumptions
in constructing a basis the actuary will consider the future experience expected for the contract concerned and modify it as appropriate given the purpose of the basis.
the guiding principle in constructing any basis os consistency. this means that the relationships between assumptions in a basis are realistic, reflecting the correlations that exist between variables.
what does consistency in assumption setting refer to?
the guiding principle in constructing any basis os consistency. this means that the relationships between assumptions in a basis are realistic, reflecting the correlations that exist between variables.
mortality and morbidity assumptions
an assumption is required for both base mortality and the mortality trend. mortality is a key assumption for life insurance products.
an allowance should be made for expected changes in mortality rates over time using a combination of the following
- expectation approaches
- extrapolation approaches
- explanatory approaches
in some countries, observed mortality improvements can vary significantly by year of birth or cohort. .
how would you set mortality assumptions
the actuary will consider the company’s recent experience on the contract or related contracts. this will allow appropriate adjustments to be made to standard tables. industry data and reinsurers data may be useful, especially if the company has little relevant data.
adjustments should allow for differences between the lives for which the assumptions are being set and the lives from which the data is obtained. there may be differences in target market, distribution channel or underwriting approach.
investment return assumption
this will be set bearing in mind the significance of reserves for the contract, the extent of investment guarantees, the importance of reinvestment and the intended asset mix for the contract.
the impact of taxation must be considered.
expense and commission assumptions
expenses will be loaded for in accordance with the results of the most recent expense investigation. some expense modelling work might be entailed for new ventures. in deciding on the split of expenses between per policy and per R1 of premium, some cross subsidy might be necessary for competitive reasons.
expense inflation assumption
this will depend on expected future earnings inflation. it must be consistent with the investment return assumption.
persistency assumption
the assumption will take, as a starting point, the most recent investigation for that contract or related contracts or, in the absence of suitable data, industry statistics. some adjustment may be necessary.
the commercial and economic environment is important.
margins in assumptions
margins will be necessary to guard against adverse future experience. however, competitive pressure forbids too much prudence in the pricing basis.
risk may be allowed for through the risk discount rate, stochastic modelling or margins in the parameter assumptions.
risk discount rate assumption
those who provide capital to the life company expect a return n their capital of
- that which they could obtain from a risk free asset
- plus a risk premium to compensate for the volatility of return
this return on capital demanded by the investors is the risk discount rate (rdr = rfr+rp). the actuary will need to price products to meet that rate if the company as a whole is to earn that rate.
how is the risk discount rate determined
the rdr can be determined by quantifying the risk premium appropriate for the company. one way of doing this is y using the capital asset pricing model.
the capital available in the market should also be taken into account.
the markets view of the rdr is not necessarily the most apt for any given product or project, as different products will have different levels of riskiness
factors that increase product riskiness
- lack of historical data
- high guarantees
- policyholder options
- overhead costs
- complexity of design
- untested market
statistical risk may be assessed analytically, using sensitivity analysis or using stochastic modelling.
profit criteria in assumptions
premiums are set to satisfy specific target measures e.g. a function of the npv. the specified criteria are part of the pricing basis.
market consistent valuation
if a market consistent valuation is used then the expected investment return can be set as the rfr regardless of the actual assets held. however, the investment return volatility and correlation assumptions depend on the actual assets held.
a margin is likely to be included in the other parameter values to allow for the risk in their estimation.
