Valuation of Contingent Pension Liabilities and Guarantees Under Sponsor Default Risk

Abstract

This article analyzes the relationship between a pension fund with contingently indexed defined benefit liabilities and its sponsor, using contingent claims analysis. As pension funds generally choose to 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 article 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 by reverse engineering option valuation formulas. The main conclusion is that sponsor default risk negatively impacts the optimum risk profile and thereby the market value of contingent pension liabilities.