A 7-Factor Heath, Jarrow, and Morton Stochastic Volatility Model for the Government of Canada Yield Curve, Using Daily Data from January 2, 2001 through February 28, 2022

Donald R. van Deventer[1]

First Version: March 8, 2022

This Version: March 8, 2022

ABSTRACT

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This paper analyzes the number and the nature of factors driving the movements in the Canada Government Securities yield curve from January 2, 2001 through February 28, 2022. Consistent with prior work on Canada and with other country studies, we confirm a number of conclusions. 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. Second, quantitative measures of smoothness and international comparisons of smoothness provide a basis for measuring the quality of simulated yield curves. Third, we outline a process for incorporating insights from the Japanese and European experience with negative interest rates into term structure models with stochastic volatility in Canada and other countries. Fourth, we compare data availability for Canada with broad international experience to measure the risk that a simulation beyond historical rate levels in Canada 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 Canada Government Securities market. We also recommend that Canada Government Securities interest rate risk analysis employ the full “World” 13-country term structure model rather than relying solely on Canada data alone.

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Footnotes

[1] Kamakura Corporation, 2222 Kalakaua Avenue, Suite 1400, Honolulu, Hawaii, USA, 96815. E-Mail dvandeventer@kamakuraco.com. The author wishes to thank Prof. Robert A. Jarrow for 28 years of conversations on this topic. The author is grateful to Daniel Dickler, Dr. Xiaoming Wang, and Theodore Spradlin for analytical and data-related assistance. The author also wishes to thank the participants at seminars organized by the Bank of Japan and the Federal Reserve Bank of San Francisco at which a paper addressing similar issues in a Japan and U.S. government bond context was presented.