Overview

This chapter and the next two chapters discuss duration and convexity. We develop duration as a time measure and also as a measure of risk. We take a historical approach by developing a set of measures for this length of time and presenting duration as the natural extension of a series of such measures. All these measures have some use in finance. You should know about them, how to compute them, and when some of them might be used.

Chapter 16 examines convexity, once more in a traditional way, as an equation involving the sum of future payments, present values, time periods, and constants. We use convexity to compute an additional adjustment in the predicted bond price for a given yield change.

Chapter 17 presents a calculus derivation of duration and convexity and uses a Taylor s Series expansion to demonstrate the use of duration and convexity for estimations of percentage change in bond price, given a change in yield. This chapter presents a different development of duration and convexity, which may make more sense to a person who has studied calculus. This approach leads immediately to additional ideas on mathematical applications in finance. These ideas include negative duration and negative convexity.

If you have studied calculus, read all three chapters. They will give you an insight into the historical development of an important concept of fixed-income mathematics and an intuitive idea of where they might be used, as well as the mathematical background for further use. If you have...