COMPARATIVE ANALYSIS OF UNFUNDED ACTUARIAL LIABILITY BASED ON HULL–WHITE INTEREST RATE ESTIMATION USING ORDINARY LEAST SQUARES AND JACKKNIFE - Mahrani, Dwi; Alfarizi , Mhd Rayhan Jovely; Wulandari , Winda (Parameter: Journal of Statistics, 2025)
Pension programs are designed to provide financial security after retirement, requiring accurate actuarial valuation to ensure funding adequacy. A key determinant of actuarial liabilities is the interest rate assumption, which directly affects the present value of future pension obligations and the level of unfunded actuarial liability (UAL). Despite its importance, most pension valuation studies rely on deterministic interest rates, while empirical evidence on the use of stochastic interest rate models combined with robust parameter estimation techniques remains limited. This study addresses this gap by evaluating actuarial liability adequacy using the Frozen Initial Liability (FIL) method under a stochastic interest rate framework. The Hull–White one-factor model is employed to capture the dynamic behavior of interest rates, with parameters estimated using Ordinary Least Squares (OLS) and the Jackknife method. The Jackknife approach is introduced to improve estimation robustness, particularly in the presence of small samples and influential observations. Empirical results show that the Jackknife method produces an average interest rate of 0.0678 with a Mean Absolute Percentage Error (MAPE) of 24.4%, while OLS yields an average rate of 0.0665 with a MAPE of 26.1%. Both approaches result in negative UAL values, indicating a fully funded pension scheme with a surplus position. However, the surplus obtained under the Jackknife estimation is lower despite the higher interest rate estimate, suggesting an inverse relationship between interest rates and surplus levels within the FIL framework.