An 8-Factor Heath, Jarrow, and Morton Stochastic Volatility Model for the Japanese Government Bond Yield Curve, Using Daily Data from September 24, 1974 through November 30, 2022

Daniel Dickler, Robert A. Jarrow, Stas Melnikov, Alexandre Telnov, Donald R. van Deventer and Xiaoming Wang[1]

First Version: February 21, 2023

This Version: February 22, 2023

ABSTRACT

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This paper analyzes the number and the nature of factors driving the movements in the Japanese Government Bond yield curve from September 24, 1974 through November 30, 2022. The process of model implementation confirms a number of important insights for interest rate modeling generally. First, model validation of historical yields is important because those yields are the product of a third-party curve fitting process that may produce spurious indications of interest rate volatility. That is particularly true in the case of Japan. Second, quantitative measures of smoothness and international comparisons of smoothness provide a basis for measuring the quality of simulated yield curves. This too is especially important for Japan given the attempt at “Yield Curve Control” via the 10-year Japanese Government Bond that began in 2016. Third, we outline a process for incorporating insights from the World-wide experience with negative interest rates into term structure models with stochastic volatility in Japan and other countries. Fourth, we compare data availability for Japan with broad international experience to measure the risk that a simulation beyond historical rate levels in Japan could go awry. Finally, we illustrate the process for comparing stochastic volatility and affine models of the term structure. We conclude that stochastic volatility models, when out of sample performance is the primary interest, have a superior fit to the history of yield movements in the Japanese Government Bond market. We also recommend that Japanese Government Bond interest rate risk analysis employ the full “World” 13-country term structure model rather than relying solely on Japan data alone.

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Footnotes

[1] SAS Institute Inc., 2222 Kalakaua Avenue, Suite 1400, Honolulu, Hawaii, USA, 96815. E-Mail donald.vandeventer@sas.com. The authors wish to thank Prof. Robert A. Jarrow for 28 years of conversations on this topic. The authors are grateful to Theodore Spradlin for analytical and data-related assistance. The authors also wish to thank the participants at seminars organized by the Bank of Japan and the Federal Reserve Bank of San Francisco at which papers addressing similar issues in a Japan and U.S. government bond context were presented.