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An Evaluation of MLE in a Model of the Nonlinear Continuous-Time Short-Term Interest Rate

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  • Ingrid Lo

Abstract

The author compares the performance of three Gaussian approximation methods--by Nowman (1997), Shoji and Ozaki (1998), and Yu and Phillips (2001)--in estimating a model of the nonlinear continuous-time short-term interest rate. She finds that the performance of Nowman's method is similar to that of Shoji and Ozaki's method, whereas the window width used in the Yu and Phillips method has a critical influence on parameter estimates. When a small window width is used, the Yu and Phillips method does not outperform the other two methods. Choosing a suitable window width can reduce estimation bias quite significantly, whereas too large a window width can worsen estimation bias and the fit of the model. An empirical study is implemented using Canadian and U.K. one-month interest rate data.

Suggested Citation

  • Ingrid Lo, 2005. "An Evaluation of MLE in a Model of the Nonlinear Continuous-Time Short-Term Interest Rate," Staff Working Papers 05-45, Bank of Canada.
  • Handle: RePEc:bca:bocawp:05-45
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    References listed on IDEAS

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    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 1209-1227, July.
    2. 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.
    3. Jun Yu & Peter C.B. Phillips, 2001. "Gaussian Estimation of Continuous Time Models of the Short Term Interest Rate," Cowles Foundation Discussion Papers 1309, Cowles Foundation for Research in Economics, Yale University.
    4. 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.
    5. Yacine Aït-Sahalia, 2001. "Transition Densities For Interest Rate And Other Nonlinear Diffusions," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar(Volume II), chapter 1, pages 1-34, World Scientific Publishing Co. Pte. Ltd..
    6. 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: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    7. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    8. 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.
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    Cited by:

    1. Tunaru, Diana, 2017. "Gaussian estimation and forecasting of the U.K. yield curve with multi-factor continuous-time models," International Review of Financial Analysis, Elsevier, vol. 52(C), pages 119-129.

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    More about this item

    Keywords

    Interest rates; Econometric and statistical methods;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • E4 - Macroeconomics and Monetary Economics - - Money and Interest Rates

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