Financial Evaluation of Early Retirement Benefit in A Defined Benefit Plan

Abstract

American options can be exercised at anytime 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.