Flashcards in APN 110-Allowance for Embedded Value Investment Derivatives Deck (13)

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1

## List the various embedded investment derivatives covered by this guidance note? (7)

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• Minimum investment maturity guarantees

• Guaranteed annuity options

• Minimum investment related deaths or other risk benefits

• Minimum investment related surrenders

• Minimum increase rate guarantees on variable annuities

• Implied investment guarantees on conventional with-profit polices and smoothed bonus in the form of vested/guaranteed bonus

• Explicit or implicit minimum investment return on universal life polices fund accounts

2

## Outline why allowance for embedded value investments are more relevant presently than in the past? (3)

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• Many life insurers have in the past and currently write polices with embedded investment derivative e.g. smooth bonus or market related polices with guarantee returns

• Inflation was high in the past relative to guaranteed investment return therefore the derivative was not particularly onerous and the issue did not receive much attention

• However now long-term inflation expectations are at a level where these potential costs of derivatives are no longer immaterial

3

## Outline the methodology for the valuation of embedded investment derivatves? (3)

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• Deterministic investment methods are not appropriate to quantify what must be held to fund shortfalls under embedded value investments

• In order to quantify reserves stochastically simulate future economic variables which are used to project liabilities from embedded investment derivatives

• The additional liabilities (i.e. shortfalls) at the claim date are then discounted at an appropriate discount rate to determine the required reserves at the valuation date

4

## Outline the type of stochatic model and a general approach to setting the parameters of a stochastic model? (7)

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• The actuary may use a market consistent actuarial model that is deemed appropriate

• Each stochastic model will have a its own unique set of parameters however most models will require as inputs

o The volatility of investment returns of assets backing the policies

o Term structure of interest rates

• It is recommended that for market consistent liabilities are valued using a zero coupon yield curve which are based on the swap market or zero coupon government bonds

• Volatilities of the stochastically simulated returns should be in line with those implied by tradable derivative with appropriate underlying assets

• The parameters should be set using tradable derivatives in the market to determine implied volatilities as well as historic market volatilities (if market values of appropriate maturity term is not available)

• The relationship between two volatilities can then be extrapolated

• The volatility parameter may be time dependent and be itself a stochastic process

5

## Describe the consdierations regarding the Expected returns as well as mean reversion in market consistent stochastic models? (3)

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Expected Return

• Expected returns in theory should not affect the reserves in the investment guarantee i.e. should only be affected by volatility

• The state price deflator will exactly offset the higher return on the asset used for discounting the additional liabilities

Mean-reverting returns

• If the actuary is using a model consisting of mean reverting returns they need to ensure that the market consistency assumption is not violated

6

## Outline considerations regarding the number simulations that should be projected when using a stochastic model? (3)

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• The actuary must decide on the number of iterations/simulations of future asset price scenarios

• The recommended number of required iterations is 1000 (preferably 2000 should be performed)

• Variance reduction techniques may allow simulations to be reduce (judgement would be required)

7

## Describe how a guarantee resreve will be calculated for minimum investment maturity guarantee for market-linked funds? (10)

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• The market value of the assets (i.e. the value of the unit fund) is used as the starting point

• This value is then accumulated with future premiums at stochastically simulated investment returns allowing for changes in tax to determine the projected maturity value

• The maturity values are calculated on best estimate assumptions for all future contingences other than decrements and future investment returns

• The decrements should be divided into “partial off” decrements (partial surrenders and paid ups) as well as “final off” decrements (death, lapse, surrender)

• Allowance for partial off decrements in the build-up of fund values and guarantees will depend on the nature of the guarantee offered

• The projected fund value is compared to the projected guaranteed minimum maturity value without an allowance for decrements

• If shortfall liability due to the guarantee is the maximum of excess minimum guarantee value less fund value or zero

• The actuary must take credit for the accumulated value of premiums explicitly charged and if they are greater than the shortfall a surplus will be recorded

• The shortfall or surplus in each simulation must be discounted to the valuation date (the appropriate discount rate is discussed below) and then multiplied by the probability of policy reaching maturity taking into account decrements

• The average guaranteed discounted shortfall across all simulations is taken to be the guarantee reserve required

8

## Describe how a guarantee resreve will be calculated for minimum investment maturity guarantee for smooth bonus funds? (10)

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• Existing policyholders subsidise guaranteed benefit payments when returns are low

• The use of the full shortfall (guaranteed value less value of assets in the fund) may therefore not be consistent with the way the fund is managed

• The actuary will project the future assets share (allowing for premium and investment returns)

• The projection of the underlying assets should allow for the investment policy of the fund

• The benefit liability will also be projected in conjunction with the asset share taking into account the bonus

distribution policy to determine rate under different economic conditions but also allowing for the principles and practices of financial management

• The guaranteed maturity value should also be projected allowing for vested bonuses

• The guaranteed minimum maturity value over the policyholder liabilities constitutes a future liability that must be reserved for

• The actuary should bear in mind that the deterioration of the funding level i.e. difference between asset share and policyholder liabilities which may constitute an additional guaranteed cost

• Where applicable allowance for offsetting management actions may be made in calculating potential losses to shareholders

• To the extent that costs are Bourne by shareholders the reserve may not be used to reduce bonus fluctuation reserves

9

## Describe how a guarantee resreve will be calculated for minimum investment maturity guarantee for reversionary bonus funds (7)

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• The life office has discretion regarding the bonus distribution as well as investment policy which will both influence the cost of the guarantee

• The higher the reversionary bonuses relative to the terminal bonus will increase the cost of the minimum maturity guarantee

• The assets held to match the guarantee will reduce the cost of the guarantee

• Application of discretion in the distribution of profit and changes to the investment policy must be allowed for in the calculation of reserves

• The discretion in the bonus distribution needs to take into account bonus distribution philosophy, policyholder reasonable expectations as well as principles and practice of financial management

• The asset share will have to be projected in conjunction with future guaranteed liability at maturity (i.e. basic benefits plus attaching vested bonuses)

• A shortfall will be recorded if the asset share is less than the guaranteed liability at maturity

10

## Ouline the appropriate discount rate to value the cost of guarantee? (3)

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• The appropriate discount rate will depend under which probability measure investment returns were simulated under

• If the simulation was done using a risk neutral measure then the discount will be done using the risk-free rate applicable to the interval

• Otherwise an appropriate state price deflator associated with the probability measure associated with the simulation will be used

11

## Describe how taxation can be allowed for in the value of guarantees/option (contingent) liability? (6)

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• Allowance for tax of lined assets or asset share can be made at the actual tax rate taking into account the appropriate fund for the policyholder

• In order to calculate the market consistent value of a contingent liability the composition of the hedging portfolio at each time point will be required to appropriately apply the tax

• An alternative pragmatic approach is as follows:

o First calculate the market consistent value of the liabilities ignoring tax on the assets backing the guaranteed liability (denoted A)

o Next calculate the real world CTE(0) conditional tail expectation ignoring tax on guaranteed liabilities (denoted B)

o Calculate the real world CTE(0) but assume that income and capital gains on investment guarantee at applicable rates (denoted C)

o Calculate the market consistent reserve allowing for tax assuming that tax is proportionally the same in risk neutral (market consistent) and real world cases

12

## Describe how other assumptions and margins should be determined for the valuation of guarantees/options? (5)

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Other assumptions

• The reserves will be calculated using best estimate assumptions used in valuations

• Interactions between decrements such and lapses/surrender and investment returns should be allowed for

• Take-up rates may also be assumed regarding premium increases

Margins

• The guarantee reserve does not require compulsory margins

• However under certain circumstance discretionary margins may be applied

13