Important to memorize Flashcards
(15 cards)
Asset Liability Matching
- General points
- Annuity
- Unit-Linked
- With Profit
General Points (For every product mention)
- asset to reflect the nature, term and currency of the liability
- also to consider any regulatory restriction
- and the company level of free asset
- and the risk apetite to maximize profit
- some cash likely to be held for liquidity purpose.
- there are also expense reserve for each products type, and could be matched with index-linked bond where index is closest to what expected expense increase driver is.
Annuity
- (look at the benefits term and nature) describe that it is guaranteed in monetary terms
- or could be guaranteed in terms of index linked
- match with fixed income bonds, with the term being life expectancy of the annuity
- or buy government bonds or corporate bonds
- corporate bonds have higher credit risk
- there may be no asset available of long enough duration to match the liabilities
Unit linked
- Unit fund generally held assets that are chosen by the policyholders selected funds
- non-unit fund generally are required to be in liquid asset like cash as they need to covert any shortfall between charges and expenses.
With profit
- (look at the benefits term and nature) describe that it is partially guaranteed in monetary terms and can split into guaranteed and non-guaranteed
- guaranteed include sum assured and bonuses declared
- match with fixed rate bonds with term match with expected term of the life assurance.
- For non-guaranteed benefit, to maximize return, subject to risk appetie of tcompany based on amout of free assets available, PRE invest in equity/property
Unit - Pricing
- Expropriation and apprioriation price calculation
- Offer basis and Bid basis
(bid basis) Expropriation price - price at which units are cancelled
calculate as:
- market bid price of assets held by the fund
- less expense inccured on sale of units
- plus value of any current asset
- less value of any current liability
- plus accrued income
- less outgo such as fund charges
- less tax
divide by number of unit inforce at valuation date
(offer basis) Appropriation - price at which units are created
(normally higher than expropriation price)
market offer price is used instead of bid price
expense incurred on purchase of units instead of sale
Steps to determine expense assumption
-expense data need to be inflated to the time where it is being used
- adjust for any changes since analysis took place
- use the expense analysis for the product that most resembles the new products as starting point
- with cost adjusted to allow for any new features
- allow development cost/new computer
- include overheads and spread across the business/ direct expense depend on new buss
- prudent margin for uncertainty
- recent data/ period data to be used
- homogenous group
- reinsurer data if its new
-terminal/ initial renewal
-marketting expense
- comission (excluded as it is known)
unit reserve and non-unit reserve
unit reserve
- bid price * number of units
non-unit reserve
Under a regulatory regime which requires mathematical reserves to be prudent (rather than best estimate), the non-unit reserve is typically defined as the amount required to ensure that the
company is able to pay claims and meet its continuing expenses without recourse to further
finance. [1]
- discounted cashflow method
- cashflow will be projected monthly on reserving basis
- first project unit fund value allowing alloc prem, expected fund growth and cost of insurance charges, policy fee
- non-unit csahflow include all charges expense, comission, death payments and surrender penalties
Then start witt the time period which latest negative cashflow occurs
calculate NUR at start of the period sufficient to zerorise the negative cashflow
deduct this NUR from cashflow from end of previous time period. repeat for each succesive time period until reach valuation date.
if the cashflow is negative, nur is set up equal to the negative amount.
negative NUR represent a loan that will be repaid by emerging profit.
Define asset share (4)
- Asset share is accumulation of premiums…
- …less deductions associated with the contract…
- …(plus, for with-profits policies, allocation of profits on without-profits business and surrender profits on with-profits business if applible & appropriate)…
- …all accumulated at the actual rate of return earned on investments
Explain in words how an asset share may be calculated using a recursive formula (5)
- Asset share can be calculated recursively on year-to-year basis
- Initially, earned asset share is zero
- Each year cashflows, including premiums received and deductions made, e.g. to cover cost of benefits, are recorded
- Suitable rate of return on investments is used to accumulate asset share plus premiums less deductions (plus, for with-profits policies, allocation of any miscallaneous profits) to the year end to determine asset share
- Process is repeated for subsequent years
Product Design
Profitability
Marketability
Sensitivity of profit
oneronous of guarantee
extend of cross subsidies
competitiveness
distribution channel
regulations
consistency with other products
Risk
Investment Risk
- consider guarantee/non-guarantee risk with insurer or pass to policyholder
Mortality Risk
- anti selection/ longevity
- -parameter/random fluctation/model risk
Persistency Risk
- selective withdrawal -> lead to loss at early(asset share)/ expense/worsen mortality
Expense Risk
- erode with inflation
Credit Risk
Different approaches used to project mortality trends (3)
- expectations: uses expert opinion + subjective judgement to specify range of future scenarios
can implicity include all relevant knowledge, incuding quantitative factors
subjective and subject to bias - extrapolation of historical trends
project historical mortality trends into the future
some subjectvity: choice of period to determine trends - explanatory projection techniques,
modelling bio-medical processes that cause death
only effective to extent process understood and mathematically model-able
Describe how a risk discount rate could be determined that reflects the expected level of
statistical risk, for a given new product, including the use of the following:
deterministic sensitivity analysis
stochastic simulation.
