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For Immediate Release
New Research by Robert Jarrow Integrates Yield Curve Smoothing and Interest Rate Modeling:
Techniques Used by Many Central Banks Inconsistent with “No Arbitrage”

Robert Jarrow NEW YORK, June 24, 2014: Kamakura Corporation announced Tuesday that it has released an important new research paper by Managing Director for Research Prof. Robert A. Jarrow entitled “Forward Rate Smoothing,” forthcoming in November in the Annual Review of Financial Economics. The key contribution of the paper, in the words of Prof. Jarrow, is “to link the static curve fitting exercise to the dynamic and arbitrage-free models of the term structure of interest rates.” Two of the key conclusions of the paper are that the Svensson and Nelson Siegel yield curve smoothing techniques, widely used by central banks around the world, do not satisfy no arbitrage constraints. In addition they generate forward rate curves whose implied zero-coupon bond price curve does not contain all of the ‘observed’ zero coupon bond prices. Prof. Jarrow provides examples using early term structure models like the Ho and Lee model and the Extended Vasicek model to illustrate the violation of no-arbitrage when these yield curve smoothing techniques are used. By contrast, the maximum smoothness forward curves of Adams and van Deventer, states Prof. Jarrow, “satisfy the spanning property” explained in the paper and are consistent with standard no arbitrage conditions.

The conclusion of the new Jarrow paper summarizes its findings in more detail:

“The key contribution of this review is to link the static forward rate curve fitting exercise to the dynamics of the forward rate curve’s stochastic evolution. This linkage is missing in the literature, and it generates new economic insights about the static curve fitting exercise. In particular, it is shown that the basis set of functions used in a static setting to fit a forward rate curve is almost completely determined by the forward rate curve evolution’s drift and volatility functions. It is conjectured that these new insights should generate improved forward rate curve estimates when applied in practice.”

The observation that the Svensson smoothing technique and its special caseNelson-Siegel violate the no-arbitrage constraints described byHeath, Jarrow and Morton [1992] is consistent with earlier papers byBjork and Christensen and Filipovic. The process for systematically reviewing yield curve smoothing techniques for consistency with no arbitrage constraints outlined in the new Jarrow paper is particularly important because of the wide-spread use of inconsistent models by central banks around the world.

A 2005 paper by the Bank for International Settlements summarizes the yield curve smoothing methods in use by central banks at that time:

     Belgium:                Svensson or Nelson-Siegel
     Canada:                Merrill Lynch exponential spline
     Finland:                 Nelson-Siegel
     France:                  Svensson or Nelson-Siegel
     Germany:              Svensson
     Italy:                      Nelson-Siegel
     Japan:                   Smoothing splines
     Norway:                Svensson
     Spain:                   Svensson
     Sweden:                Smoothing splines and Svensson
     Switzerland:          Svensson
     United Kingdom:   Variable roughness penalty spline smoothing
     United States:       Smoothing splines

Only central banks in Japan, Sweden (when using splines), the United Kingdom, and the United States were using smoothing techniques in 2005 that were consistent with the no arbitrage constraints of Heath, Jarrow and Morton. Since 2005, the Reserve Bank of Australia has published a paper using the Merrill Lynch exponential spline, which violates no arbitrage. In the United States, the U.S. Department of the Treasury uses quasi-cubic hermite splines for the nominal U.S. Treasury curve and cubic splines for the Treasury Inflation Protected Securities yield curve . Both techniques used by the U.S. Treasury, following the Jarrow methodology, are consistent with no arbitrage. Federal Reserve researchers, however, have recently published data using the Svensson technique and required banks subject to the 2014 Comprehensive Capital Analysis and Review to use such data (see page 19 descriptions of the 5 and 10 year Treasury yields for reference to Svensson data).

Kamakura Corporation founder and chief executive officer Donald R. van Deventer summarized the implications of the Jarrow paper for financial market participants and researchers, “The Jarrow findings provide a concrete screening process for proposed yield curve smoothing techniques, supporting earlier results by Bjork and Christensen and Filipovic. Market practitioners and researchers using cubic splines or the quartic forward rates of the Adams and van Deventer ‘maximum smoothness’ approach have a safe harbor finding in the Jarrow paper: those techniques conform with no-arbitrage constraints. Conversely, the use of exponential splines, Svensson, and Nelson-Siegel smoothing were shown clearly by the Jarrow methodology to be inconsistent with no arbitrage. A careful market participant or researcher, then, should not use data generated from these techniques to benchmark interest rate and macro factor models, because the shape of the curves themselves does not fit the data and does not fit the changes in the data. In fact, these techniques change the data, rather than letting market prices inform the shape of the curve. For these reasons, the interest rate data provided by Kamakura Risk Information Services has always been generated carefully on a no-arbitrage basis with maximum goodness of fit to observable market prices.”

For information on the maximum smoothness forward rate technique of Adams and van Deventer, see van Deventer, Imai and Mesler, Advanced Financial Risk Management , 2nd edition, John Wiley & Sons, Singapore, 2013, especially chapters 5 and 17.

For copies of the new Jarrow paper, please contact your Kamakura representative or e-mail Kamakura Corporation at

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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 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 has served more than 220 clients ranging in size from $1.5 billion to $1.6 trillion in assets. Kamakura’s risk management products are currently used in 37 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.

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