Understanding the liquidity premium

The liquidity premium has moved from theory to practical reality, first in the market-consistent embedded value metric and then the Solvency II directive. Barrie & Hibbert’s Craig Turnbull explains the theory behind the liquidity premium and how to implement it

The liquidity premium, the concept that illiquid assets have lower prices than their equivalent liquid ones, has recently emerged from relative obscurity to become a major issue for European insurance, both in market-consistent embedded value (MCEV) reporting and the proposed Solvency II directive. Research on this topic has focused on how to observe the level of liquidity premium embedded in the market prices of assets such as corporate bonds. Less work has been done on how to apply these estimates to the market-consistent valuation of complex insurance liabilities.

This note explores how market-consistent liability valuation methodology can be adjusted to allow for liquidity premiums, and the implications this has for the behaviour of the valuations of different types of liabilities. Incorporating an allowance for liquidity premium into the market-consistent valuation of insurance liabilities is a three-stage process:

1. estimating the liquidity premium embedded in asset prices;

1. estimating the illiquidity of the insurance liabilities, so as to derive the liquidity premium applicable to the liability under consideration; and

1. application of the liquidity premium estimate (stage 2) in the market-consistent valuation of the liability.

The first two stages

Considerable work has been done in this area and a number of methodologies have emerged for the estimation of the liquidity premiums that can be found in asset classes such as corporate bonds.

These approaches derive liquidity premium estimates by comparing the prices of two assets that are equivalent except for liquidity. The methods differ by the choice of assets that are used for this comparison, and whether these assets have market prices that can be directly observed or need to be estimated by a model.

Measuring the relative liquidity of insurance liabilities

The next stage of the process involves determining the liquidity of the liability. This isn’t necessarily a binary decision, although interestingly, the fifth quantitative impact survey (QIS 5) specification has taken a simplifying approach by assuming that liability liquidity can be grouped into four buckets:

• liabilities maturing in less than one year (assumed to be perfectly liquid, so get 0% of the liquidity premium);

• immediate annuities (assumed to be perfectly illiquid, so get 100% of the liquidity premium);

• life insurance contracts with profit participation (deemed somewhat illiquid, and therefore get 75% of the liquidity premium);

• and everything else (gets 50% of the liquidity premium).

Barrie & Hibbert published research in December 2009 that explored a more granular and sophisticated modelling approach to measuring liability liquidity, A Measure of Liquidity of Liabilities. Its central idea is that the liquidity needs of a liability can be assessed by measuring how often a matching asset portfolio needs to be rebalanced due to unexpected changes in the liability cashflow outcomes, for example, due to unexpectedly high mortality rates in an immediate annuity book.

Relative to the QIS 5 method, it is a modelling approach that inevitably involves more model and parameter choices, but offers a less arbitrary and more granular approach to liability liquidity assessment.

Market-consistent valuation methodology for illiquid liabilities

Once armed with an estimate of the applicable liability liquidity premium, how should it be incorporated into the valuation of insurance liabilities?

For liabilities of a sufficiently simple form that market-consistent valuation only requires the discounting of expected liability cashflows using a risk-free curve, the adjustment is minor: add the liquidity premium to the risk-free yield curve and discount those expected cashflows using the adjusted yield curve.

What about more complex liabilities such as those that require market-consistent simulations to value them? In QIS 5, the approach is again quite simple: the risk-free yield curve used for the valuation is directly adjusted for the addition of the liquidity premium. The natural next step is for risk-neutral valuation to then proceed as usual – this adjusted yield curve is used both in the risk-neutral stochastic projection of the assets and in the discounting of the resultant contingent liability cashflows.

This implementation sounds simple, but one area of potential confusion and ambiguity that can arise here is over whether the stochastic model’s volatility parameters should be re-parameterised so that the calibration undoes the impact of the liquidity premium adjustment on the model’s fit-to-option prices. Where liquidity premiums have been used to date (MCEV and, in the UK, regulatory capital assessment), the standard practice has been to not re-calibrate the model’s volatility parameters, and it is expected to be the same for QIS 5 and Solvency II implementation.

This is broadly intuitive in the sense that if the intention was to keep the valuation basis consistent with the pre-liability-premium basis, there would be no reason to change it in the first place. Put another way, a swaps + 20 basis points calibration isn’t consistent with swap prices, so why should it have to be consistent with swaption prices? We use option prices to derive market-implied volatility levels, and there is no obvious reason for this derivation to assume the market is using the same liquidity premium adjustment in its derivative valuations as QIS 5. But it should be noted that retaining a fit-to-option implied volatilities instead of option prices arguably contravenes aspects of the draft QIS 5.

The approach of merely adjusting the starting yield curve has the benefit of apparent simplicity, but it will produce a counter-intuitive effect: the inclusion of the liquidity premium will reduce the value of some forms of contingent liabilities (as expected), but will result in an increase in the valuation of some contingent liabilities – options and guarantees that increase in value when interest rates increase. The following example illustrates this effect.

Example: standard fixed deferred annuity contract
This case is straightforward: the market-consistent valuation of a fixed deferred annuity is calculated by discounting the expected liability cashflows using the risk-free yield curve (adjusted for the inclusion of the applicable liquidity premium).

