Financial Valuation of Early Retirement Benefit in a Defined Benefit Pension Plan

Abstract

American options can be exercised at any time the holder wishes to do so before its expiry date. It therefore, becomes important to know when this option should be exercised to maximize gain. The study considers one pricing formulation of American options, namely, the optimal stopping formulation as an equivalence of a free-boundary problem. An optimal stopping problem on perpetual American put option was formulated and its solutions found. The solutions were analysed systematically by applying matching value condition, smooth pasting condition, asset equilibrium condition and the boundary condition. We used the free-boundary approach to derive the solution. The result compares favourably with that of [2]). We recommend application of the model by individuals wanting to exercise early retirement option.