The following steps could be performed.
(1) Calculate some trial premiums for the product, based on best estimate assumptions of
future experience, and using the shareholders’ required return as the risk discount rate.
(2) Calculate the return on capital generated by these premiums, on the basis of a range of
different deterministic scenarios for the future experience. The scenarios used should
include adverse outcomes that have a feasible likelihood of occurring, for example with a
5% probability. (The actuary would need to devise these scenarios using his or her
judgement, based on historical experience, and on analysis of all the factors likely to
affect the experience in the future.) Should the return on capital obtained fall below
some required minimum level (such as the risk-free rate of return), then the premium
should be increased until this criterion is satisfied.
Alternatively, should the return on capital be consistently much in excess of the required
minimum level, then there may be justification in reducing the premium. (The company
would have to consider whether the product concerned represented a ‘lower than typical’
level of riskiness for the company in order to justify this – we have to keep in mind that
the overall required return reflects other factors than just statistical risk (eg the
availability of capital)).
Use these new premium levels in the next step.
(3) Repeat step (2), only this time modelling the variables stochastically. Calculate the
frequency (out of many simulations) with which the return on capital falls below the
required minimum rate. If this frequency is too high (say more than 5%), then the
premiums could be further raised until a 5% frequency is obtained. (Or premiums could
be reduced if the frequency is too low). Use these new premium levels in the next step.
(4) Calculate the return on capital obtained from any new level of premium produced from
steps (2) or (3), using best estimate experience assumptions. This new return on capital
can then be used as the new risk discount rate. This new risk discount rate now takes
account of the levels of statistical risk for the product.
Calculation of embedded value
Embedded value is the present value of shareholder profits in respect of the existing
business of a company, including the release of shareholder-owned net assets.
It can be calculated as the sum of:
The shareholder-owned share of net assets, where net assets are defined as the
excess of assets held over those required to meet liabilities.
The present value of future shareholder profits arising on existing business.
Solvency capital requirements: Value at Risk approach
Outline the Value at Risk (VaR) approach to dervicing the risk-based solvency capital required by an insurance company.
- Supervisory balance sheet subject to stress tests:
supervisory balance sheet=>often market consistent for this approach type
conduct stress tests/shocks on supervisory balance sheet for each risk factor separately, at defined confidence level, over the defined period.
eg calculate R100mil capital required to cover mortality mortality risk
each stress test involves projecting the company’s future assets and liabilities, based on the actual liabiltiies and assets currently held.
for each risk factor, amount of capital needed at the present time, in excess of its liabilities due to stress test, is calculated to ensure that assets exceed liabitlities at the end of the defined period with the required probability.
alternatively, determine single shock scenario with 99.5% confidence which involved simultaneously shocking mortality, expenses, investment return, withdrawals, etc => currently too computationally difficult, so seperate stress test used instead - Aggregate capital requirement
for individual stress tests done, combine capital required over all risk factors, allowing appropriately for interactions, eg via correlation matrix
aggregate capital requirement…
= sqrt[ SumOveri( SumOverj (Corr(i,j) * Cap(i) * Cap(j))) ]
where Cap(i) is the capital requirement under risk i and Corr(i,j) is the correlation between risks i and j
under extreme event condition being tested, correlations may differ from those observed under normal conditions=> copulas may also be use
Additional capital may be needed across individual risks to cover any
non-linearity (1% increase in shock <> 1% change in cap required)
non-seperability (events happen together > if happen seperately)
Stochastic modelling on guarantee
The company will need to stochastically model the future price of assets (or the
investment return) [1]
using an assumed asset mix which corresponds to the company’s planned asset
strategy for the funds [½]
and a probability distribution reflecting the possible performance of assets [½]
allowing for any correlation between asset types. [½]
For each simulation and each maturing policy, the model needs to calculate the
excess of the fixed guaranteed benefit over the projected unit fund at the maturity
date. [½]
If this is negative, it should be set to zero or take the higher of the above amount and
zero. [½]
The present value of the liability can then be determined by discounting these
simulated costs of the guarantee. [½]
A large number of simulations of guarantee costs would be run to obtain a reliable
outcome. [½]
The average of this cost across all simulations gives the expected value. [½
Option pricing model on guarantee
This type of maturity guarantee corresponds to a put option on the investment funds. [1]
It would be a European style option [½]
on the investment funds at an exercise price corresponding to the maturity guarantee. [½]
The whole investment fund will not be equivalent to a single option traded on the
market [½]
but the company can approximate this [½]
by selecting options written on assets that most closely represent the assets within the
unit funds [½]
