The various contingent claims in a pension fund, such as the parent guarantee (corporate covenant) or conditional indexation, can be valued with the same techniques that are used to value options on stocks.
An application to a real life pension case shows how risk absorption by employers and beneficiaries varies widely, depending on such variables as asset allocation and rating of the sponsor.
This valuation technique is an indispensable tool for improving pension fund risk management, redesigning pension contracts, and supporting Chief Financial Officers in their decision-making process with regard to mergers or acquisitions.
Pension funds in their defined benefit (DB) form and the alternative structures that have evolved over time are among the most complex risk-sharing institutions ever created, not least because they involve many stakeholders (such as employers, retirees, and employees), all of whom assume different risks.
The employers assume some of the risks by, for example, being obligated to replenish any shortfall in the pension fund. The pensioners and actives assume some of the risk via, for example, partial (instead of full) compensation for inflation.
Unlike with a corporate balance sheet, where it is clear who owns the equity (and hence takes the highest risk and first loss accordingly) and who owns senior debt, there is little agreement on ownership within pension funds. In fact, there is little knowledge about the risks assumed by each stakeholder. Usually, risk is measured for the pension funds as a whole and is typically expressed in terms of the risk of funding shortfall. However, this does not equal the risk that each of the stakeholders may face.
A better quantification of the risks that the various parties assume, which would enable more effective risk management, would prove very valuable. It could be used to negotiate pension contracts and to agree on any entitlements that stakeholders may have to the potential upside (surplus) in the pension fund. As a further illustration, Chief Financial Officers (CFOs) are interested in the specific share of risk that they assume—and the value of those risks—when acquiring a firm with a DB pension fund. With the knowledge provided by the embedded option technique, the CFO could assess what kind of policy measures applied to the pension fund would result in acceptable risks when a target firm—including the firm’s obligation to the pension fund—is acquired.
The single most objective way of dealing with multi-stakeholder risk situations that arise in pension funds is the embedded options approach. The risks various stakeholders assume in a pension fund are formulated in terms of options—contingent claims—which stakeholders have written to the pension fund. These options have a certain value that can be determined by employing the same techniques as are applied in the financial markets to price financial options. Since most of the variables relevant to the pension fund have a basis in financial markets (riskless assets such as government bonds, risky assets such as equity and corporate bonds, and interest rate-related liabilities), this is an approach that provides reliable market-consistent values.
Determining the value of these embedded options can be well worth the effort. As will be shown in the analysis below, the contingent claims that stakeholders have in pension funds can easily exceed 20% or 30% of total liabilities in a pension fund. Considering that the estimated value of, for instance, the joint liabilities of UK and Dutch pension funds alone already exceeds 2,000 billion euro, the value of the embedded options is at least hundreds of billions of euros.
Identifying the Various Embedded Options
To start with, some of the most significant embedded options identified in pension funds are discussed. One of the most important embedded options the employer writes to the pension fund is the so-called parent guarantee, also known as the sponsor covenant. This is the guarantee to support the pension fund in case of funding shortfalls. This option depends on, among other factors, the exact trigger levels at which the parent will pay, as well as (from the perspective of the pension fund) the development of the default probability of the parent company over time.
Two important options that the beneficiaries write to the pension fund are the indexation option and the pension put.
The indexation option is the right the pension fund has to waive indexation in case of, say, an insufficient funding level.1 In case of a very low funding ratio, this implies that the beneficiary’s maximum value loss compared to full indexation is roughly the expected inflation multiplied by the duration of his contract.
The pension put is the occurrence of a joint “default” event (i.e. a deficit of the pension fund’s funding and at the same time a default of the sponsor). Such a joint event will imply write-offs of the pension entitlements, which is defined as the “payout” of the embedded option. The value of the option depends on, among other things, the (assumptions made with respect to) default probability as a function of time, recovery rates, and correlation between financial markets and the default probability.
Many pension funds have additional embedded options, such as the option to increase contributions (paid by employers and often also partially by the employees) in case of a low funding ratio.2 And in exceptional cases, such as BAE Systems’ pension fund, even longevity options are written by active employees to the pension fund, allowing the fund to reduce pension entitlements in case of an unanticipated rise in longevity. Many other embedded options are implicitly present in pension funds, although the set described above covers the majority of options in DB funds.
The embedded options described above can be explicitly calculated using market-consistent valuation. The values of the embedded options in this article are measured using arbitrage-free option pricing techniques and assuming complete markets. Monte Carlo simulations are used because of the complex nature of the options. It is outside the scope of this essay to discuss these valuation techniques and their underlying assumptions in further detail, since literature is abundant.3
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