Chapter Six Interest Rate Risk Management

This is the final chapter of a sequence dealing with the elementary mathematics of interest rates and basic fixed-income securities, and it kind of summarizes all we have seen from Chapter 3 on. We had a taste of what interest risk is in Section 3.5.5, where we have seen that a shift in the level of interest rates may have a significant impact on the value of a bond. There, we have considered the bond price as a function of one risk factor, yield-to-maturity (YTM), and we have introduced the classical concept of duration for fixed-coupon bonds. However, this is just an approximation, since a bond price actually depends on the whole term structure of interest rates. From Section 2.2.3.3, we also know how first-order immunization against multiple risk factors may be achieved by using a set of hedging instruments and by measuring the first-order portfolio sensitivities to each risk factor. In this chapter, we analyze duration in more depth and extend it in order to deal with a broader set of securities, most notably interest rate swaps, and show in more detail how risk factor sensitivities may be used to measure and manage interest rate risk. Later, we shall need more sophisticated stochastic models in order to cope with interest rate options, which provide additional flexibility to the risk management toolkit.

The classical definition of duration has several limitations, and a more flexible one is provided in Section 6.1, allowing us ...

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