Pricing inflation-linked bonds

Abstract

This paper proposes a pricing model for inflation-linked bonds. Our proposal is developed starting from a Vasicek model of the instantaneous inflation rate process and the Cox, Ingersoll and Ross model for the nominal instantaneous risk-free interest rate process. Instead of adopting the standard approach of a cross-section estimation of the term structure of real interest rates, this work proposes a pricing model based on estimation of the inflation risk premium. The model is applied to Treasury Inflation Protected Securities, which are inflation-linked bonds issued by the U.S. Department of the Treasury. Empirical validation is carried out on data for the period 1999–2005.

Keywords:

• Interest rates
• Inflation-linked bonds
• Continuous time stochastic models
• Inflation rates
• Treasury Inflation Protected Securities

Acknowledgements

We are grateful to Professor Paris for his original idea concerning this work. His example of strength with untold suffering is evidence that everything in our life is pure gift. We would like to thank the two anonymous referees for their helpful comments on a previous version of this work.

Notes

† Note that, in our framework, r(t) has zero credit risk, while it can be subject both to inflation and interest rate risks.

† The correlation between the new Brownian motions is equal to the old one, i.e. , as clearly pointed out by Joshi (2003, p. 248).

‡ If t falls in the first half of month m, generally IE _m−1 has not yet been published; therefore, t′ represents the end of month m. If t falls in the second half of month m, generally IE _m−1 is known and t′ represents the end of month m + 1.

§ The result follows immediately from d, which can also be written as d. Substituting by , we obtain d which represents a stochastic differential equation à la CIR. The results from the estimation and pricing of stochastic zero coupon bonds based on can be used in the case of by making the substitutions mentioned in the main text.

† See Glasserman (2003, pp. 121–123).

† The approximation is feasible because the diffusion term, σ _i , is constant and the drift term, α[β − i(t)], is linear in i(t).

† The sample mean of month m, , is needed for the estimation of parameters a and b of the nominal interest rate process. Its value was calculated every month over a fixed window of N = 12 months, rather than from January 1979.