The Value of Guarantees on Pension Fund Returns

Contingent claims analysis is used to value government guarantees associ-ated with defined contribution pension plans. Values are derived for two types of guarantees on the rate of return earned by an individual pension fund: a guarantee of a fixed minimum rate of return and a guarantee of a minimum rate of return that is set relative to the performance of other pen-sion funds. The value of a minimum pension benefit guarantee for a par-ticipant in a mandatory defined contribution pension plan is also derived. Values for each of these guarantees are illustrated using typical parameter values. Martingale pricing theory provides a unifying framework for valu-ing these guarantees by either an explicit formula or numeric computation using a Monte Carlo simulation. Social Security reform has been a serious concern to many countries. In Latin America, a number of reforms have been implemented by partially or fully privatizing pen-sion obligations. Proposals to reform the United States Social Security system have also included privatization features.1 Most often, these privatization reforms have encouraged or required that individuals switch from a government-run defined ben-efit pension plan to a privately run defined contribution system. A potential obstacle George G. Pennacchi is Professor of Finance, Department of Finance, at the University of Illinois. A non-technical description of this research as well as a review of defined benefit pension guarantees is presented in “Government Guarantees for Old Age Income, ” Chapter