The Valuation of TIPS with an Analytical Two-Factor Cox-Ingersoll-Ross Term Structure Model with Correlated Factors

Abstract

In this paper, we study Treasury Inflation Protection Securities (TIPS) with an analytical two-factor Cox-Ingersoll-Ross (CIR) model with correlated real rate and inflation. The analytical formula facilitates the estimation of the model parameters and improves the accuracy of the valuation of TIPS, and especially enables us to estimate the inflation risk premium from bond prices. We use the two-factor model to evaluate the inflation-index bonds and study the relationship between the real rate and the expected inflation rate implied in nominal CMT rates for the period of January 1999 through December 2003. We use the Unscented Kalman Filter (UKF) to estimate the model and the inflation risk premium. Our results indicate that the expected inflation rate is quite stable, especially for the long-term bond. The average inflation risk premia range from 0.07 to 99.65 basis points for different maturity bonds.