B2 C20 SR and CR 2 Flashcards
Discuss the relationship between pricing and reserving assumptions.
Relationship between pricing and reserving assumptions
Premiums could be calculated using prudent assumptions, with same
assumptions used for supervisory reserves.
– Suitable for with-profits, as surplus will emerge relative to the
prudent assumptions; less justifiable for without-profits.
Premiums could be calculated using broadly realistic assumptions, with
risks to company being allowed for mainly through risk discount rate.
– Supervisory regime may require prudent reserving assumptions,
in which case the premium and reserving bases will be different.
– Supervisory regime may use best estimate or market-consistent
reserving assumptions, in which case the premium and reserving
bases could be same. However, additional allowances for risk
would be needed for each.
State how, in theory, the assets and liabilities should ideally be valued when
using a market-consistent approach.
Market-consistent approach
Assets should be valued at market value.
In theory, liabilities would be valued as the price that someone would
charge for taking responsibility for them, in a market in which such
liabilities are freely traded. In the usual absence of such a market, an
approximate approach has to be taken.
The value of the liabilities should be equivalent to the current market
value of a notional portfolio of risk-free assets that match the liability
cashflows exactly.
Describe how the investment return assumption would be determined for a
market-consistent valuation of the liabilities.
Market-consistent valuation – investment return
This would be based on the risk-free rate, irrespective of the type of
asset actually held.
This risk-free rate may be based on government bond yields, or on
swap rates (if there is a sufficiently deep and liquid market for these).
A deduction may be made for credit risk, as appropriate.
Credit might be taken for the illiquidity premium in corporate bond
yields, provided the liabilities for which the rates are to be used
a) are long term and
b) have a reasonably predictable duration, and
c) for which matching assets can be held to maturity (eg immediate annuities).
Explain what is meant by the ‘illiquidity premium’ in the context of corporate
bond yields, and why it might be possible to take credit for the illiquidity
premium when determining the risk-free rate of return from these yields.
Market-consistent valuation – illiquidity premium
Corporate bonds are less marketable (liquid) than government bonds,
for example, so their prices are more volatile.
The difference between corporate bond yields and government bond
yields that is due to this difference in liquidity (as opposed to their
greater default risk), is the illiquidity premium.
Lack of liquidity is not a problem if the assets are held to maturity.
So, provided the liability cashflows have relatively fixed and predictable
durations, there is no risk due to illiquidity and so the illiquidity premium
can be added to the ‘risk-free’ rate.
Where this practice is permitted by regulation, there would normally be
strict rules about how and when it can be applied, eg there may be a
requirement that matching bonds are held to maturity.
Explain the approach that normally has to be used to obtain market-consistent
assumptions for mortality, persistency and expenses.
Market-consistent valuation – other assumptions
It is usually impossible to obtain market values of these assumptions
directly, because there are usually insufficiently deep or liquid markets
available to base them on.
Instead, the approach is normally to take a best estimate of the future
experience, plus a ‘risk margin’.
The risk margin would reflect the extra price that the market would
require, in order to compensate for the uncertainties inherent in the
liability cashflows due to the assumption.
Alternatively, an overall reserving margin in respect of these risks could
be determined using the ‘cost of capital’ approach.
Outline the ‘cost of capital’ approach to calculating an overall risk margin for
the mortality, persistency and expense assumptions, for the purpose of a
market-consistent valuation of the liabilities.
Cost of capital approach to calculating a risk margin
Project the amount of capital we are required to hold in excess of the
market-consistent estimate of the liabilities, at the end of each future
year, with respect to current business in force.
Multiply the capital amounts by an appropriate cost of capital rate for
each future year, discount at the appropriate risk-free rate of return for
each term, and sum to obtain the risk margin.
The cost of capital rate is the excess of the actual cost of capital over
the risk-free rate, representing the loss in return caused by holding the
capital within the company rather than being able to invest it freely.
Projection of future capital is complex and approximations are usually
used: eg, by expressing the capital required as a simple formula based
on drivers such as the size of the reserves and the sum at risk.
Give two broad areas of risk where solvency capital can protect policyholders.
Solvency capital
Can protect policyholders against:
1. reserves being underestimated, ie adverse future experience relative to
reserving assumptions
2. a drop in asset values (including individual asset defaults).
Discuss the relationship between the reserves and the solvency capital
requirements.
Relationship between reserves and solvency capital
Adequacy of reserves must be considered in relation to solvency capital
requirements and not in isolation, and vice versa.
Relative balance between two varies between countries:
– In some countries, reserves are set up on a relatively realistic
basis (relatively small margins from expected values), but with
requirement for substantial level of solvency capital determined
using risk-based capital techniques.
– In other countries, reserves are set up on a relatively prudent
basis (relatively large margins), but with relatively small solvency
capital requirement, which isn’t specifically related to the risks
borne by the company.
Outline the Value at Risk (VaR) approach to deriving the risk-based solvency
capital required by an insurance company.
Value at Risk (VaR) approach to risk-based capital
Establish a minimum required confidence level, eg 99.5%, over a
defined period, eg one year.
Carry out a stress test at the defined confidence level over the defined
period for each risk factor separately.
Each stress test involves projecting the company’s future assets and
liabilities, based on the actual liabilities and assets currently held.
The amount of capital the company needs at the present time, in
excess of its liabilities, is calculated to ensure that assets exceed
liabilities at the end of the defined period with the required probability.
Combine the capital required over all risk factors, allowing appropriately
for the effect of interactions, for example using a correlation matrix.
Additional capital may be needed to cover any non-linearity and/or nonseparability
of the individual risks.
Describe the use of stochastic modelling to quantify the capital requirements
in relation to economic risks.
Stochastic modelling required for economic risks
A real-world asset model would be used, which should be arbitrage
free.
Calibration of the model can be made by reference to historical
experience, but it is important to reproduce the more extreme ‘tail’
behaviours accurately, both in terms of the size of the tail of the
distribution and (where appropriate) in the path taken.
In particular, the model must not understate the frequency of the more
extreme outcomes occurring.
Define what is meant by a passive valuation approach and state three
advantages of passive valuations.
Passive valuation approach
A passive valuation approach is one which uses a valuation methodology
which is relatively insensitive to changes in market conditions and a valuation
basis which is updated relatively infrequently.
The advantages of passive valuation approaches are that they:
tend to be more straightforward to implement
involve less subjectivity
result in relatively stable profit emergence.
Define what is meant by an active valuation approach and state the
advantages of active valuations.
Active valuation approach
An active approach would be based more closely on market conditions (than a
passive valuation), with the assumptions being updated on a frequent basis.
Active valuation approaches are more informative in terms of understanding
the impact of market conditions on the ability of the company to meet its
obligations, particularly in relation to financial guarantees and options.
