Coupon Bond Duration and Convexity Analysis

Coupon bond duration and convexity are the primary risk measures for bonds. Given their importance, there is abundant literature covering their analysis, with calculus being used as the dominant approach. On the other hand, some authors have treated coupon bond duration and convexity without the use of differential calculus. However, none of them provided a complete analysis of bond duration and convexity properties. Therefore, this chapter fills in the gap. Since the application of calculus may be complicated or even inappropriate if the functions in question are not differentiable (as indeed is the case with the bond duration and convexity functions), in this chapter the properties of bond duration and convexity functions by using elementary algebra only are proved. This provides an easier way of approaching this problem, thus making it accessible to a wider audience not necessarily familiar with tools of mathematical analysis. Finally, the properties of these functions are illustrated by using empirical data on coupon bonds.