Authors: Ioannis Kandylas, Ioannis Demetriou

Title: A method for calculating convexity in discrete fixed-income securities data

Abstract

Bonds are the most important type of fixed-income security for investment. Bonds are usually analyzed by computing the Yield to Maturity (YTM), which is the interest rate that makes the present value of promised bond payments equal to current bond price. The calculation is reversed: the bond price can be found as a function of yield, by the price-yield curve whose slope is a measure of price sensitivity to changes in yield. Convexity is the degree of curvature of a bond’s value-YTM relationship. Whereas duration approximates linearly the bond’s value change for a change in interest, convexity measures how much this change deviates from a straight line. Hence, convexity refines the estimate of bond’s sensitivity to changes in the YTM. Since real YTM data are defined by discrete values that include errors and since convexity is usually lost due to errors, there is no general mathematical function appropriate for this estimation. In this paper we address the question of calculating convexity by a least squares data smoothing technique that makes use of non-negative second divided differences. The numerical results suggest that it is quite suitable for this purpose.