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, 2022

Daniel Dickler, Robert A. Jarrow, Stas Melnikov, Alexandre Telnov,

Donald R. van Deventer, and Xiaoming Wang[1]

• First Version: January 5, 2023
• This Version: January 13, 2023

ABSTRACT

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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, 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. 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. That being said, we believe that the current procedures for estimating stochastic volatility parameters can be improved, and that work is in progress. 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.

Footnotes

[1] SAS Institute Inc. and Kamakura Corporation, 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 Daniel Dickler, Dr. Xiaoming Wang, and 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.