The need for clearly articulated arrangements between pension stakeholders has recently gained in importance. It is no longer acceptable for large corporations to base their relationship with their pension funds on vague promises as far as annual contribution rates, shortfall recovery plans and refunds in abundant market situations are concerned.
More explicit contracts between all parties constitute the only real alternative to arranging a defined benefit (DB) pension scheme on the whole. In the absence of a well-defined ‘pension deal’, a DB pension fund is a source of risk that cannot be neglected by business or government. To secure this explicit pension deal, or change an existing one, it is first necessary to clarify who bears which portion of risk in the deal proposal. Knowledge of risk sharing is the basis for negotiating over possible excess returns – for example, in the form of a reduction in contributions to the pension fund.
The risk contained in a pension fund can best be quantified with an option approach. All claims on participants (employers, employees, pensioners) are contingent on the financial strength of the fund and therefore similar to financial options as traded on the international markets. This approach, and how it can help in the process of pension deal negotiations, is the basis of this article.
Many products and contracts we deal with on a day-to-day basis have these financial options embedded in them. Well-known examples are the possibility to redeem a home mortgage loan before the original term has ended and guaranteed return levels in a host of insurance products, such as guaranteed annuity rates and minimum investment return levels in certain unit linked products. The options in these products are nowadays fairly well understood by those who sell them to their customers, and the associated risks are more often actively managed by means of option contracts in the financial markets.
Less well examined, at least quantitatively, are the embedded options that feature in pension schemes. Here, several embedded options can be specified in respect of typical pension schemes, for instance1:
q Indexation option: scheme members expect their pension benefits to be indexed by price or wage inflation to maintain a constant real spending or welfare level. However, this indexation is not granted unconditionally. If funding drops below a certain level, no or only partial indexation takes place. The scheme members can therefore see this indexation option as a written put option on the funding level of the fund.
q Sponsor guarantee option: a written put option on the funding level by the sponsor to make generally large additional contributions in case of an asset shortfall.
q Pension put option: a written put option by the scheme members to write off accrued pension benefits. This could happen if a sponsor company were to default on its guarantee option in case of ultimate distress. This option entails the scheme members’ credit exposure to the pension fund and ultimately the sponsor company.
There are two main techniques for determining the market-related value of these embedded options in a pension environment:
q Pricing based on arbitrage-free simulations (often referred to as ‘risk-neutral’ simulations), which is the market practice for derivative pricing by investment banks.
q Pricing based on a simulation including risk premium assumptions and adjusted discounting factors (state price deflators), which was fairly recently introduced as a valuation technique in the actuarial community.
These pricing techniques are fully equivalent and lead to the same valuation results since they are both based on arbitrage-free pricing principles2.
Our illustration of the embedded option approach takes a stylised pension fund and a ‘commonplace’ pension deal as its basis.
Let us consider an indexed average-pay pension scheme with an initial pension liability of e1bn and 110% funding. Active benefits are indexed unconditionally with wage inflation while inactive benefits are indexed conditionally by price inflation for funding levels above 100%. The actuarial base premium is calculated at 21.6% of the salary base and is split on a 67:33 basis between the scheme sponsor and the employees. In case of a funding deficit, the BB-rated scheme sponsor has agreed to make additional contributions to restore the funding level to 100%. However, if the sponsor defaults and is not capable of making its guarantee contributions, total benefits of the scheme members will be written off to attain a funding level of 100%.
An important element for the valuation of the embedded options is the exact order in which the options can be exercised. In these illustrations, the indexation option for inactive members is exercised first, followed by the sponsor guarantee option and the pension put agreement.
Two different examples will now be used to show how the embedded option approach can serve as input to the pension deal negotiating process:
q The first example illustrates the effects of a policy change to a more defensive investment strategy on stakeholder risk participation.
q The second illustrates what will happen if the BB-rated sponsor company is taken over by a financially strong company or conglomerate, which would improve its credit rating from BB to AA.
Besides evaluating the influence that these changes have on the levels of embedded option risk, suggestions are also made on how to adjust the pension deal such that it reflects these changing levels of risk participation.
Monte Carlo simulations under the arbitrage-free conditions are used to determine the market-related values of several embedded options. An arbitrary 10-year time horizon has been assumed for simplicity’s sake and the contribution rates are based on current investment policy.
Suppose that the board of trustees of the stylised pension fund sought to analyse the implications of a change to a more defensive investment strategy: from a 50% equity and 50% fixed income allocation to 25% equity and 75% fixed income. This change in investment strategy will affect the degree of risk sharing between the stakeholders in the fund, as can be seen from Table 1, which shows the market related values of the embedded pension options before and after a change in investment strategy. These results can be used to adjust the pension deal.
As can be seen from the change in the absolute values of the embedded options, the change in strategy has a significant impact on the risks associated to this pension scheme:
q The value of the risk of additional payments by the scheme sponsor into the scheme to cover a funding deficit decreases by almost 60% (from e181.9m to e78.3m), which is a very welcome effect for the scheme sponsor.
q The value of the risk of not receiving indexations on pension benefits decreases by 20% (from e58.5m to e46.8m), which is a favourable result for the scheme members.
q The value of the third embedded option, the pension put in the situation of ultimate distress, decreases by 50% to a value of e22.4m, also a welcome result for the scheme members.
