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

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, inflation-linked 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 inflation-linked annuities.