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Estimating Bond Price Changes with Duration and Convexity

Article Quant Q&A · Author: Chandramouli Raman
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Summary

The question asks how to estimate the price change of a long-term coupon bond after its yield rises, using modified duration alone and then adding convexity. It supplies the bond’s maturity, par value, coupon, starting yield, modified duration, convexity, and the yield change, but does not include an answer or worked calculation.

The useful concept is that duration provides a first-order approximation of the percentage price response to a yield move, while convexity adjusts for the curvature in the price-yield relationship. The poster is unsure how to proceed because Macaulay duration is not supplied, although modified duration and convexity are given. The document therefore identifies a common bond mathematics question and the distinction between the two approximations, but offers no numerical result, derivation, or discussion of approximation error or conventions.

Key ideas

  • Modified duration approximates a bond’s percentage price change for a small yield change.
  • The duration estimate can be refined by adding a convexity adjustment.
  • The question provides modified duration and convexity but does not show the requested calculations.
  • Macaulay duration is not needed to apply a price-change approximation when modified duration is already known.

Tags

Fixed incomeDerivatives pricingRisk management
Full text
# How to calculate the new price of a bond using duration rule and duration with convexity rule?


# How to calculate the new price of a bond using duration rule and duration with convexity rule?












A bond with a 30 year maturity, par value of $1000 and is 8% p.a. coupon is selling at an yield to maturity of 8% p.a. The modified duration of the the bond at its yield is 11.26%, and its convexity is 212.4. If the bond's yield increases from 8% to 10%, how to calculate the new price of the bond using the duration rule and how to compare this answer with one calculated using the duration with convexity rule.?

I know the formula for Modified Duration is -1/(1 + y) * Macaulay Duration and formula for convexity is (Modified Duration)^2 - ▲ Modified Duration / ▲ y.

But since Macaulay's duration is not given, I am unable to proceed in solving this problem. Any solution would be highly helpful.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.