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Donald van Deventer
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Donald R. van Deventer founded the Kamakura Corporation in April, 1990 and is currently Chairman and Chief Executive Officer. Dr. van Deventer's emphasis at Kamakura Corporation is enterprise wide risk management and modern credit risk technology. The second edition of his newest book, Advanced... More
My company:
Kamakura Corporation
My blog:
Donald R. van Deventer's Kamakura Blog
My book:
Advanced Financial Risk Management, 2nd Edition 2013
  • New Research By Robert Jarrow Integrates Yield Curve Smoothing And Interest Rate Modeling 0 comments
    Jun 19, 2014 3:50 PM | about stocks: TLT, BUND, JGBL

    Techniques Used by Many Central Banks Inconsistent with "No Arbitrage"

    Kamakura Corporation announced today 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 case Nelson-Siegel violate the no-arbitrage constraints described by Heath, Jarrow and Morton [1992] is consistent with earlier papers by Bjork 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

    Disclosure: The author has no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

    Stocks: TLT, BUND, JGBL
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