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Design and Estimation of a Quadratic Term Structure Model with a Mixture of Normal Distributions

Author

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  • Kentaro Kikuchi

    (Deputy Director and Economist, Institute for Monetary and Economic Studies, Bank of Japan (E-mail: kentarou.kikuchi@boj.or.jp))

Abstract

To keep yields non-negative in a quadratic Gaussian term structure model (QGTM), the short rate is represented by the quadratic form of the Gaussian state variables. The QGTM is among the most attractive candidate tools for analyzing yield curves for countries with low interest rates. However, the model is unlikely to capture the fat- tailed feature of changes in yields observed in actual bond markets. This study extends the QGTM by introducing state variables whose future distributions follow a mixture of normal distributions. This extension allows our model to accommodate vast changes in non-negative yields. As an illustrative empirical study, we applied our model to Japanese government bond (JGB) yields using the unscented Kalman filter. We then used the parameters obtained to investigate market views on past JGB interest rates by simulating future interest rate probability distributions under the physical measure and by decomposing interest rates into expected short rates and term premia.

Suggested Citation

  • Kentaro Kikuchi, 2012. "Design and Estimation of a Quadratic Term Structure Model with a Mixture of Normal Distributions," IMES Discussion Paper Series 12-E-08, Institute for Monetary and Economic Studies, Bank of Japan.
    • Handle: RePEc:ime:imedps:12-e-08
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    File URL: http://www.imes.boj.or.jp/research/papers/english/12-E-08.pdf
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    References listed on IDEAS

    as
    1. Dong-Hyun Ahn & Robert F. Dittmar, 2002. "Quadratic Term Structure Models: Theory and Evidence," The Review of Financial Studies, Society for Financial Studies, vol. 15(1), pages 243-288, March.
    2. McCulloch, J Huston, 1975. "The Tax-Adjusted Yield Curve," Journal of Finance, American Finance Association, vol. 30(3), pages 811-830, June.
    3. Qiang Dai & Kenneth J. Singleton, 2000. "Specification Analysis of Affine Term Structure Models," Journal of Finance, American Finance Association, vol. 55(5), pages 1943-1978, October.
    4. Markus Leippold & Liuren Wu, 2003. "Design and Estimation of Quadratic Term Structure Models," Review of Finance, European Finance Association, vol. 7(1), pages 47-73.
    5. Nyholm, Ken & Vidova-Koleva, Rositsa, 2010. "Nelson-Siegel, affine and quadratic yield curve specifications: which one is better at forecasting?," Working Paper Series 1205, European Central Bank.
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    Cited by:

    1. Kei Imakubo & Jouchi Nakajima, 2015. "Estimating inflation risk premia from nominal and real yield curves using a shadow-rate model," Bank of Japan Working Paper Series 15-E-1, Bank of Japan.
    2. Hibiki Ichiue & Yoichi Ueno, 2013. "Estimating Term Premia at the Zero Bound: An Analysis of Japanese, US, and UK Yields," Bank of Japan Working Paper Series 13-E-8, Bank of Japan.

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    More about this item

    Keywords

    affine term structure model; quadratic Gaussian term structure model; mixture of normal distributions; unscented Kalman filter; maximum likelihood method;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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