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Gaussian Estimation of Continuous Time Models of the Short Term Interest Rate

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Author Info
Jun Yu (University of Auckland)
Peter C.B. Phillips () (Cowles Foundation, Yale University)

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Abstract

This paper proposes a Gaussian estimator for nonlinear continuous time models of the short term interest rate. The approach is based on a stopping time argument that produces a normalizing transformation facilitating the use of a Gaussian likelihood. A Monte Carlo study shows that the finite sample performance of the proposed procedure offers an improvement over the discrete approximation method proposed by Nowman (1997). An empirical application to U.S. and British interest rates is given.

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File URL: http://cowles.econ.yale.edu/P/cd/d13a/d1309.pdf
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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1309.

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Length: 22 pages
Date of creation: Jul 2001
Date of revision:
Publication status: Published in Econometrics Journal (December 2001), 4(2): 211-225
Handle: RePEc:cwl:cwldpp:1309

Note: CFP 1124
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Related research
Keywords: Gaussian estimation; nonlinear diffusion; normalizing transformation;

Find related papers by JEL classification:
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing

This paper has been announced in the following NEP Reports:

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Chan, K C, et al, 1992. " An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-27, July. [Downloadable!] (restricted)
  2. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November. [Downloadable!] (restricted)
  3. Yacine Aït-Sahalia, 1999. "Transition Densities for Interest Rate and Other Nonlinear Diffusions," Journal of Finance, American Finance Association, vol. 54(4), pages 1361-1395, 08. [Downloadable!] (restricted)
  4. 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. [Downloadable!]
  5. Pritsker, Matt, 1998. "Nonparametric Density Estimation and Tests of Continuous Time Interest Rate Models," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 11(3), pages 449-87.
  6. Duffie, Darrell & Singleton, Kenneth J, 1993. "Simulated Moments Estimation of Markov Models of Asset Prices," Econometrica, Econometric Society, vol. 61(4), pages 929-52, July. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
  8. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring. [Downloadable!] (restricted)
  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, 02. [Downloadable!] (restricted)
  10. 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. [Downloadable!] (restricted)
  11. Nowman, K B, 1997. " Gaussian Estimation of Single-Factor Continuous Time Models of the Term Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 52(4), pages 1695-1706, September. [Downloadable!] (restricted)
  12. Andrews, Donald W K, 1993. "Exactly Median-Unbiased Estimation of First Order Autoregressive/Unit Root Models," Econometrica, Econometric Society, vol. 61(1), pages 139-65, January. [Downloadable!] (restricted)
  13. Bergstrom, A.R., 1984. "Continuous time stochastic models and issues of aggregation over time," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 20, pages 1145-1212 Elsevier. [Downloadable!] (restricted)
  14. David A. Chapman & Neil D. Pearson, 1998. "Is the Short Rate Drift Actually Nonlinear?," Finance 9808005, EconWPA. [Downloadable!]
  15. Babbs, Simon H. & Nowman, K. Ben, 1999. "Kalman Filtering of Generalized Vasicek Term Structure Models," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(01), pages 115-130, March. [Downloadable!]
  16. 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, Oxford University Press for Society for Financial Studies, vol. 5(4), pages 613-36. [Downloadable!] (restricted)
  17. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1980. " An Analysis of Variable Rate Loan Contracts," Journal of Finance, American Finance Association, vol. 35(2), pages 389-403, May. [Downloadable!] (restricted)
  18. Bergstrom, Albert Rex, 1983. "Gaussian Estimation of Structural Parameters in Higher Order Continuous Time Dynamic Models," Econometrica, Econometric Society, vol. 51(1), pages 117-52, January. [Downloadable!] (restricted)
  19. Brennan, Michael J. & Schwartz, Eduardo S., 1980. "Analyzing Convertible Bonds," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 15(04), pages 907-929, November. [Downloadable!]
  20. Yacine Ait-Sahalia, 2002. "Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-form Approximation Approach," Econometrica, Econometric Society, vol. 70(1), pages 223-262, January. [Downloadable!] (restricted)
  21. Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 9(2), pages 385-426. [Downloadable!] (restricted)
    Other versions:
  22. 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. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Terence D.Agbeyegbe & Elena Goldman, 2005. "Estimation of threshold time series models using efficient jump MCMC," Hunter College Department of Economics Working Papers 406, Hunter College: Department of Economics, revised 2005. [Downloadable!]
  2. Ingrid Lo, 2005. "An Evaluation of MLE in a Model of the Nonlinear Continuous-Time Short-Term Interest Rate," Working Papers 05-45, Bank of Canada. [Downloadable!]
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