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The Use of the Black Model of Interest Rates as Options for Monitoring the JGB Market Expectations

September 2006
Yoichi Ueno*1
Naohiko Baba*2
Yuji Sakurai*3

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Abstract

This paper analyzes the Japanese government bond (JGB) yield curve using the Black-Gorovoi-Linetsky (BGL) model of interest rates as options with a view to monitoring the JGB market expectations about the Bank of Japan's (BOJ) zero interest rate policy (ZIRP). Main findings are as follows. First, overall fitting performance of the BGL model is much better than that of the original Vasicek model in our sample period from the start of the quantitative monetary easing policy on March 19, 2001 through the end of the ZIRP on July 14, 2006. Second, the shadow interest rate is estimated to be negative throughout the period and rise toward zero quite recently. Third, the first hitting time until the negative shadow interest rate first hits zero shows a very good performance in predicting the ending time of the ZIRP with an error of only about one month. Fourth, the estimated probability density function of the first hitting time shows that the JGB market expectations rapidly converge to the mode value as the ending time of the ZIRP approaches.JEL Classification: E43, E44, E52, G12

Key Words:
Term Structure of Interest Rates, Zero Lower Bound, Options Approach, Shadow Interest Rate, First Hitting Time

The authors are grateful to the participants of the conferences held at the Bank of Japan and the European Central Bank for invaluable comments and suggestions, particularly to the two discussants, David Longworth and Anthony Richards, as well as Christine Cumming, Kazumasa Iwata, Don Kim, Manfred Kremer, Ken Kuttner, Kiyohiko Nishimura, Frank Packer, Marcello Pericoli, Glenn Rudebusch, and Masaaki Shirakawa, among others. The authors also greatly benefited from discussions with Ken Singleton, Vadim Linetsky, and the staff members of the Bank of Japan. The views expressed in this paper are solely ours, and do not necessarily reflect the official views of the Bank of Japan.

  • *1 Economist, Financial Markets Department, Bank of Japan
    e-mail: youichi.ueno@boj.or.jp
  • *2 Senior Economist and Director, Financial Markets Department and Institute for Monetary and Economic Studies, Bank of Japan
    e-mail: naohiko.baba@boj.or.jp
  • *3 Graduate School of Information Science and Technology, University of Tokyo
    e-mail: yuji_sakurai@mist.i.u-tokyo.ac.jp

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