A Revised Closed-Form Solution for Bond Convexity

Abstract

Since duration works best for only small changes of the interest rate, convexity helps to improve the estimation accuracy. Traditionally, convexity is displayed with a formula, which depends on the number of outstanding payments. Closed-form solutions do exist, typically building on the work of Chua (1984). Based on the slightly different approach of Kruschwitz and Schöbel (1986a), who also developed a closed-form equation for the duration, I derive a shorter closed-form solution for convexity than previously known.

Keywords: Bonds, Duration, Convexity, Closed-Form Solution

JEL Classification: G12