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

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  • Jacob Boudoukh
  • Matthew Richardson
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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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    Bibliographic Info

    Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 7213.

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    Date of creation: Jul 1999
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    Handle: RePEc:nbr:nberwo:7213

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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. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-60, May.
    3. 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.
    4. Campbell, John, 1995. "Some Lessons from the Yield Curve," Scholarly Articles 3163264, Harvard University Department of Economics.
    5. 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.
    6. 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.
    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. Torben G. Andersen & Luca Benzoni, 2009. "Stochastic volatility," Working Paper Series WP-09-04, Federal Reserve Bank of Chicago.
    9. 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.
    10. 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.
    11. Campbell, John Y & Shiller, Robert J, 1991. "Yield Spreads and Interest Rate Movements: A Bird's Eye View," Review of Economic Studies, Wiley Blackwell, vol. 58(3), pages 495-514, May.
    12. 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.
    13. 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.
    14. 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.
    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. 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.
    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. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
    19. Fama, Eugene F., 1986. "Term premiums and default premiums in money markets," Journal of Financial Economics, Elsevier, vol. 17(1), pages 175-196, September.
    20. Darrell Duffie & Rui Kan, 1996. "A Yield-Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406.
    21. 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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    Cited by:
    1. 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.
    2. 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.

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