Low Rate and Negative Rate Model Validation for Interest Rate Risk and Asset and Liability Management

The author wishes to thank his colleague, Managing Director for Research Prof. Robert A. Jarrow, for twenty years of guidance and helpful conversations on this critical topic.

As zero interest rate policies and negative interest rates ripple through world financial markets, many legacy interest rate risk systems and asset and liability management systems have been unable to keep pace. In this note, we use 100,000 scenarios from a modern 9 factor Heath, Jarrow and Morton interest rate simulation from Kamakura Corporation to illustrate the model validation issues that arise when one admits that negative interest rates have a probability that is not zero.

The model validation procedures we outline are used by Kamakura in both its Kamakura Risk Information Services macro factor scenario sets and in Kamakura Risk Manager (“KRM”). KRM has allowed users to simulate and analyze negative interest rates for more than 20 years.

Negative Interest Rates: An International Perspective
Even with negative interest rates making the headlines in European markets daily, one sometimes hears the phrase “It can’t happen in the United States.” The same phrase, of course, was used to deny the possibility that home prices could fall in the United States prior to the 2006-2010 financial crisis. Negative interest rates have already been observed in the secondary market for U.S. Treasury securities, as confirmed by this phrase quoted from the February 17 version of the U.S. Department of the Treasury yield reporting web page:


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The Association of International Wealth Management of India (AIWMI) is a not-for-profit organization and a globally recognized membership association for finance professionals. AIWMI primarily focuses on the broad and strategic role of developing a more robust and forward-looking training infrastructure for the financial services sector and to promote more active industry involvement and collaboration in training and continuing education. AIWMI is offering advanced international certification programs along with a wide variety of high-quality executive education programs. AIWMI programs combine state-of-the-art knowledge and skills with practical experience and insights into the functioning of the financial sector. All AIWMI courses and educational events have an intense and pragmatic curriculum. Participants are exposed to the latest developments within the financial services sector. AIWMI plays a key role in guiding the development of the financial services sector. AIWMI works with key industry participants’ viz. the Government, the Regulators, the Industries/Associations, the Corporate, the Media and the General Public to achieve its objectives. Besides enhancing technical competence and professionalism in the industry, AIWMI organizes events and facilitates discussions to promote best practices in leadership and talent development in the financial sector with an aim to become Asia’s premier center of excellence for financial education.

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