IDEAS home Printed from
   My bibliography  Save this paper

A Multifactor, Nonlinear, Continuous-Time Model of Interest Rate Volatility


  • Jacob Boudoukh
  • Matthew Richardson
  • Richard Stanton
  • Robert F. Whitelaw


This paper presents a general, nonlinear version of existing multifactor models, such as Longstaff and Schwartz (1992). The novel aspect of our approach is that rather than choosing the model parameterization out of thin air,' our processes are generated from the data using approximation methods for multifactor continuous-time Markov processes. In applying this technique to the short- and long-end of the term structure for a general two-factor diffusion process for interest rates, a major finding is that the volatility of interest rates is increasing in the level of interest rates only for sharply upward sloping term structures. In fact, the slope of the term structure plays a larger role in determining the magnitude of the diffusion coefficient. As an application, we analyze the model's implications for the term structure of term premiums.

Suggested Citation

  • Jacob Boudoukh & Matthew Richardson & Richard Stanton & Robert F. Whitelaw, 1999. "A Multifactor, Nonlinear, Continuous-Time Model of Interest Rate Volatility," NBER Working Papers 7213, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:7213
    Note: AP

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 385-426.
    2. Huizinga, John & Mishkin, Frederic S., 1986. "Monetary policy regime shifts and the unusual behavior of real interest rates," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 24(1), pages 231-274, January.
    3. Fama, Eugene F., 1986. "Term premiums and default premiums in money markets," Journal of Financial Economics, Elsevier, vol. 17(1), pages 175-196, September.
    4. John Y. Campbell, 1995. "Some Lessons from the Yield Curve," Journal of Economic Perspectives, American Economic Association, vol. 9(3), pages 129-152, Summer.
    5. Jacob Boudoukh & Matthew Richardson & Tom Smith & Robert F. Whitelaw, 1999. "Ex Ante Bond Returns and the Liquidity Preference Hypothesis," Journal of Finance, American Finance Association, vol. 54(3), pages 1153-1167, June.
    6. Hansen, Lars Peter & Scheinkman, Jose Alexandre, 1995. "Back to the Future: Generating Moment Implications for Continuous-Time Markov Processes," Econometrica, Econometric Society, vol. 63(4), pages 767-804, July.
    7. Chen, Ren-Raw & Scott, Louis O, 1992. "Pricing Interest Rate Options in a Two-Factor Cox-Ingersoll-Ross Model of the Term Structure," Review of Financial Studies, Society for Financial Studies, vol. 5(4), pages 613-636.
    8. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters,in: Theory Of Valuation, chapter 5, pages 129-164 World Scientific Publishing Co. Pte. Ltd..
    9. David A. Chapman & Neil D. Pearson, 2000. "Is the Short Rate Drift Actually Nonlinear?," Journal of Finance, American Finance Association, vol. 55(1), pages 355-388, February.
    10. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
    11. Brenner, Robin J. & Harjes, Richard H. & Kroner, Kenneth F., 1996. "Another Look at Models of the Short-Term Interest Rate," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 31(01), pages 85-107, March.
    12. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-560, May.
    13. Torben G. Andersen & Luca Benzoni, 2009. "Stochastic volatility," Working Paper Series WP-09-04, Federal Reserve Bank of Chicago.
    14. Ball, Clifford A. & Torous, Walter N., 1995. "Regime Shifts in Short Term Riskless Interest Rates," University of California at Los Angeles, Anderson Graduate School of Management qt5hs021jf, Anderson Graduate School of Management, UCLA.
    15. Schaefer, Stephen M. & Schwartz, Eduardo S., 1984. "A Two-Factor Model of the Term Structure: An Approximate Analytical Solution," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 19(04), pages 413-424, December.
    16. John Y. Campbell & Robert J. Shiller, 1991. "Yield Spreads and Interest Rate Movements: A Bird's Eye View," Review of Economic Studies, Oxford University Press, vol. 58(3), pages 495-514.
    17. 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.
    18. Sanders, Anthony B. & Unal, Haluk, 1988. "On the Intertemporal Behavior of the Short-Term Rate of Interest," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 23(04), pages 417-423, December.
    19. Brown, Stephen J & Dybvig, Philip H, 1986. " The Empirical Implications of the Cox, Ingersoll, Ross Theory of the Term Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 41(3), pages 617-630, July.
    20. Stambaugh, Robert F., 1988. "The information in forward rates : Implications for models of the term structure," Journal of Financial Economics, Elsevier, vol. 21(1), pages 41-70, May.
    21. Darrell Duffie & Rui Kan, 1996. "A Yield-Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406.
    22. 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.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. repec:wsi:qjfxxx:v:01:y:2011:i:03:n:s2010139211000146 is not listed on IDEAS
    2. Ang, Andrew & Bekaert, Geert, 2002. "Short rate nonlinearities and regime switches," Journal of Economic Dynamics and Control, Elsevier, vol. 26(7-8), pages 1243-1274, July.
    3. John Knight & Fuchun Li & Mingwei Yuan, 2006. "A Semiparametric Two-Factor Term Structure Model," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(2), pages 204-237.

    More about this item

    JEL classification:

    • G00 - Financial Economics - - General - - - General

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:nbr:nberwo:7213. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.