Press Release

Kamakura Releases 10 Factor Heath Jarrow and Morton Stochastic Volatility Model for U.S. Treasuries to Clients
Bayesian Out-of-Sample Model Validation Predicts Modest Chance of Negative Rates

 NEW YORK, June 29, 2017: Kamakura Corporation announced today that it has released a new 10 factor Heath, Jarrow and Morton term structure model for the U.S. Treasury yield curve to Kamakura Risk Manager and Kamakura Risk Information Services subscribers. The menu of model options includes 1, 2, 3, 6, and 10 factor models featuring both constant (“affine”) interest rate volatility and stochastic volatility. The best fitting model is the stochastic volatility 8 factor model, benchmarked on daily data from the U.S. Department of the Treasury from January 2, 1962 through March 31, 2017. The model development effort has been overseen by Kamakura’s Managing Director for Research Prof. Robert A. Jarrow, whose 1992 paper with David Heath and Andrew Morton provides the underlying framework for model estimation. 

A paper providing an overview of the model is available on this link in both web-compatible and PDF form: 


Martin Zorn, President and Chief Operating Officer for Kamakura Corporation, said Thursday, “Many traders and risk managers in the U.S. have spent most or all of their careers in a declining rate environment. The updated Treasury model provides a more realistic roadmap to the future than personal experience, since it is based on 55 years of daily U.S. interest rate movements. The modeling effort has benefitted enormously from the perspective of Kamakura clients in 47 countries. In particular, the evidence on interest rate movements in a negative rate economy captured in the Japanese Government Bond model released last week has been invaluable in maximizing the realism of the new U.S. Treasury model.”

“The model documentation includes a significant section on Bayesian model validation, where a large out of sample simulation of 250,000 scenarios is used to measure the consistency of the model’s predictions with both history and expert knowledge about interest rate movements world-wide. The Bayesian process of model fitting, simulation, and revision is both analytically elegant and eminently practical. The model documentation for the U.S. Treasury HJM model shows realistic variation in both risk neutral and empirical interest rates over time. The simulation is consistent with world-wide experience in that negative rates are both possible and yet much less likely than positive rates. Simulated rates reach highs like those last seen in the 1970s and 1980s but with low probability. The Kamakura standard Bayesian out-of-sample model validation provides assurance to risk managers, auditors, regulators and Boards of Directors that the interest rate simulation technology used in Kamakura Risk Information Services (‘KRIS’) and Kamakura Risk Manager (‘KRM’) is both best practice and exceptionally realistic.”

Kamakura’s analytical team regularly updates term structure models from all of the major markets around the world. Model documentation and parameters are available by subscription from Kamakura Risk Information Services’ default probability and bond information service. All of the models are consistent with the need to perfectly mark to market observable securities prices in each market. They provide the basis for very high scenario simulation of correlated risks and for interest rate factor-driven and other macro-factor driven stress tests using Kamakura Risk Manager, both with and without default modeling turned on.

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About Kamakura Corporation
Founded in 1990, Honolulu-based Kamakura Corporation is a leading provider of risk management information, processing and software. Kamakura was named to the World Finance 100 by the Editor and readers of World Finance magazine in 2016 and 2012. In 2010, Kamakura was the only vendor to win 2 Credit Magazine innovation awards. Kamakura Risk Manager, first sold commercially in 1993 and now in version 8.1, is the first enterprise risk management system with users focused on credit risk, asset and liability management, market risk, stress testing, liquidity risk, counterparty credit risk, and capital allocation from a single software solution. The KRIS public firm default service was launched in 2002. The KRIS sovereign default service, the world’s first, was launched in 2008, and the KRIS non-public firm default service was offered beginning in 2011. Kamakura added its U.S. Bank default probability service in 2014. Kamakura has served more than 330 clients ranging in size from $1.5 billion to $1.6 trillion in assets. Kamakura’s risk management products are currently used in 43 countries, including the United States, Canada, Germany, the Netherlands, France, Austria, Switzerland, the United Kingdom, Russia, the Ukraine, Eastern Europe, the Middle East, Africa, South America, Australia, Japan, China, Korea, India and many other countries in Asia.

Kamakura has world-wide alliances with Fiserv ( and SCSK Corporation ( making Kamakura products available in almost every major city around the globe.

For more information contact
Kamakura Corporation
2222 Kalakaua Avenue, Suite 1400, Honolulu, Hawaii 96815
Telephone: 1-808-791-9888
Twitter: @Kamakuraco
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