IDEAS home Printed from https://ideas.repec.org/p/ime/imedps/12-e-08.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.imes.boj.or.jp/research/papers/english/12-E-08.pdf
    Download Restriction: no
    ---><---

    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sorwar, Ghulam & Barone-Adesi, Giovanni & Allegretto, Walter, 2007. "Valuation of derivatives based on single-factor interest rate models," Global Finance Journal, Elsevier, vol. 18(2), pages 251-269.
    2. Driessen, Joost & Melenberg, Bertrand & Nijman, Theo, 2005. "Testing affine term structure models in case of transaction costs," Journal of Econometrics, Elsevier, vol. 126(1), pages 201-232, May.
    3. Bruno Feunou & Jean-Sébastien Fontaine & Anh Le & Christian Lundblad, 2022. "Tractable Term Structure Models," Management Science, INFORMS, vol. 68(11), pages 8411-8429, November.
    4. Inci, Ahmet Can, 2007. "US-Swiss term structures and exchange rate dynamics," Global Finance Journal, Elsevier, vol. 18(2), pages 270-288.
    5. Peter Feldhütter & Christian Heyerdahl-Larsen & Philipp Illeditsch, 2018. "Risk Premia and Volatilities in a Nonlinear Term Structure Model [Quadratic term structure models: theory and evidence]," Review of Finance, European Finance Association, vol. 22(1), pages 337-380.
    6. Gourieroux, Christian & Sufana, Razvan, 2011. "Discrete time Wishart term structure models," Journal of Economic Dynamics and Control, Elsevier, vol. 35(6), pages 815-824, June.
    7. Peng Cheng & Olivier Scaillet, 2002. "Linear-Quadratic Jump-Diffusion Modeling with Application to Stochastic Volatility," FAME Research Paper Series rp67, International Center for Financial Asset Management and Engineering.
    8. Qiang Dai & Kenneth Singleton, 2003. "Term Structure Dynamics in Theory and Reality," The Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 631-678, July.
    9. Torben G. Andersen & Luca Benzoni, 2010. "Do Bonds Span Volatility Risk in the U.S. Treasury Market? A Specification Test for Affine Term Structure Models," Journal of Finance, American Finance Association, vol. 65(2), pages 603-653, April.
    10. 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.
    11. Jiang, George & Yan, Shu, 2009. "Linear-quadratic term structure models - Toward the understanding of jumps in interest rates," Journal of Banking & Finance, Elsevier, vol. 33(3), pages 473-485, March.
    12. Sanjay K. Nawalkha & Xiaoyang Zhuo, 2022. "A Theory of Equivalent Expectation Measures for Contingent Claim Returns," Journal of Finance, American Finance Association, vol. 77(5), pages 2853-2906, October.
    13. Jordan, James V. & Mansi, Sattar A., 2003. "Term structure estimation from on-the-run Treasuries," Journal of Banking & Finance, Elsevier, vol. 27(8), pages 1487-1509, August.
    14. Realdon, Marco, 2009. ""Extended Black" term structure models," International Review of Financial Analysis, Elsevier, vol. 18(5), pages 232-238, December.
    15. Matsumura, Marco & Moreira, Ajax & Vicente, José, 2011. "Forecasting the yield curve with linear factor models," International Review of Financial Analysis, Elsevier, vol. 20(5), pages 237-243.
    16. Pericoli, Marcello & Taboga, Marco, 2012. "Bond risk premia, macroeconomic fundamentals and the exchange rate," International Review of Economics & Finance, Elsevier, vol. 22(1), pages 42-65.
    17. Huse, Cristian, 2011. "Term structure modelling with observable state variables," Journal of Banking & Finance, Elsevier, vol. 35(12), pages 3240-3252.
    18. H. Bertholon & A. Monfort & F. Pegoraro, 2008. "Econometric Asset Pricing Modelling," Journal of Financial Econometrics, Oxford University Press, vol. 6(4), pages 407-458, Fall.
    19. Marco Realdon, 2006. "Equity Valuation Under Stochastic Interest Rates," Discussion Papers 06/12, Department of Economics, University of York.
    20. Samson Assefa, 2007. "Pricing Swaptions and Credit Default Swaptions in the Quadratic Gaussian Factor Model," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 3-2007, January-A.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ime:imedps:12-e-08. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Kinken (email available below). General contact details of provider: https://edirc.repec.org/data/imegvjp.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.