Analisis Perbandingan Premi Asuransi Jiwa Berjangka Model Diskrit dan Kontinu dengan Suku Bunga CIR

Abstract

This study aims to analyze and compare the calculation of the net single premium of term life insurance using the discrete and continuous model approaches with the Cox-Ingersoll-Ross (CIR) stochastic interest rate. The data used are the BI Rate interest rate for the period January 2022 to February 2026, as well as the 2023 Indonesian Population Mortality Table (TMPI) for the female category. The CIR model parameter estimation was carried out using the Ordinary Least Squares (OLS) method. The estimation results show that the model has mean reversion characteristics with a long-term average of 0.05 (5%) and a variance of 0.0000002, which indicates relatively stable interest rate fluctuations. The interest rate rate (force of interest) is obtained at δ = 0.036025. Furthermore, the model is used to calculate the discount factor and premium. The calculation results show that the net single premium with the discrete approach is Rp 911,088.22, smaller than the continuous approach of Rp 927,703.73. This difference is due to the timing of benefit payments. The discrete model assumes payment at the end of the year of death, while the continuous model assumes payment at the time of death. Therefore, the continuous approach yields a greater present value of future benefits. This study shows that the choice of premium model and interest rate assumptions significantly influence premium amounts.