Discussion Paper Series 2012-E-8

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

Kentaro Kikuchi

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.

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

Views expressed in the paper are those of the authors and do not necessarily reflect those of the Bank of Japan or Institute for Monetary and Economic Studies.

Copyright © 2012 Bank of Japan All Rights Reserved.

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