Pension Regulation and the Market Value of Pension Liabilities - A Contingent Claims Analysis Using Parisian Options

Abstract

Defined benefit pension plans provide their beneficiaries with a prespecified retirement income related to years of service and wage. However, as pension contracts are not entirely legally enforceable, such payments of defined benefit pension plans are not completely irreversible. The pension deal can be closed early or converted, i.e. the sponsor might be tempted to change the nature of the pension fund liabilities from defined benefit to defined contribution to avoid excessive premium increases when the pension plan funding ratio deteriorates and crosses the regulatory minimum. This paper is the first to analyze market - consistent valuation of option - adjusted pension liabilities in a contingent claim framework whereby a knock - out barrier framework is built into the model in order to capture early closure of a pension plan. We mainly investigate two cases which we call 'immediate closure procedure' and 'delayed closure procedure'. In an immediate closure procedure, when the assets value hits the regulatory boundary, the pension plan is terminated immediately. Whereas in a delayed closure procedure, a grace period is given to the pension fund for reorganization and recovery and only an underfunding longer than a certain period leads to premature closure. The framework is then used to analyze fair pension deals.

Keywords: pension funds, DB and DC pension plans, barrier options, Parisian barrier options

JEL Classification: G11, G23