考量隨機利率下物價連動保證對退休金制度年金成本評價之分析

Effect of Inflation on the Cost of Inflation-Linked Annuities Considering Stochastic Interest Rate and Inflation Rate Models

為保障退休金給付的實質購買力，提供具有物價連動的年金為常見的設計，然而該設計也會增加退休金制度之年金成本，在年金改革因應財務健全性中也是需了解的因素。本研究的主要目的將分析不同年金設計的成本比較，包括普通年金、與物價連動的年金、具上限型的物價連動年金及具下限型的物價連動年金，並導出一理論解模型，該模型為一般化模型，在特定的參數設定下，可以變成與通貨膨脹無關的年金模型、一般與物價連動的年金模型、上限型的物價連動年金模型、下限型的物價連動年金模型。數值結果得知當上限或下限的門檻值提高，年金的價格大多也隨之增加；波動度的敏感度大致比相關係數的敏感度高，本研究的架構可以提供台灣退休金制度及年金改成本分析的參考。 To protect the real income from retirement pensions against the risk of inflation, developing an annuity model that can be linked to the inflation index is necessary. Although inflation-linked annuities increase the cost of retirement pensions for governments, the risk posed by inflation to retirement annuities must be understood. In this paper, an inflation-linked annuity with a cap and floor model is developed. The model is a general form that can be reduced to special forms such as ordinary annuities, inflationlinked annuities without barriers, inflation-linked annuities with a cap model, and inflation-linked annuities with a floor model. Interest rate risk and inflation risk are considered within the model. Furthermore, we derive a closed-form solution for the model. The valuation framework can benefit annuity providers to understand the cost of inflation-linked annuities. The empirical results indicate that the prices of the annuities with cap and floor generally increase when the cap values increase. In addition, the sensitivities of volatilities are larger than those of the correlation coefficients. The valuation framework can benefit annuity providers to understand the cost of inflationlinked annuities.