In this case, the lower exposure to volatile equity investments also leads to lower funding level volatility. The new strategy will therefore have a strong mitigating effect on total stakeholder exposure. However, the change to a more defensive strategy also decreases the expected reductions to the actuarial base premium. This expected reduction decreases from 10.2% (21.6% minus 11.4%) to a level of 6.2% (21.6% minus 15.4%) owing to the lower level of expected investment returns.
A way to deal with this contribution increase and with the shift in the level of risk participation is to adjust the contribution split between the stakeholders3. A fair adjustment can be derived from the new values of the embedded options and the new contribution reduction level. If the stakeholders were not willing to accept any investment risk at all, the contribution level would have to be 21.6%. By taking on investment risk and by having implicitly written embedded options, the contribution level can be reduced by 6.2% to 15.4%. Because the scheme members now bear 47% of the risk and the scheme sponsor 53%, it would be fair to split the achieved reduction accordingly. So, 47% of the 6.2% reduction can be attributed to the scheme members and 53% of the 6.2% reduction to the scheme sponsor4.
Bearing in mind the initial 67:33 split of the actuarial base premium and the new contribution level of 15.4%, the latter for the scheme sponsor could be set at 11.2% (67% times 21.6% minus the reduction of 53% times 6.2 %). The new contribution level for the scheme members would then be 4.2% (33% times 21.6% minus the reduction of 47% times 6.2%), resulting in a new 73:27 split5. This illustrates how being able to value the embedded options will help to assess the risk and contribution consequences of policy changes for the different stakeholders. This embedded option approach can therefore be very helpful in negotiating a pension deal.
Next, let’s suppose that a financially strong company acquires the BB-rated sponsor company in an M&A transaction. Consequently, the company’s credit rating improves from BB to AA. This acquisition will have a significant impact on the value of some of the embedded options. It will spark off a substantial shift in the level of risk sharing and might even justify a renegotiation of the pension deal.
Assuming the same stylised pension fund with the 50% fixed income/50% equity investment policy, the effects of the acquisition are illustrated in Table 2.
The improved credit rating shifts the value from the pension put option to the sponsor guarantee option, which clearly illustrates the transfer of risk from scheme members to scheme sponsor. The value of the sponsor guarantee option increases because the contributions that are needed to make up any asset shortfalls are paid out more frequently thanks to the less likely defaults of the now AA-rated sponsor. Consequently, these less likely defaults will lead to lower benefit write-offs, thereby decreasing the value of the pension put option.
Now, how can this information be used for negotiating a renewed pension deal? Similar to the previous example of changing investment policy, the level of risk participation can be used to determine a fair contribution split between the stakeholders. In this case however, the contribution level remains the same (11.4%) but the level of risk sharing between the stakeholders changes.
After the acquisition, the scheme members bear e61.3m of the embedded option risks, which represent 21% of the total risk value, while the scheme sponsor’s share of the risk increases to e231.4m, representing 79% of the risk value. Bearing in mind the initial 67:33 split of the actuarial base premium, the new contribution level for the scheme sponsor could be set at 6.4% (67% times 21.6% minus the reduction of 79% times 10.2 %). The contribution level for the scheme members would then become 5% (33% times 21.6% minus the reduction of 21% times 10.2%), resulting in a new 56:44 split for the contributions.
Again, these examples illustrate that the embedded option approach can be very helpful for negotiating a pension deal.
Derivative pricing techniques for embedded options are slowly but surely gaining the attention of a broad group of practitioners in the pension industry. Their adoption of such techniques often stems from the increased interest in fair value calculations where embedded options have to be valued as well.
Because these derivative pricing techniques can be used to value the specific amounts of risk taken by the different stakeholders in a pension scheme, these techniques also come in quite handy when negotiating specific pension deals6.
Martin Coppens and Theo Kocken are with Cardano Risk Management in Rotterdam

1 For a more elaborate description of these embedded options see ‘Proprietary issues in pension funds from an option theoretical point of view’ by Kocken, Capelleveen and Engel (see the publications section on www.cardano-riskmanagement.com)
2 Further information on derivative pricing techniques can be found in any standard textbook on option valuation. More specific information on state price deflators can be found in ‘Modern Valuation Techniques’ by Jarvis, Southall and Varnell, as presented to the Staple Inn Actuarial Society in 2001 (see the papers section on www.sias.org.uk
3 Another way to deal with the contribution increase and the shift in risk participation is to adjust other conditions of the pension deal, for instance the minimum funding level that triggers the sponsor guarantee
4 The suggestion presented here implies that the active scheme members are willing to bear the cost of the lower risk for inactive members as well, as they are regarded as one and the same stakeholder. In the negotiation process for an updated pension deal this aspect can be taken into account by regarding the inactive scheme members as a separate group of stakeholders
5 Similarly, the mentioned 67:33 split of the actuarial base premium has been calculated using the assumed current 70:30 split in actual contributions and the current risk exposures of the stakeholders
6 Similar examples can be found in ‘Pensions, Funding and Risk’ by Chapman, Gordon and Speed, as presented to the Institute of Actuaries in 2001

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