Daniel Dickler, Robert Jarrow, Stas Melnikov, Alexandre Telnov, Donald R. van Deventer and Xiaoming Wang
First Version: October 15, 2022
This Version: October 28, 2022
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This paper analyzes the number and the nature of factors driving the movements in the U.S. Treasury yield curve from January 2, 1962 through September 30, 2022, updating prior documentation through March 31, 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 Japanese and European experience with negative interest rates into term structure models with stochastic volatility in the United States and other countries. Finally, we illustrate the process for comparing stochastic volatility and affine models of the term structure. We conclude that stochastic volatility models have a superior fit, when out-of-sample simulation is the objective, to the history of yield movements in the U.S. Treasury market.
A copy of the full text of the article is available here:Kamakura-AnUpdatedHJMModelforUSTreasuriesv2-20220930
 SAS Institute Inc., 2222 Kalakaua Avenue, Suite 1400, Honolulu, Hawaii, USA, 96815. Kamakura Corporation is a subsidiary of SAS Institute Inc. E-Mail email@example.com. Theodore Spradlin provided invaluable data on which this note is based. 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 were presented.