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

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

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    Paper provided by New York University, Leonard N. Stern School of Business- in its series New York University, Leonard N. Stern School Finance Department Working Paper Seires with number 99-042.

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    Date of creation: Jun 1999
    Date of revision:
    Handle: RePEc:fth:nystfi:99-042
    Contact details of provider: Postal: U.S.A.; New York University, Leonard N. Stern School of Business, Department of Economics . 44 West 4th Street. New York, New York 10012-1126
    Phone: (212) 998-0100
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    1. 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.
    2. Yacine Ait-Sahalia, 1995. "Testing Continuous-Time Models of the Spot Interest Rate," NBER Working Papers 5346, National Bureau of Economic Research, Inc.
    3. 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, 06.
    4. Darrell Duffie & Rui Kan, 1996. "A Yield-Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406.
    5. Lars Peter Hansen & Jose Alexandre Scheinkman, 1993. "Back to the Future: Generating Moment Implications for Continuous-Time Markov Processes," NBER Technical Working Papers 0141, National Bureau of Economic Research, Inc.
    6. John Y. Campbell & Robert J. Shiller, 1989. "Yield Spreads and Interest Rate Movements: A Bird's Eye View," NBER Working Papers 3153, National Bureau of Economic Research, Inc.
    7. 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.
    8. John Y. Campbell, 1995. "Some Lessons from the Yield Curve," Harvard Institute of Economic Research Working Papers 1713, Harvard - Institute of Economic Research.
    9. 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 617-30, July.
    10. 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, 02.
    11. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
    12. 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.
    13. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-60, May.
    14. 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.
    15. 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 613-36.
    16. 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.
    17. 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.
    18. 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.
    19. Andersen, Torben G. & Lund, Jesper, 1997. "Estimating continuous-time stochastic volatility models of the short-term interest rate," Journal of Econometrics, Elsevier, vol. 77(2), pages 343-377, April.
    20. Fama, Eugene F., 1986. "Term premiums and default premiums in money markets," Journal of Financial Economics, Elsevier, vol. 17(1), pages 175-196, September.
    21. 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.
    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 1259-82, September.
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