Press Release

Kamakura Releases 14 Factor Heath Jarrow and Morton Stochastic Volatility Model for German Bunds to Clients
Incorporates Bayesian Modifications for Negative Interest Rates

New York, July 19, 2017: Kamakura Corporation announced today that it has released a new 14 factor Heath, Jarrow and Morton term structure model for the German Bund yield curve to Kamakura Risk Manager and Kamakura Risk Information Services subscribers. The menu of model options includes 1, 2, 3, 6, and 14 factor models featuring both constant (“affine”) interest rate volatility and stochastic volatility. The best fitting model is the stochastic volatility 14 factor model, benchmarked on daily data from the Deutsche Bundesbank and Bloomberg from January 1, 1996 through March 27, 2017. The model is the 4th of a series of HJM model development effort 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. The German Bund yield dynamics are critical for world-wide understanding of the negative rate phenomenon given that the experience with negative rates in Germany now rivals that of Japan.

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 Tuesday,“The HJM Model for German Bunds is the fourth in series released on behalf of Kamakura’s clients in 47 countries. The model documentation for the German Bund market again includes a significant section on Bayesian model validation, with a special treatment of both yield curve smoothing validation and negative rates.”

Kamakura’s analytical team regularly updates term structure models from all of the major markets around the world. Both risk neutral and empirical interest rate simulations can be produced from the term structure model parameter sets. 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
Web site: