Bond price and duration

How it works

The price is the value of every coupon and the final repayment, each discounted at the yield to maturity. Macaulay duration is the average time to those cash flows, weighted by their value; modified duration turns it into the percentage change in price for a one-point change in yield; convexity measures how that sensitivity itself changes. DV01 is the price change for one basis point. The solid line is the price at each yield, the dashed line what duration alone predicts: the gap between them is convexity.

Assumptions

A plain bullet bond priced on a coupon date (no accrued interest), coupons paid annually or semi-annually, the same yield for every cash flow, no default. Maturity is rounded to whole coupon periods.

For information and education only. Not investment advice.