長期低利率造成利率模型評價之偏誤—以退休基金之利率模型為例

Abstract

退休基金在配置資產時須遵守投資政策，僅有在基金資產價值大於基金負債價值時才可投資於風險性資產，因此基金負債價值評估的準確性相當重要，若誤差過大將影響基金的投資成效。而基金負債價值估計與退休基金使用的利率模型相關，一般常見的利率模型為Vasicek模型，此模型假設利率以長期平均利率為基準，呈現常態分布，但此假設與現實利率情形不符。現實中存在一個利率下界，當利率低於此數值便不會再下降。過去因為長期平均利率距離利率下界相對較遠，因此產生的誤差小，可以忽略不計算。近年各國長期實施低利率政策，使長期平均利率貼近於零，模型估計出現低於利率下界的負利率，造成嚴重之模型誤差。 本文以利率下界的概念修改Vasicek模型。並以情境分析的方式，選取特定利率走勢，比較不同投資方案對於退休基金投資成效之影響，尋找退休基金最佳的投資方式。

Pension funds have to obey several rules to allocate their fund. They can invest in risky asset only if their portfolio value is larger than pension fund’s liability value. Therefore the accuracy of pension fund’s liability estimating is very important which is decided by interest rate model. One of common interest rate model of pension fund is Vasicek model, which describes interest rate movements as a normal distribution’s randomness jump basing on its long term mean level. However this didn’t consist with historical data. In real market, there exists a lower bound which means interest rate cannot lower than it. In the past, the long term mean level of Vasicek model is far away from lower bound thus the modeling error is negligible. But the low interest rate environments caused by governments’ monetary policy let the long term mean level of Vasicek model close to zero and negative rate appears which is lower than lower bound, causing undesired modeling error. In this paper, we modified Vasicek model by the idea of the lower bound and found the best investing method of pension fund by analyzing the performance of pension fund’s portfolio under certain rate path situation.