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An Introduction to Derivative Securities, Financial Markets, and Risk ManagementAdvanced Financial Risk Management, 2nd ed.

 Blog Entries

Kamakura Corporation Named to World Finance 100

August 26, 2014
Transfer Pricing and Valuation Yield Curves without Swap Data: A KeyBank and KeyCorp Example

August 18, 2014
More Evidence on the Funding “Subsidy” of the Too Big to Fail Banks

August 14, 2014
Mortgage Servicing Rights Values Close Mixed for the Week as Current and Forward Mortgage Rates Drop 0.03%

August 13, 2014
Liquidity At Risk – A stochastic look at cashflows

August 12, 2014
Five of Seven Regional Banks Trade at Credit Spreads Better than the Too Big to Fail Banks

August 12, 2014
Kinder Morgan Energy Partners Leads the 20 Best Value Bond Trades with Maturities of 10 Years or More

August 11, 2014
Measuring the Funding Costs of the Too Big to Fail Banks:
The U.S. Dollar Cost of Funds Index™


August 8, 2014
Forward 1 Month T-Bill Rates Plunge 0.26% in 2 Years but Forward 10 Year U.S. Treasury Yield Drops Only 0.04% from Last Week

August 6, 2014
Credit Spreads and Default Probabilities: A Simple Model Validation Example

August 5, 2014
Vodafone Group PLC: Default Risk is Down Sharply But Value Ranks in the Bottom 10% of Bonds

July 30, 2014
American International Group Inc. Bonds:
A Reward to Risk Ratio Twice as High as the Median Bond Issue


July 29,2014
AT&T Inc. Bonds: Ten Times the Risk of IBM and Below Average Value

July 15, 2014
Brazil, Italy, Spain, Credit Default Swaps and the
European Commission Short Sale Ban, 2010-2014


July 14, 2014
Bank of America and MBIA Lead U.S. Bank Credit Default Swap Trading Volume, 2010-2014

March 19, 2014
Stress Testing and Interest Rate Risk Models: A Multi-Factor Stress Testing Example

March 13, 2014
Stress Testing: A Credit Spread Ranking of 12 U.S. and 12 International Banks

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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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