Chapter 8

HJM Interest Rate Modeling with Two Risk Factors

In Chapters 6 and 7, we provided worked examples of how to use the yield curve simulation framework of Heath, Jarrow, and Morton (HJM) with 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 and most other fixed income markets. In this chapter, we generalize the model to include two risk factors in order to increase the realism of the simulated yield curve.


In this chapter, we use the same data as inputs to the yield curve simulation process that we used in Chapters 6 and 7. A critical change in this chapter is to enhance our ability to model twists in the yield curve as shown in Exhibit 8.1.

EXHIBIT 8.1 Summary of U.S. Treasury Yield Curve Shifts Percentage Distribution of Daily Rate Shifts January 2, 1962, to August 22, 2011


It shows that, ...

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