Kamakura Releases New Multi-Factor Interest Rate Models for 13 Countries and World Government Bond Yields

03/22/2021 09:15 AM

Kamakura Releases New Multi-Factor Interest Rate Models
13 Countries and World Government Bond Yields
1, 2, 3, 6 and “All” Factors Available with Constant and Stochastic Volatility

New York, March 23, 2021: Kamakura Corporation has released a suite of new multi-factor term structure models for government bond yields in 13 countries and an integrated “World” term structure model for Kamakura Risk Manager and Kamakura Risk Information Services subscribers. Development of the model was led by Robert A. Jarrow, Kamakura’s Managing Director for Research and the Ronald P. and Susan E. Lynch Professor of Investment Management at Cornell University’s Johnson Graduate School of Management. Professor Jarrow’s 1992 paper, written with David Heath and Andrew Morton and known as “HJM,” provides the underlying no arbitrage framework for the model’s estimations.

The menu of options includes 1, 2, 3, 6, and all- factor models featuring both constant (“affine”) interest rate volatility and stochastic volatility. Each of the models is benchmarked on the full daily history available for country. The number of factors in the “all-factor” model for each country is determined statistically using modern generalized linear models. The number of factors and the beginning of the time series in each market is listed here:

Australia Commonwealth Government Securities, 1996 11 factors
Canada Government of Canada Securities, 2005 11 factors
France French Government Bonds, 2015 7 factors
Italy Italian Government Bonds, 2015 11 factors
Germany Bunds, 1997 15 factors
Japan Japanese Government Bonds, 1974 10 factors
Russia Russian Government Bonds, 2003 11 factors
Singapore Singapore Government Securities, 1998 10 factors
Spain Spanish Government Securities, 1987 11 factors
Sweden Swedish Government Securities, 1987 11 factors
Thailand Thai Government Securities, 1999 11 factors
United Kingdom Government Securities, 1979 15 factors
United States Treasury Securities, 1962 10 factors
World Government Securities in 13 Countries, 1962 12 factors


Martin Zorn, President and Chief Operating Officer of Kamakura Corporation, said Tuesday, “Kamakura’s original work in yield curve analytics was heavily focused on the largest bond markets in the world, recognizing the special nature of the Japanese government bond market. From the development of maximum smoothness forward rate smoothing (Adams and van Deventer, Journal of Fixed Income, 1994) to early implementations of the HJM model, Kamakura’s insights into the Japanese market date from the first experience with negative rates in the mid-1990s. The interest rate factors driving the 13-country yield curves in the updated Kamakura implementation of HJM analytics also drive Kamakura’s equity factor models for the same markets and the default models for the 40,500 firms in the KRIS Public Firm default probability service. This approach is much more accurate than the traditional assumption in legacy equity factor models and Merton default probability models that interest rates are constant.”

Robert A. Jarrow, Kamakura’s Managing Director for Research

Professor Robert Jarrow, Kamakura Managing Director for Research since 1995, added “Kamakura’s international portfolio of HJM models is unprecedented in the risk management business. The lessons of the COVID crisis, the Great Financial Crisis of 2008-2010, the Asia crisis of 1997-1998, and the collapse of Japan’s bubble economy make it clear that multiple factors drive interest rates and that interest rate risk and credit risk are deeply interconnected. I am very pleased with Kamakura’s implementation of my research and I enjoy working with the world’s most capable risk managers in their implementations of Kamakura Risk Manager and the portfolio of HJM models from Kamakura.”

The updated World and 13-country term structure models provide a more realistic roadmap for predicting the future than a simple extrapolation from current yields, since the models incorporate 88,132 daily observations on government yield movements. The model documentation includes a significant section on Bayesian model validation, in which 500,000 out-of-sample scenarios were used to measure the consistency of the model’s predictions, taking into account both expert knowledge and the history of interest rate movements worldwide.

The Bayesian process of model fitting, simulation, and revision is both analytically elegant and eminently practical.The model documentation for the HJM models shows realistic variation in both risk- neutral and empirical interest rates over time. The simulation is consistent with worldwide experience with both negative rates and historical bouts with high levels of inflation and high interest rates. A link to the U.S. Treasury HJM model is available here.

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) sets a new standard for industry best practice and is exceptionally realistic.

Kamakura’s analytical team regularly updates term structure models from all major markets around the world. Model documentation and parameters are available by subscription to Kamakura Risk Information Services’ default probability and bond information services. All of the models mark to market observable securities prices. 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.

About Kamakura Corporation
Founded in 1990, Honolulu-based Kamakura Corporation is a leading provider of risk management information, processing, and software. Kamakura was recognized as a category leader in the Chartis Report, Technology Solutions for Credit Risk 2.0 2018. Kamakura was named to the World Finance 100 by the editor and readers of World Finance magazine in 2017, 2016 and 2012. In 2010, Kamakura was the only vendor to win two Credit Magazine innovation awards.  Kamakura Risk Manager, first sold commercially in 1993 and now in version 10.1.1, is the first enterprise risk management system for 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 with assets ranging in size from $1.5 billion to $7.0 trillion. Current clients have a combined “total assets” or “assets under management” in excess of $28 trillion. Its risk management products are currently used in 47 countries, including the United States, Canada, Germany, the Netherlands, France, Austria, Switzerland, the United Kingdom, Russia, Ukraine, South Africa, Australia, China, Hong Kong, India, Indonesia, Japan, Korea, Malaysia, Singapore, Sri Lanka, Taiwan, Thailand, Vietnam, and many other countries in Asia, Europe and the Middle East.

To follow risk commentary by Kamakura on a daily basis, please follow:
Kamakura CEO, Dr. Donald van Deventer (www.twitter.com/dvandeventer)
Kamakura President, Martin Zorn (www.twitter.com/riskmgrhi)
Kamakura’s official twitter account (www.twitter.com/KamakuraCo).

For more information, please contact:
Kamakura Corporation
2222 Kalakaua Avenue, Suite 1400,
Honolulu, Hawaii 96815

Facsimile: 1-808-791-9898
Information: info@kamakuraco.com
Web site: www.kamakuraco.com