Valuation of Cash Balance Pension Plans with Hull-White Method

In a pension fund with the cash balance (CB) plan, the pension contributions with a guaranteed rate are accumulated and at retirement the lump sum is paid to the beneficiary of the fund. CB plans are subcategorized in defined benefit (DB) plans. However CB plans have fundamental differences with DB ones. Generally, approaches which are used in valuation of defined benefit plans, are applied to valuation of cash balance plans that are not always suitable. In this article, we consider the benefits of pension CB plans as a financial liability and a derivative of interest rate. Using financial models, we calculate the market consistent value of the liabilities. One and two factors Hall-White model are used for modeling the crediting rate based on zero coupon bond and then an analytical response for market consistent valuation is obtained. The results gained in this approach are compared with two common approaches used in CB plans valuation. We concluded that with use of the market consistent method problems of liabilities underestimation and sharply increase in normal costs are solved. Due to the above observations, market consistent valuation are more suitable for CB plans valuations.