Power law bond price and yield approximation

Abstract

Purpose

This paper determines a simple transformation that nearly linearizes the bond price formula. The transformed price can be used to derive a highly accurate approximation of the change in a bond price resulting from a change in interest rates.

Design/methodology/approach

A logarithmic transformation exactly linearizes the price function for a zero coupon bond and a reciprocal transformation exactly linearizes the price function for a perpetuity. A power law transformation combines aspects of both types of transformations and provides a superior approximation of the bond price sensitivity for both short-term and long-term bonds.

Findings

It is demonstrated that the new formula, based on power-law transformation, is a much better approximation than either the traditional duration-convexity approximation and the more recently developed approximations based on logarithmic transformation of the price function.

Originality/value

The new formula will be used by risk managers to perform stress-testing on bond portfolios. The new formula can easily be inverted, making it possible to relate the distribution of prices (which are observable in the market) to the distribution of yields (which are numerical solutions that are not directly observable).

Citation

Barber, J.R. (2022), "Power law bond price and yield approximation", Journal of Risk Finance, Vol. 23 No. 1, pp. 14-31. https://doi.org/10.1108/JRF-10-2020-0217