Using calculus to find bond duration and convexity

More advanced courses in finance and quantitative methods may require you to use calculus to find a bond’s duration (related to the first derivative of price with respect to yield) and convexity (related to the second derivative, so you have to differentiate twice). These allow you investigate how sensitive bond prices are to changes in interest rates.

This worksheet includes the key formulas you need, and example questions with fully worked solutions on finding bond prices, duration and convexity, and using these to estimate the percentage change in price of a bond when the yield changes.

This worksheet was written for students taking MSc courses in Trade and Finance at City University, London, but is suitable for any students taking comparable advanced undergraduate or postgraduate modules in financial mathematics.

If you have comments or queries about this sheet, or are looking for additional support in this area, please contact me.