| Abstract: | This study develops a contingent claims model for valuing the implicit market value of the pension claim associated with defined benefit pension plans. In this model, the firm issues pension, debt, and equity claims. These claims have joint access to two underlying portfolios: corporate and pension. The changes in the market values of these two portfolios are assumed to follow a joint lognormal diffusion process. By imposing terminal boundary conditions implied by Employment Retirement Income Security Act (ERISA) rules and the pension insurance provisions of the Pension Benefit Guaranty Corporation (PBGC) on the partial differential equation, a solution for the pension value is obtained. This quasi-market measure of the value of the pension claim may be represented by a portfolio consisting of four components: (1) a risk-free discount bond with face value equal to promised pension benefits; (2) a short put on pension assets with exercise price equal to pension benefits; (3) a long call on 30 percent of corporate assets with exercise price equal to the face value of secured corporate debt; and (4) a short call on 30 percent of corporate assets with a stochastic exercise price which depends on the terminal value of the pension fund. A numerical example using 1992 and 1993 financial statement data from six major U.S. corporations is provided. This example illustrates the usefulness of the model's prediction and the potential effect of theoretical pension values on corporate debt-equity ratios. |
