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

Chen, F. Y., Yang, S. S., and Huang, H. C. 2019. Effect of Inflation on the Cost of Inflation-Linked Annuities Considering Stochastic Interest Rate and Inflation Rate Models. NTU Management Review, 29 (2): 29-60. doi:10.6226/NTUMR.201908_29(2).0002

Fen-Ying Chen, Department of Finance, Shih Hsin University
Sharon S. Yang, Department of Finance, National Central University
Hong-Chih Huang, Department of Risk Management and Insurance, National Chengchi University

Abstract

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. 


Keywords

inflation-linked annuityinterest rate riskinflation riskforward interest rate model


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