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

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

    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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    File URL: http://www.stern.nyu.edu/fin/workpapers/papers99/wpa99042.pdf
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    Bibliographic Info

    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
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    Handle: RePEc:fth:nystfi:99-042

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    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
    Web page: http://w4.stern.nyu.edu/finance/
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    References

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    1. John Y. Campbell, 1995. "Some Lessons from the Yield Curve," Harvard Institute of Economic Research Working Papers 1713, Harvard - Institute of Economic Research.
    2. 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.
    3. David A. Chapman & Neil D. Pearson, 1998. "Is the Short Rate Drift Actually Nonlinear?," Finance 9808005, EconWPA.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
    10. Fama, Eugene F., 1986. "Term premiums and default premiums in money markets," Journal of Financial Economics, Elsevier, vol. 17(1), pages 175-196, September.
    11. John Y. Campbell & Robert J. Shiller, 1991. "Yield Spreads and Interest Rate Movements: A Bird's Eye View," NBER Working Papers 3153, National Bureau of Economic Research, Inc.
    12. Darrell Duffie & Rui Kan, 1996. "A Yield-Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406.
    13. 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.
    14. Yacine Ait-Sahalia, 1995. "Nonparametric Pricing of Interest Rate Derivative Securities," NBER Working Papers 5345, National Bureau of Economic Research, Inc.
    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. 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.
    17. 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.
    18. 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.
    19. 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.
    20. 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.
    21. 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.
    22. 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.
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    Cited by:
    1. 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.
    2. D H Kim, 2005. "Nonlinearity in the Term Structure," Centre for Growth and Business Cycle Research Discussion Paper Series 51, Economics, The Univeristy of Manchester.

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