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Empirical tests of two state-variable HJM models

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  • Robert R. Bliss
  • Peter H. Ritchken

Abstract

Models for pricing interest rate claims, developed under the Heath-Jarrow-Morton paradigm, differ according to the volatility structure imposed on forward rates. For most general HJM structures the resultant path dependence creates implementation problems. Ritchken and Sankarasubramanian have recently identified necessary and sufficient conditions on the class of volatility structures of forward rates that enable the term structure dynamics to be captured by a finite set of state variables. The class is quite rich. The instantaneous spot rate volatility may be quite general, but the model curtails the structure of forward rate volatilities relative to this spot rate volatility. This paper provides empirical tests for this class of volatility structures. Unlike other studies, the volatility structure is examined over the a broad section of maturities in the yield curve. Using Treasury data over the period 1982-1994, we find support for this class. Furthermore, unlike other studies, no evidence of a \"volatility\" hump is identified.

Suggested Citation

  • Robert R. Bliss & Peter H. Ritchken, 1995. "Empirical tests of two state-variable HJM models," FRB Atlanta Working Paper 95-13, Federal Reserve Bank of Atlanta.
    • Handle: RePEc:fip:fedawp:95-13
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    References listed on IDEAS

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    1. Ho, Thomas S Y & Lee, Sang-bin, 1986. "Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-1029, December.
    2. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    3. Li, Anlong & Ritchken, Peter & Sankarasubramanian, L, 1995. "Lattice Models for Pricing American Interest Rate Claims," Journal of Finance, American Finance Association, vol. 50(2), pages 719-737, June.
    4. Dothan, L. Uri, 1978. "On the term structure of interest rates," Journal of Financial Economics, Elsevier, vol. 6(1), pages 59-69, March.
    5. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-384, March.
    6. Heath, David & Jarrow, Robert & Morton, Andrew, 1990. "Bond Pricing and the Term Structure of Interest Rates: A Discrete Time Approximation," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(4), pages 419-440, December.
    7. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    8. Robert A. Jarrow & Arkadev Chatterjea, 2019. "Interest Rates," World Scientific Book Chapters, in: An Introduction to Derivative Securities, Financial Markets, and Risk Management, chapter 2, pages 22-52, World Scientific Publishing Co. Pte. Ltd..
    9. Peter Ritchken & L. Sankarasubramanian, 1995. "Volatility Structures Of Forward Rates And The Dynamics Of The Term Structure1," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 55-72, January.
    10. Brennan, Michael J. & Schwartz, Eduardo S., 1979. "A continuous time approach to the pricing of bonds," Journal of Banking & Finance, Elsevier, vol. 3(2), pages 133-155, July.
    11. Amin, Kaushik I. & Morton, Andrew J., 1994. "Implied volatility functions in arbitrage-free term structure models," Journal of Financial Economics, Elsevier, vol. 35(2), pages 141-180, April.
    12. Michael J. Brennan and Eduardo S. Schwartz., 1979. "A Continuous-Time Approach to the Pricing of Bonds," Research Program in Finance Working Papers 85, University of California at Berkeley.
    13. Longstaff, Francis A & Schwartz, Eduardo S, 1992. "Interest Rate Volatility and the Term Structure: A Two-Factor General Equilibrium Model," Journal of Finance, American Finance Association, vol. 47(4), pages 1259-1282, September.
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