Press Release

Kamakura Announces 8 Factor Heath Jarrow and Morton
Stochastic Volatility Model for Japanese Government Bond Yields
Model Updates Made Available to Kamakura Risk Manager Users via KRIS

Robert Jarrow  TOKYO, June 22, 2017: Kamakura Corporation announced today that it has released a new 8 factor Heath, Jarrow and Morton term structure model for the Japanese Government Bond yield curve to Kamakura Risk Manager and Kamakura Risk Information Services subscribers. The menu of model options includes 1, 2, 3, 6, and 8 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 Ministry of Finance in Japan from September 24, 1974 through December 30, 2016. 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:
PDF link
PDF Download

Martin Zorn, President and Chief Operating Officer for Kamakura Corporation, said Monday, “As higher interest rates become more prevalent in the United States, major financial institutions have become concerned that their legacy asset and liability management systems have led bank management to confuse the low-interest-rate-tailwind with ALM skill. As rates rise, the yield curve twists that represent 85-90% of yield movements simply can’t be modeled accurately in legacy 1 factor term structure models using technology largely developed in the 1970s. It’s now apparent that the lack of ALM risk management problems has been, in large part, the good luck of low rates.”

Martin Zorn “Risk managers have moved rapidly to adopt the lessons learned and the multi-factor models in wide use among Kamakura’s Kamakura Risk Manager and KRIS client base in 47 countries. Japan provides perhaps the best laboratory because of the long data history beginning in 1974 and because of the Japan bubble and low interest experience that the U.S. Treasury market has subsequently mimicked. Kamakura updated its Japanese Government Bond term structure model at the request of clients seeking insights from the Japan experience. The results are clear: (a) 8 factors are needed to model Japanese Government Bond yields accurately, (b) interest rate volatility does not go to zero even when rates are negative—it hits a floor described in the paper, (c) interest rate volatility is random and driven by rate levels, not constant as many legacy rate models assume, and (d) users of one factor term structure models should fail a model validation audit by any reputable firm in the financial model audit business.”

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.

To follow the troubled company index and other risk commentary by Kamakura on a daily basis, please follow
Kamakura CEO Dr. Donald van Deventer (
Kamakura President Martin Zorn ( and
Kamakura’s official twitter account (

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
Twiter: @Kamakuraco
Web site: