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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

September 19, 2014
Primary Mortgage Yields Rise 0.11% and 30 Year Fixed Rate Mortgage Servicing Values Rise 0.36% This Week

September 13, 2014
Comparing the Marginal Cost of Funds for Berkshire Hathaway with BAC and WFC

September 11, 2014
Primary Mortgage Yields Rise 0.02% and 30 Year Fixed Rate Mortgage Servicing Values Rise 0.13% This Week

September 10, 2014
Bank of America: A Pre-Stress Test Credit Risk Report Shows Dramatic Progress

September 9, 2014
Bank of America and Its High Marginal Cost of Funds

September 8, 2014
Royal Dutch Shell Bond Issue Leads the 20 Best Value Bond Trades with Maturities of 1 Year or More

September 4, 2014
Forward 1 Month T-bill Curve Twists, Jumps 0.16% to Peak at 3.33% in February, 2021

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


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Today’s forecast for U.S. Treasury yields is based on the November 23, 2011 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 pm November 25, 2011 because interest rate data was not available for November 24 due to the holiday. 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 our blog of November 7, 2011, we showed that the one–factor term structure models in wide use in the financial services business for interest rate management analytics were consistent with actual daily movements of the U.S. Treasury curve less than 38% of 12,286 business days since 1962.  In this blog, we repeat the analysis on the Libor-swap curve and reach an even more devastating conclusion: once the full interest rate swap curve came into view in 1988, daily yield curve shifts were consistent with one factor models less than 8% of the time.  This blog explains how we arrived at those conclusions.

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Today’s forecast for U.S. Treasury yields is based on the November 17, 2011 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 pm November 18, 2011. 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 November 9, 2011 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 pm November 10, 2011 because interest rate data was not available for November 10 due to the holiday. 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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One factor models of the term structure of interest rates were developed to provide insights into the valuation of fixed income options.  Since the models’ early development from 1977 to 1993, they have been consistently misapplied in asset and liability (interest rate risk) management.  Many analysts, choosing one of the common one factor models, create random interest rate scenarios to evaluate the interest rate risk of the firm.  This blog post uses 50 years of U.S. Treasury yield curve information to prove that the major implications of one factor term structure models are inconsistent with historical data.  A multi-factor approach is necessary to create realistic interest rate simulations. The author wishes to thank Professor Robert A. Jarrow for helpful comments. Any errors that remain are those of the author alone.
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