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Estimating real and nominal term structures using treasury yields, inflation, inflation forecasts, and inflation swap rates

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Author Info
Joseph G. Haubrich
George Pennacchi
Peter Ritchken

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Abstract

This paper develops and estimates an equilibrium model of the term structures of nominal and real interest rates. The term structures are driven by state variables that include the short term real interest rate, expected inflation, a factor that models the changing level to which inflation is expected to revert, as well as four volatility factors that follow GARCH processes. We derive analytical solutions for the prices of nominal bonds, inflation-indexed bonds that have an indexation lag, the term structure of expected inflation, and inflation swap rates. The model parameters are estimated using data on nominal Treasury yields, survey forecasts of inflation, and inflation swap rates. We find that allowing for GARCH effects is particularly important for real interest rate and expected inflation processes, but that long–horizon real and inflation risk premia are relatively stable. Comparing our model prices of inflation-indexed bonds to those of Treasury Inflation Protected Securities (TIPS) suggests that TIPS were underpriced prior to 2004 but subsequently were valued fairly. We find that unexpected increases in both short run and longer run inflation implied by our model have a negative impact on stock market returns.

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Paper provided by Federal Reserve Bank of Cleveland in its series Working Paper with number 0810.

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Date of creation: 2008
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Handle: RePEc:fip:fedcwp:0810

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Keywords: Interest rates ; Inflation (Finance) ; Asset pricing;

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. John Y. Campbell & Adi Sunderam & Luis M. Viceira, 2009. "Inflation Bets or Deflation Hedges? The Changing Risks of Nominal Bonds," NBER Working Papers 14701, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  2. Buraschi, Andrea & Jiltsov, Alexei, 2005. "Inflation risk premia and the expectations hypothesis," Journal of Financial Economics, Elsevier, vol. 75(2), pages 429-490, February. [Downloadable!] (restricted)
  3. Dean Croushore, 1993. "Introducing: the survey of professional forecasters," Business Review, Federal Reserve Bank of Philadelphia, issue Nov, pages 3-15. [Downloadable!]
  4. Andrew Ang & Geert Bekaert & Min Wei, 2008. "The Term Structure of Real Rates and Expected Inflation," Journal of Finance, American Finance Association, vol. 63(2), pages 797-849, 04. [Downloadable!] (restricted)
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  5. Boyle, Phelim P., 1977. "Options: A Monte Carlo approach," Journal of Financial Economics, Elsevier, vol. 4(3), pages 323-338, May. [Downloadable!] (restricted)
  6. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March. [Downloadable!] (restricted)
  7. Refet S. Gürkaynak & Brian Sack & Jonathan H. Wright, 2008. "The TIPS yield curve and inflation compensation," Finance and Economics Discussion Series 2008-05, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  8. Haubrich, Joseph G & Ritter, Joseph A, 2000. "Dynamic Commitment and Incomplete Policy Rules," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 32(4), pages 766-84, November.
  9. Benninga, Simon & Protopapadakis, Aris, 1983. "Real and Nominal Interest Rates under Uncertainty: The Fisher Theorem and the Term Structure," Journal of Political Economy, University of Chicago Press, vol. 91(5), pages 856-67, October. [Downloadable!] (restricted)
  10. Pierluigi Balduzzi & Sanjiv Ranjan Das & Silverio Foresi, 1998. "The Central Tendency: A Second Factor In Bond Yields," The Review of Economics and Statistics, MIT Press, vol. 80(1), pages 62-72, February. [Downloadable!] (restricted)
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  11. Michael D. Bordo & Joseph G Haubrich, 2004. "The Yield Curve, Recessions and the Credibility of the Monetary Regime: Long Run Evidence 1875-1997," NBER Working Papers 10431, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  12. Jarrow, Robert & Yildirim, Yildiray, 2003. "Pricing Treasury Inflation Protected Securities and Related Derivatives using an HJM Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 38(02), pages 337-358, June. [Downloadable!]
  13. Qiang Dai & Kenneth J. Singleton, 2000. "Specification Analysis of Affine Term Structure Models," Journal of Finance, American Finance Association, vol. 55(5), pages 1943-1978, October. [Downloadable!] (restricted)
  14. Ang, Andrew & Bekaert, Geert & Wei, Min, 2007. "Do macro variables, asset markets, or surveys forecast inflation better?," Journal of Monetary Economics, Elsevier, vol. 54(4), pages 1163-1212, May. [Downloadable!] (restricted)
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  15. Tobias Adrian & Hao Wu, 2009. "The term structure of inflation expectations," Staff Reports 362, Federal Reserve Bank of New York. [Downloadable!]
  16. Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 9(2), pages 385-426. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. John Y. Campbell & Robert J. Shiller & Luis M. Viceira, 2009. "Understanding Inflation-Indexed Bond Markets," NBER Working Papers 15014, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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