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Don founded Kamakura Corporation in April 1990 and currently serves as its chairman and chief executive officer where he focuses on enterprise wide risk management and modern credit risk technology. His primary financial consulting and research interests involve the practical application of leading edge financial theory to solve critical financial risk management problems. Don was elected to the 50 member RISK Magazine Hall of Fame in 2002 for his work at Kamakura. Read More

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The magnitude of a “term premium” or risk premium in long term U.S. Treasury yields is a major focus of research by economists in the Federal Reserve System.  A recent paper by Canlin Li, Andrew Meldrum, and Marius Rodriguez summarizes two important papers on this topic and reviews their methodologies.  Adrian, Crump, Mills and Moench (2014) summarize their term premium findings as follows: “The evolution of term premia has been of particular interest since the Federal Reserve began large-scale asset purchases. Over this time, short-term interest rates have been close to zero, and our estimates show that the term premium has been compressed and has at times even been negative.” Estimates of the term premium are a function of the data used, the modeling approach taken, and market expectations.
 

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This paper analyzes the number and the nature of factors driving the movements in the German Bund yield curve from January 1, 1996 through March 27, 2017. The process of model implementation reveals 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 historical and simulated yield curves. We find that the yield curve smoothing by the third-party vendor used for Germany required careful vetting. Third, we outline a process for incorporating insights from the Japanese experience with negative interest rates into term structure models with stochastic volatility in Germany and other countries.
 

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This paper analyzes the number and the nature of factors driving the movements in the United Kingdom Government Securities Yield Curve from January 2, 1979 through January 31, 2017. The process of model implementation reveals 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 experience with negative interest rates into term structure models with stochastic volatility in the United Kingdom and other countries.

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Government yield curves are a critical input to the risk management calculations of central banks, bank regulators, major banks, insurance firms, fund managers, pension funds, and endowments around the world.  With the internationalization of fixed income investing, it is important to understand the dynamics of movements in yield curves world-wide, in addition to the major bond markets like those in Frankfurt, London, New York and Tokyo. In this paper, we fit a multi-factor Heath, Jarrow and Morton model to daily data from the U.S. Treasury market over the period from January 2, 1962 to March 31, 2017. The modeling process reveals a number of important implications for term structure modeling in other government bond markets.

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This paper analyzes the number and the nature of factors driving the movements in the Japanese Government Bond yield curve from September 24, 1974 through December 30, 2016. The process of model implementation reveals a number of important insights for interest rate modeling generally. First, model validation of observed 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.

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