Implementasi Model Suku Bunga Vasicek dan Cox-Ingersoll-Ross pada Perhitungan Dana Pensiun dengan Metode Aggregate Cost

Abstract

Uncertainty in interest rates is a major challenge in the calculation of long-term pension funds. To address this, the present study implements the stochastic interest rate models of Vasicek and Cox-Ingersoll-Ross (CIR) as approaches that realistically represent interest rate dynamics. These models aim to handle interest rate uncertainty influenced by inflation. The data analyzed consist of the Indonesian Mortality Table IV and historical BI-Rate data from January 2015 to December 2024. Parameter estimation for both the Vasicek and CIR models is performed using the Maximum Likelihood Estimation (MLE) method, and it is theoretically proven that the estimators used are unbiased. Long-term interest rate simulations are conducted using the Milstein method. The results show that the Vasicek model produces a Mean Absolute Percentage Error (MAPE) of 14.97%, while the CIR model yields a MAPE of 19.06%. The calculations indicate that applying the Vasicek and CIR models results in higher present values of pension benefits compared to the constant interest rate approach. Moreover, normal contributions for younger participants tend to be lower due to longer working periods. This study concludes that the Vasicek model provides greater accuracy in estimating interest rates for pension fund calculations.