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Pricing Treasury Inflation Protected Securities and Related Derivatives using an HJM Model

Published online by Cambridge University Press:  06 April 2009

Robert Jarrow  and
Yildiray Yildirim
Robert Jarrow
Affiliation:
raj [email protected], Johnson Graduate School of Management, Cornell University, Ithaca, NY 14853 and Kamakura Corporation
Yildiray Yildirim
Affiliation:
[email protected], School of Management, Syracuse University, Syracuse, NY 13244.
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Abstract

This paper uses an HJM model to price TIPS and related derivative securities. First, using the market prices of TIPS and ordinary U.S. Treasury securities, both the real and nominal zero-coupon bond price curves are obtained using standard coupon bond price stripping procedures. Next, a three-factor arbitrage-free term structure model is fit to the time-series evolutions of the CPI-U and the real and nominal zero-coupon bond price curves. Then, using these estimated term structure parameters, the validity of the HJM model for pricing TIPS is confirmed via its hedging performance. Lastly, the usefulness of the pricing model is illustrated by valuing call options on the inflation index.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 38 , Issue 2 , June 2003 , pp. 337 - 358
Copyright
Copyright © School of Business Administration, University of Washington 2003

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References

Adams, K., and Deventer, D.. “Fitting Yield Curves and Forward Rate Curves with Maximum Smoothness.” Journal of Fixed Income, 4 (1994), 52–62.CrossRefGoogle Scholar
Amin, K., and Jarrow, R.. “Pricing Foreign Currency Options under Stochastic Interest Rates.” Journal of International Money and Finance, 10 (1991), 310–329.CrossRefGoogle Scholar
Barnett, V., and Lewis, T.. Outliers in Statistical Data. New York, NY: John Wiley and Sons, Inc. (1978).Google Scholar
Bliss, R. R. “Testing Term Structure Estimation Methods.” Advances in Futures and Options Research, 9 (1996), 197–231.Google Scholar
Brown, S., and P. Dybvig, . “The Empirical Implications of the Cox, Ingersoll, Ross Theory of the Term Structure of Interest Rates.” Journal of Finance, 41 (1986), 617–630.CrossRefGoogle Scholar
Brown, R., and Schaefer, S.. “The Term Structure of Real Interest Rates and the Cox, Ingersoll, and Ross Model.” Journal of Financial Economics, 35 (1994), 4–42.CrossRefGoogle Scholar
Brown, R., and Schaefer, S.. “Ten Years of the Real Term Structure: 1984–1994.” Journal of Fixed Income, 5 (1996), 6–22.CrossRefGoogle Scholar
Durrett, R.Stochastic Calculus. New York, NY: CRC Press (1996).Google Scholar
Elton, E. J.; Gruber, M. J.; Agrawal, D.; and Mann, C.. “Explaining the Rate Spread on Corporate Bonds.” Journal of Finance, 56 (2001), 247–277.CrossRefGoogle Scholar
Frachot, A. “Factor Models of Domestic and Foreign Interest Rates with Stochastic Volatilities.” Mathematical Finance, 5 (1995), 167–185.CrossRefGoogle Scholar
Greene, H. W.Econometric Analysis. New York, NY: Macmillan Publishing Co. (1993).Google Scholar
Gibbons, M., and Ramaswamy, K.. “A Test of the Cox, Ingersoll, and Ross Model of the Term Structure.” Review of Financil Studies, 6 (1993), 619–658.CrossRefGoogle Scholar
Health, D.; Jarrow, R.; and Morton, A.. “Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claim Valuation.” Econometrica. 60 (1992), 77–105.CrossRefGoogle Scholar
Jarrow, R.Modelling Fixed Income Securities and Interest Rate Options, 2nd ed.Palo Alto, CA: Stanford Univ. Press (2002).CrossRefGoogle Scholar
Jarrow, R., and Turnbull, S.. “A Unified Approach for Pricing Contingent Claims on Multiple Term Structures.” Review of Quantitative Finance and Accounting, 10 (1998), 5–19.CrossRefGoogle Scholar
Karatzas, I., and Shreve, S.. Brownian Motion and Stochastic Calculus. New York, NY: Springer-Verlag (1991).Google Scholar
McCulloch, J. H. “Measuring the Term Structure of Interest Rates.” Journal of Business, 19 (1971), 19–31.CrossRefGoogle Scholar
Musiela, M., and Rutkowski, M.. Martingale Methods in Financial Modelling. New York, NY: Springer-Verlag (1997).CrossRefGoogle Scholar
Protter, P.Stochastic Integration and Differential Equations: A New Approach. New York, NY: Springer-Verlag (1990).CrossRefGoogle Scholar
Roll, R. “U.S. Treasury Inflation-Indexed Bonds: The Design of a new Security.” Journal of Fixed Income, 6 (1996), 9–28.CrossRefGoogle Scholar
Shea, G. “Interest Rate Term Structure Estimation with Exponential Splines: A Note.” Journal of Finance, 40 (1985), 319–325.CrossRefGoogle Scholar
Sundaresan, S.Fixed Income Markets and Their Derivatives. Cincinnati, OH: South-Western Publishing (1997).Google Scholar
Vankudre, P., and Lindner, P.. Treasury Inflation-Protection Securities: Opportunities and Risks. New York, NY: Lehman Brothers (1997).Google Scholar
Vasicek, O., and Fong, H.. “Term Structure Modeling Using Exponential Splines.” Journal of Finance, 37 (1982), 339–348.CrossRefGoogle Scholar
Woodward, T. “The Real Thing: A Dynamic Profile of Term Structure of Real Interest Rates and Inflation Expectations in the United Kingdom, 1982–89.” Journal of Business, 63 (1990), 373–398.CrossRefGoogle Scholar