A Contingent Claims Model for Pension Costs

Abstract

Financial statements contain pension plan information, including an estimate of the unfunded pension liability. The unfunded pension liability represents the present value of the expected difference between the pension plan assets and the retirement benefits (obligations). The distribution of possible differences provides a valuation problem for actuaries and accountants. However, this valuation problem is similar to the putcontingent-claim valuation problem. In this paper I develop an estimate of the unfunded pension liability using the Black and Scholes [1973] and Merton [1973] put valuation model. The model includes a riskless discount rate to discount future differences, and as such may reduce the range of possible values to assign to pension liabilities. A surrogate for the riskless discount rate is the treasury bill or bond rate. Since corporations may have an incentive to manipulate the values reported for unfunded pension liabilities, their market-determined discount rates can limit this potential through restrictions on the discounting process. The contingent claims model also assumes the plan portfolio is a market portfolio. The market portfolio as described in Markowitz [1952] represents an aggregate of the risk preferences and beliefs of a market-based set of individuals and, as such, should fit the requirements of the 1974 ERISA prudent man rule. Finally, the returns to a market portfolio provide a benchmark of pension plan manager performance. Part of the