The purpose of this paper is to derive an easy‐to‐implement and highly accurate formula to approximate the change in the bond price resulting from a change in interest rates.
The bond price is raised to an infinitesimal power and the Taylor series expansion is applied. Then, using the well‐known modified duration and convexity, the new formula is obtained as a limiting case.
It is proved mathematically and illustrated by numerical examples that the new formula generates better results than both the traditional duration‐convexity and the exponential duration approximation formulas.
The new formula derived in this paper will be used by risk managers to perform stress‐testing on bond portfolios.
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