Contingent Claims Valuation of "Greater of" Benefits

Pension funds are usually either defined benefit or defined contribution funds. In Australia in recent years, for a number of reasons, some pension funds have offered the "greater of these two benefits. Such a benefit design can be valued using contingent claims valuation techniques since it is equivalent to an option on the maximum of two random benefit amounts - one equal to a multiple of salary and the other the accumulation of a percentage of salary at an earings rate. This paper overviews some of the issues in applying contingent claims valuation techniques to the valuation of this style of benefit including: - incorporation of decrements, - the dependence of the accumulation benefit on the two stochastic state variables, salary and fund earnings rate and the resulting path- dependency, - the numerical techniques for efficient calculation of benefit values including discrete lattice models, finite difference techniques, simulation and approximations based on bivariate log-normal assumption, the lack of traded assets to price salary risk and implications for valuation. Numerical evaluation of benefit values and the assessment of computational efficiency of alternative techniques is the next stage of this research.