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

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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))

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    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.

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    File URL: http://www.imes.boj.or.jp/research/papers/english/12-E-08.pdf
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    Bibliographic Info

    Paper provided by Institute for Monetary and Economic Studies, Bank of Japan in its series IMES Discussion Paper Series with number 12-E-08.

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    Date of creation: Jun 2012
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    Handle: RePEc:ime:imedps:12-e-08

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    Related research

    Keywords: affine term structure model; quadratic Gaussian term structure model; mixture of normal distributions; unscented Kalman filter; maximum likelihood method;

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    1. Markus Leippold & Liuren Wu, 2002. "Design and Estimation of Quadratic Term Structure Models," Finance 0207014, EconWPA.
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