Donald R. van Deventer
First Version: January 24, 2022
This Version: January 25, 2022
ABSTRACT
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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 December 31, 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 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.
Kamakura-AnUpdatedHJMModelforUSTreasuriesv2-20220125