Comparison of Projected Unit Credit and Entry Age Normal Methods in Pension Fund Vasicek and Cox-Ingersoll-Ross Models

Abstract

The pension program is one of the pension fund's efforts to anticipate the risks that will be experienced by participants in old age. Actuarial calculations help to determine the benefits that participants will receive by considering life chances, interest rates, age when becoming a participant, and normal retirement age. This study aims to determine normal contributions and actuarial liabilities with the Projected Unit Credit and Entry Age Normal methods using stochastic interest rates, namely Vasicek and Cox-Ingersoll-Ross (CIR). The data used in this study are civil servants who work at the Natural Resources Management Office, Bulukumba Regency. The results of the calculation analysis showed that normal cost using the Projected Unit Credit (PUC) method with the Vasicek and Cox-Ingersoll-Ross (CIR) model interest rates increased as the length of service increased, and at the end of the working period the Cox-Ingersoll-Ross (CIR) model interest rate reached Rp14.773.176,- which was higher than Vasicek by Rp3.849.898,-. The results of the calculation of normal cost using the Entry Age Normal (EAN) method with the Vasicek model increase in the period 0-20 years of service, then decrease towards the contribution value at the beginning of the service period of Rp1.499.725,-. At the beginning of the working year, the normal cost using the Entry Age Normal method with the Cox-Ingersoll-Ross (CIR) model interest rate is Rp7.581.593,- then decreases for 24 years of service to Rp5.849.854,- after which it increases again towards the initial contribution value of the working year. The results of the calculation of actuarial liabilities show an increase as the length of service increases, for the Entry Age Normal (EAN) and Projected Unit Credit (PUC) methods with the Cox-Ingersoll-Ross (CIR) interest rate model at the end of the service period, it is found that both are the same value, namely Rp443.195.285,-. By using the Vasicek interest rate model for both methods, the same result is obtained at the end of the service period of Rp115.496.951,-. This shows that the actuarial liabilities for both methods used are affected by interest rates, and the Cox-Ingersoll-Ross (CIR) model is higher than Vasicek