Transactions of The Institute of Actuaries of Australia – 1995

704 Pages·2014·19.09 MB·English

THE INSTITUTE OF ACTUARIES OF AUSTRALIA
A.C.N. 000 423 656
Transactions
1995
Volume II
ISSN 1033-0763
© 1996 The Institute of Actuaries of Australia
765
PRICING: THEORY, PRACTICE & CONTROL
By
S 0 Ferris, BA,FIAA
0 J Finnis, BSc,ARCS,FIA,FIAA
M A Munns, BEc,FIAA
0 Shuttleworth, BSc,FIA,FIAA
CONTENTS
Scope 766
2 Pricing Strategies 766
3 Theoretical Approaches to Pricing 768
4 Problems with the Theoretical Approaches
- Some Practical Approaches 775
5 Problems with Practical Pricing 782
6 Control & Management 788
7 Future Developments 792
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SECTION 1: SCOPE
This paper has been written to stimulate discussion on the issues arising from
the following pricing activities in each of the four main actuarial practice
areas:
Practice Area Pricing Activity
General Insurance Product Pricing
Investments Derivative Pricing
Life Insurance Product Pricing
Superannuation Contribution Rate Setting
The paper is structured into the following sections.
Section 2 Pricing philosophies and strategies.
Section 3 Theoretical approaches to pricing.
Section 4 Constraints on theoretical approaches and practical approaches
to pricing adopted in the marketplace.
Section 5 Potential dangers arising from some of the practical approaches.
Section 6 Control and management of risks.
Section 7 Possible future developments in pricing and control.
The commentary has been written from the perspective of each of the
actuarial disciplines relating to these practice areas. In addition, some
observations have been included on the pricing of other financial service
products and the opportunities for actuaries in these areas.
It should be noted that the aim of the paper is to raise issues for discussion
rather than resolve them.
SECTION 2: PRICING STRATEGIES
Pricing is part of marketing which in turn is part of an organisation's planning.
Strategic planning indicates the direction an institution should travel in;
marketing is the vehicle for the execution of those plans and pricing is a key
component of marketing.
The factors that can affect the price of any product or service are shown in
the following diagram.
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PRICING: THEORY, PRACTICE & CONTROL
Factors affecting price
It is arguable that actuaries and also accountants focus too heavily on the
cost factors that influence prices and insufficiently on the other more market
related factors.
Four pricing strategies exist for pricing anything, whether a product or a
service.
(a) Cost-based pricing this has an internal focus, and adds a profit margin
or mark-up to the production cost of the good or service in order to set
the price.
(b) Competition pncmg - focuses entirely on other firms, examines their
prices, and sets prices in order to place one's own firm relative to the
competition.
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PRICING: THEORY, PRACTICE & CONTROL
(c) Relationship pricing aggregates all the services used by a customer
and singularly prices the entire amount of services purchased. This
pricing strategy allows some products to be priced at a loss, since the
relationship as a whole is profitable.
(d) Value pricing - this is an external strategy which prices products and
services based on the perceived value as determined by market
research.
All four pricing strategies need to be seriously considered in pricing any type
of good or service. Focusing on one strategy to the exclusion of the others
will eventually isolate the firm from its customers, its shareholders, or the
marketplace.
We have assumed that the main objective in pricing both insurance and
investment derivative products is to maximise returns commensurate with the
risks undertaken. This is not always the case and many financial institutions
have often had a growth orientation rather than a profit orientation.
In setting contribution rates for superannuation funds, the pricing objective
has been assumed to be the provision of adequate security of benefits for
members, while taking into account the needs of the sponsor of the fund
(who will generally require stability and durability of contribution rates).
SECTION 3: THEORETICAL APPROACHES TO PRICING
General Insurance
The determination of a sound rate for a particular risk consists of the following
steps:
(i) Calculate the Risk (or "Pure") Premium
• Divide the risks into homogeneous divisions of a credible size (by
rating factors, distribution channel, new/renewal business);
• Estimate the claim frequency and average claim costs as well as
trends in claim frequency and claim cost (and claim size
distribution to cost excesses/deductibles and reinsurance
retention levels) for each sub-division; by use of the relevant
claim experience data;
• Allow for future claim inflation and investment returns;
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• Allow for any perceived correlation between rating factors (two
way analysis, etc);
• Allow for investment return on outstanding claim provisions.
The risk premium for each sub-division is the average claim cost
multiplied by the claim frequency. Where data are not so readily
available, proxies for this approach exist; for instance, the binary
approach, (also know as the Hallin and lnglebleck model) which requires
rating variables to be expressed in a dichotomous form.
Rating variables are chosen using a range of tools including least
squares and marginal totals. Their justification is aided by tests of fit
such as Anovar or Chi-square, or a more practical analysis such as
Brigstock's method. Alternatively, a probabilistic model may be used,
such as has been developed by European actuaries where the premium
P is fixed as P E(x) + G(x) : x is a variable, E(x) is its mean and G(x)
is a function depending on the distribution of x.
(ii) Add in an allowance for expenses
Allocate direct and indirect expense costs to class and rating sub
division by type, e.g. acquisition costs, claims management costs,
commission, levies, etc. and reinsurance costs.
(iii) Include a profit/contingency margin
Take into account the risk-based capital requirements for the business
• the return required on the capital determined by the riskiness of
the business;
• allow for contingency margins where applicable.
