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The author wishes to thank his colleague, Managing Director for Research Prof. Robert A. Jarrow, for twenty years of guidance and helpful conversations on this critical topic.

For a PDF copy of this note, click here.

On January 12, Kamakura Corporation released newly updated parameters for its best practice Heath Jarrow and Morton model for U.S. Treasuries.  Using the no-arbitrage conditions of Heath, Jarrow and Morton, the Kamakura suite of term structure models includes 1, 2, 3, 6 and 9 factor models of the U.S. Treasury curve under two different assumptions about interest rate volatility:

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The author wishes to thank his colleague, Managing Director for Research Prof. Robert A. Jarrow, for twenty years of guidance and helpful conversations on this critical topic.

Kamakura Corporation has released newly updated parameters for its best practice Heath Jarrow and Morton model for U.S. Treasuries. The suite of parameter sets includes the following roster of 10 models:

HJM Rate Dependent Volatility, 9 Factors (Best Practice)
HJM Rate Dependent Volatility, 6 Factors
HJM Rate Dependent Volatility, 3 Factors
HJM Rate Dependent Volatility, 2 Factors
HJM Rate Dependent Volatility, 1 Factor
HJM Constant Volatility, 9 Factors
HJM Constant Volatility, 6 Factors
HJM Constant Volatility, 3 Factors
HJM Constant Volatility, 2 Factors
HJM Constant Volatility, 1 Factors

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The author wishes to thank his colleague, Managing Director for Research Prof. Robert A. Jarrow, for twenty years of guidance and helpful conversations on this critical topic.

The Singapore Government Securities yield curve and its history is unique internationally for many reasons, but perhaps foremost among them is the pristine credit quality of the island nation. The website of the Monetary Authority of Singapore explains the background of the Singapore Government Securities market:

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In January 2005, Prof. Robert Jarrow and I published a paper in RISK Magazine entitled “ Estimating Default Correlations Using a Reduced Form Model.” Since that time, we have seen the management of portfolios of risky credits evolve in one of two directions. The best practice approach is to fully exploit the advantages of reduced form models by using that approach for both default probability estimation and forward-looking simulation of portfolio defaults and credit-adjusted values. A second approach is common among analysts making the transition from Merton default probabilities and Merton-linked copula simulation of credit portfolios. In this note, we show the linkages among three different meanings of “default correlation” for this second approach. We provide a worked example following Jarrow and van Deventer (2005).

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The author wishes to thank his colleague, Managing Director for Research Prof. Robert A. Jarrow, for twenty years of guidance and helpful conversations on this critical topic.

The Spanish Government Bond yield curve and its history, along with data from Sweden, offer one of the most important laboratories for the study of interest rate movements among the prominent bond markets world-wide. The Spanish Government Bond history made available by the Banco de España begins in 1987, and the long history includes extended periods of very high rates, very low rates, and negative rates. The experience in Sweden offers a similar history. For that reason, the Heath Jarrow and Morton (“HJM”) analysis on Spanish Government Bonds provides another important benchmark for interest rate modeling in economies where the government yield history is not as rich as it is in Spain or Sweden.

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