Now assume this contract also provides the policyholder with the option to exchange the annuity income for a lump sum at the annuity vesting date. This form of policyholder guarantee will typically be valued using market-consistent simulations. Note that the guarantee will be worth more to the policyholder when interest rates are very high: in such scenarios, the annuitant will be able to secure a higher annuity income by exercising his lump sum option and re-investing it at the market annuity rate.

So, the market-consistent valuation of this option will increase if we include a liquidity premium in the starting yield curve in the way prescribed by QIS 5. Meanwhile, a policyholder option that is more valuable when interest rates fall (such as an option to exchange a lump sum for annuity income at a pre-determined rate) will be reduced in value by the inclusion of the liquidity premium. Are these opposite effects arbitrary or logical? If the rationale for the inclusion of liquidity premiums in liability valuations is that illiquid things should cost less, does it make any sense for the value of a liability to be increased by an allowance for its illiquidity?

This counter-intuitive result is arguably indicative of the tenuous link between the liquidity premium earned on assets such as corporate bonds, and those earned by more complex contingent assets such as non-linear derivatives like options and swaptions – which most resemble the contingent liabilities under consideration.

While the link between the liquidity premium that can be earned by investing in illiquid assets such as corporate bonds and the valuation of a liability that can be replicated through a buy-and-hold strategy that uses those illiquid bonds is intuitive, how this impacts on the valuation of options – which are replicated through dynamic strategies that necessitate the use of liquid assets – is far less obvious.

In the QIS 5 methodology, the impact on the contingent liability valuation is defined by adding the liquidity premium to the underlying interest rate used in the derivative valuation. As we have discussed, sometimes this will result in the valuation going up, and sometimes it will result in the valuation going down. These valuation impacts are hard to interpret as meaningful estimates of the impact of illiquidity on the option value.

However, the behaviour of the valuation of the deferred annuity’s lump sum option may be more intuitive when considered in aggregate with the behaviour of the underlying deferred annuity. The total liability value will be equal to the sum of the value of the standard fixed deferred annuity and the lump sum option.

When a liquidity premium is added to the valuation in the QIS 5 way, the value of the standard component of the deferred annuity will fall, while the value of the option will increase. Viewed from this perspective, the increase in the option value could be considered as a claw-back of the discount produced for the standard component of the deferred annuity by the inclusion of the liquidity premium. This claw-back might be viewed as reasonable since the inclusion of the option makes the deferred annuity more liquid for the policyholder. But there are more direct and transparent ways of reducing the liquidity premium impact on these types of contracts if that is the intention.

What’s the answer?

What is the right way to allow for illiquidity in the market-consistent valuation of interest rate-contingent liabilities such as the lump sum option for the deferred annuity contract discussed above?

The process could be simplified if the impact of the liquidity premium was separated from the risk-neutral simulation modelling: there is no rationale for the liquidity premium to be wrapped up in the calibration of stochastic interest rate models, and it will further complicate the process of calibrating to interest rate swaptions and validating their quality of fit. This is particularly true when the addition of the liquidity premium will mean models that have been fitted to implied volatilities as per standard practice will now no longer reproduce market prices. It will also require multiple calibrations, scenario sets and asset liability management (ALM) model runs to be produced for no particular reason.

A simpler solution would be for market-consistent simulations to be used to value liabilities prior to any adjustment for liquidity. The liquidity premium adjustment could then be made by simply multiplying the pre-liquidity market-consistent value by a factor that is based on the applicable liquidity premium and the duration of the liability.

This would not address the question of whether adjustments to contingent liability valuation for the effects of illiquidity should always be positive, always be negative, or either depending on the direction of its rate sensitivity. But it would simplify the valuation process by reducing the economic scenario calibrations, validations and scenario sets required for market-consistent calibration of contingent liabilities.

An additional complication to consider is whether certain liabilities, which are classified as 50% or 75% liquidity premium liabilities under QIS 5, should be reduced by the liquidity premium. An example of such a liability type might be a typical UK with-profits policy, which is often considered to consist of an asset share and a value of guarantees. The asset share has many of the features of a unit-linked contract and it is unclear why the asset share value itself should be adjusted for illiquidity.

Careful consideration

The use of liquidity premiums to lower the market-consistent valuation of insurance liabilities has become a high-profile issue in Solvency II. This has led to a considerable amount of work being done by the industry on the estimation of liquidity premiums embedded in market asset prices. Significantly less work has been done on measuring liability liquidity, and how market-consistent liability valuation methodologies should be adjusted to allow for the estimated liquidity premium.

This latter topic is particularly complicated when considering the valuation of contingent liabilities such as options and guarantees. In these cases, the directional interest rate sensitivity of the liability may be opposite to that of fixed liabilities, for example a lump sum option attached to a deferred annuity contract will increase in value when interest rates are assumed to be higher.

The proposed QIS 5 methodology of adjusting the starting yield curve by the size of the liquidity premium will therefore produce counter-intuitive results for liabilities, such as the intended lowering of liability values to allow for their illiquidity not occurring. Instead the value of these liabilities will be increased by the inclusion of the liquidity premium. For some liability types, even applying this adjustment needs careful consideration.

This effect highlights the dubiety of incorporating an allowance for liquidity into contingent liability valuation by changing the starting yield curve that the stochastic interest rate model is calibrated to. It would be simpler and more transparent to use risk-neutral simulations to value the liability prior to any adjustment for illiquidity. The illiquidity adjustment could then be made by applying a factor to the pre-liquidity-adjusted value, based on the applicable liability premium and the duration of the liability.