Valuation of Contingent Pension Liabilities and Guarantees under Sponsor Vulnerability

Abstract

This paper analyzes the relationship between a pension fund with contingently indexed defined benefit liabilities and its sponsor, using contingent claims analysis. As pension funds generally run a mismatch risk, future surpluses and deficits will occur. Surpluses are divided between beneficiaries and sponsor through contingent indexation of the benefits and refunding. Covering a deficit at the pension fund level is a function of the sponsor's financial ability to do so. This paper suggests that this system creates an asymmetric allocation of the residual risk between sponsor and beneficiaries. The optimal investment policy for the pension fund in this context can be found through reverse engineering option valuation formulas. The main conclusion is that the sponsor's vulnerability negatively impacts the optimum risk profile of a defined benefit scheme with contingent indexation and thereby the market value of contingent pension liabilities.