Experience-Related Rating
The rate for a risk may be adapted using statistically-supportable individual or
pooled claims experience.
(i) Credibility Theory allows for the experience related effect on the pricing
of risk to be regulated by the size of the risk.
(ii) No claim discount is a crude way of adjusting the price for the good
experience of smaller risks.
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(iii) Retrospective rating policies such as burners, profit share or retro-rating
can be used to share with the policyholder exceptional profits (losses)
for larger risks.
Investments
Most of the assumptions used to price derivatives can be observed in the
market. These can include:
• interest rates;
• implied volatilities;
• credit spreads; and
• commodity prices.
In some instances, these assumptions cannot be directly observed in the
market, but an estimate of a "market" price can be determined from similar
products. For example, the implied volatility on the 50 Leaders Index is not
directly observable. However, an estimate can be determined by observing
both the implied volatility on All Ordinaries options, and the usual historic
volatility spread between the indices. In this way we are using market data
wherever possible to set the appropriate assumptions.
Whereas in insurance products it is the actuary's role to predict future
decrements, in derivative pricing all the assumptions are obtained from the
market. The reason for this is that the risks associated with these
assumptions e.g. risk of interest rates changing, are hedged in the market at
the then existing rate. As most risks are hedged, it is the cost of this hedge
that determines the derivative price, not the provider's expectation of the
future regarding these variables.
The practical assumptions for derivative pricing are used as inputs into a
variety of derivative pricing models. Whilst they all differ in the exact way the
pricing is performed, there are basic assumptions common to all these models.
The most important of these assumptions is known as Risk-Neutral Pricing.
Risk-Neutral Pricing
Using techniques available in actuarial science, we could price a derivative
contract as:
P E [PV(d)] where d = value of the derivative at expiration
For an option, we would then need to know the initial underlying asset price
and the distribution of the underlying asset price at expiry. This distribution
would in turn depend on the stock's volatility, riskless rates of return, and the
excess return on shares.
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However, as there is a market available to hedge the option's exposure to the
share price, this formula requires alteration in one area. The adjustment is to
simply assume that there is zero excess return on shares. That is, price the
derivatives based on the above formula but assume the future return on the
share price is equal to the riskless rate. Derivative specialists would know this
as the "Risk-Neutrality" assumption.
Risk-Neutral Pricing is common to all derivative pricing. It allows providers to
trade derivatives at prices that are independent of their view of future returns
on the underlying asset.
This approach will determine the mid-market or theoretical price. To this a
margin is added to give a profit to the provider of the derivative. This margin
is set by the market, which uses competitive pressures to ensure the
reasonableness of the margin. The more liquid the particular derivative
market, the lower the margin will be. This is economically rational as the
opportunity to offset the risk is greater in liquid markets. Therefore the
required profit on any individual transaction is lower due to its lower addition
to the risk of the pool.
Life Insurance
The basic steps involved in pncmg a life insurance "individual" business
product using a "cost plus" or "target profit" approach are as follows:
1. Establish profitability benchmarks for the life insurance company.
2. Establish a set of "best estimate" assumptions on which to test
profitability based upon the proposed product terms and conditions.
3. Determine a representative profile of the new business the company
expects to receive.
4. Project the cash flows arising from the representative portfolio of new
business for the duration of the contract using the best estimate
assumptions and proposed product structure (including price).
5. Compare the profitability results with the company benchmarks.
6. Revise all or parts of the product structure and price until the
profitability arising from steps 4 and 5 are acceptable.
The nature of most life insurance policies is that generally capital is required
in the first year of a contract followed by positive returns in following years.
There are a variety of profitability benchmarks that companies can adopt in
practice. The main ones are:
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• Value Added Benchmark e.g. the discounted value of the profits at a
specified risk discount rate are at least equal to a set percentage of
initial premiums or commissions.
• Internal Rates of Return e.g. the resultant cash flows equate to an
internal rate of return of at least X%.
• Margin on Services Benchmarks e.g. the profit margins are at least a
set percentage of the selected profit carrier.
Companies can adopt just one of these benchmarks, or a combination of
benchmarks or alternate ones for different situations.
Other factors the company will consider are the year on year cashflows or
"profit signature" of the product and the resultant capital strain and payback
periods.
The company will also test the sensitivity of the profit results to changes in
assumptions to test the volatility of the result and highlight major areas to be
monitored and controlled.
Superannuation
The theoretically correct approach to determination of a contribution rate is
1. Understand the rules of the fund
2. Collect and check all the relevant data
3. Analyse the past experience
4. Formulate assumptions for future experience
5. Value the liabilities
6. Value the assets
7. Calculate the funding indices as at the valuation date
8. Choose a funding method
9. Formulate recommendations for a contribution rate
10. Do projections to ensure that this contribution rate will achieve the
objectives of the trustees over the next few years (and revise
recommendations if necessary)
The primary goal of the process is to provide adequate security for members
benefits; however, it is not always easy to define an "adequate" level of
security. Is it sufficient to cover the legal minimums required by SIS
legislation? Should we consider the short term (vested benefits or termination
benefits) or should we consider the long term (accrued benefits)? Is it
necessary to have margins above the "best estimate" of the cost of benefits
and, if so, how wide should these margins be? When a fund fails to meet its