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Don founded Kamakura Corporation in April 1990 and currently serves as its chairman and chief executive officer where he focuses on enterprise wide risk management and modern credit risk technology. His primary financial consulting and research interests involve the practical application of leading edge financial theory to solve critical financial risk management problems. Don was elected to the 50 member RISK Magazine Hall of Fame in 2002 for his work at Kamakura. Read More

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Today’s forecast for U.S. Treasury yields is based on the March 29, 2012 constant maturity Treasury yields that were reported by the Board of Governors of the Federal Reserve System in its H15 Statistical Release at 4:15 p.m. Eastern Daylight Time March 30, 2012. The “forecast” is the implied future coupon bearing U.S. Treasury yields derived using the maximum smoothness forward rate smoothing approach developed by Adams and van Deventer (Journal of Fixed Income, 1994) and corrected in van Deventer and Imai, Financial Risk Analytics (1996). For an electronic delivery of this interest rate data in Kamakura Risk Manager table format, please subscribe via info@kamakuraco.com.

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All of us at Kamakura would like to thank our readers for the very high level of interest in this blog.  This version, updated April 19, 2012, incorporates some important revisions in previously published work by Robert A. Jarrow.  We would like to add a special thanks to Professor Jarrow for his contributions to this revision.

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Today’s forecast for U.S. Treasury yields is based on the March 22, 2012 constant maturity Treasury yields that were reported by the Board of Governors of the Federal Reserve System in its H15 Statistical Release at 4:15 p.m. Eastern Daylight Time March 23, 2012. The “forecast” is the implied future coupon bearing U.S. Treasury yields derived using the maximum smoothness forward rate smoothing approach developed by Adams and van Deventer (Journal of Fixed Income, 1994) and corrected in van Deventer and Imai, Financial Risk Analytics (1996). For an electronic delivery of this interest rate data in Kamakura Risk Manager table format, please subscribe via info@kamakuraco.com.

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Today’s forecast for U.S. Treasury yields is based on the March 15, 2012 constant maturity Treasury yields that were reported by the Board of Governors of the Federal Reserve System in its H15 Statistical Release at 4:15 p.m. Eastern Daylight Time March 15, 2012. The “forecast” is the implied future coupon bearing U.S. Treasury yields derived using the maximum smoothness forward rate smoothing approach developed by Adams and van Deventer (Journal of Fixed Income, 1994) and corrected in van Deventer and Imai, Financial Risk Analytics (1996). For an electronic delivery of this interest rate data in Kamakura Risk Manager table format, please subscribe via info@kamakuraco.com.

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In the first two blogs in this series, we provided worked examples of how to use the yield curve simulation framework of Heath, Jarrow and Morton using two different assumptions about the volatility of forward rates. The first assumption was that volatility was dependent on the maturity of the forward rate and nothing else.  The second assumption was that volatility of forward rates was dependent on both the level of rates and the maturity of forward rates being modeled.  Both of these models were one factor models, implying that random rate shifts are either all positive, all negative, or zero.  This kind of yield curve movement is not consistent with the yield curve twists that are extremely common in the U.S. Treasury market. In this blog we generalize the model to include two risk factors in order to increase the realism of the simulated yield curve.

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