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A 14-Factor Heath, Jarrow And Morton Model For The United Kingdom Government Securities Yield Curve, 1979 To 2017

Jul. 10, 2017 9:02 AM ET4 Comments


  • Many of the largest U.K. financial institutions still rely on 1-factor models of interest rate risk whose technology dates back to the 1970s.
  • Using data from the Bank of England, we show through multiple methods that it takes 14 factors to explain U.K. government movements with a high degree of accuracy.
  • Large banks which continue to rely on 1-factor models face the risk of regulatory problems, particularly with respect to the BIS Fundamental Review of the Trading Book and IRBB.

The author wishes to thank Prof. Robert A. Jarrow for 22 years of conversations on this topic. The author also wishes to thank the participants at a seminar organized by the Bank of Japan at which a paper addressing similar issues in a Japanese government bond context was presented.


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.

We find that the quality of the yield curve smoothing by the Bank of England is extremely high. 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 to the history of yield movements in the United Kingdom Government Securities market.

A 14-Factor Heath, Jarrow and Morton Model for the United Kingdom Government Securities Yield Curve, January 1979 to January 2017

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 worldwide, in addition to the major bond markets

This article was written by

Donald van Deventer profile picture
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Donald R. van Deventer is a Managing Director in the Center for Applied Quantitative Finance at SAS Institute, Inc. Prior to the acquisition of Kamakura Corporation by SAS on June 24, 2022, Dr. van Deventer was the Chairman and Chief Executive Officer of Kamakura Corporation. He founded the Kamakura Corporation in April, 1990. The second edition of his book, Advanced Financial Risk Management (with Kenji Imai and Mark Mesler) was published in 2013.  Dr. van Deventer was senior vice president in the investment banking department of Lehman Brothers (then Shearson Lehman Hutton) from 1987 to 1990. During that time, he was responsible for 27 major client relationships including Sony, Canon, Fujitsu, NTT, Tokyo Electric Power Co., and most of Japan's leading banks. From 1982 to 1987, Dr. van Deventer was the treasurer for First Interstate Bancorp in Los Angeles. In this capacity he was responsible for all bond financing requirements, the company’s commercial paper program, and a multi-billion dollar derivatives hedging program for the company. Dr. van Deventer was a Vice President in the risk management department of Security Pacific National Bank from 1977 to 1982. Dr. van Deventer holds a Ph.D. in Business Economics, a joint degree of the Harvard University Department of Economics and the Harvard Graduate School of Business Administration. He was appointed to the Harvard University Graduate School Alumni Association Council in 1999 and served through 2021. Dr. van Deventer was Chairman of the Council for four years from 2012 to 2016. From 2005 through 2009, he served as one of two appointed directors of the Harvard Alumni Association representing the Graduate School of Arts and Sciences. Dr. van Deventer also holds a degree in mathematics and economics from Occidental College, where he graduated second in his class, summa cum laude, and Phi Beta Kappa. Dr. van Deventer speaks Japanese and English.

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