A 15-Factor Heath, Jarrow, and Morton Stochastic Volatility Model
for the United Kingdom Government Bond Yield Curve,
Using Daily Data from January 2, 1979 through November 30, 2021
Donald R. van Deventer
First Version: January 5, 2022
This Version: January 6, 2022
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This paper analyzes the number and the nature of factors driving the movements in the United Kingdom Government Bond yield curve from January 2, 1979 through November 30, 2021. 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. 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 World-wide experience with negative interest rates into term structure models with stochastic volatility in United Kingdom and other countries. Fourth, we compare data availability for United Kingdom with broad international experience to measure the risk that a simulation beyond historical rate levels in United Kingdom 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 United Kingdom Government Bond market. We also recommend that United Kingdom Government Bond interest rate risk analysis employ the full “World” 13-country term structure model rather than relying solely on United Kingdom data alone.
A PDF version of the paper is available here:Kamakura-AnUpdatedHJMModelforUnitedKingdom20211130v1-20220106
 Kamakura Corporation, 2222 Kalakaua Avenue, Suite 1400, Honolulu, Hawaii, USA, 96815. E-Mail email@example.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 papers addressing similar issues in a Japan and U.S. government bond context were presented.