# What is the delta of a zero coupon bond? [closed]

I understand that zero coupon bond changes as interest rates change. But I am unsure of how to get the delta. Say I buy a 5Y zero coupon bond with notional amount 5M USD. How do I calculate the delta? Interest rates are 2.10%.

## closed as off-topic by Helin, LocalVolatility, Quantuple, JejeBelfort, amdoptSep 25 '17 at 17:46

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• Do you mean duration? – Bob Jansen Sep 22 '17 at 16:22

The delta is (value of bond) - (value of bond if rates go up 1bp) =5mm/(1.0210)^5 - 5mm/(1.0211)^5 =$2206 • We can also use the equation$\frac{\partial P}{\partial y}=\frac{1}{1+y}MacD \cdot P(y)$. Here$y=0.021$,$MacD = 5$years since it is a ZCB,$P(y)=\frac{5,000,000}{(1+0.021)^5}\$ The result, after division by 10000 to convert to "per basis point" is 2206.9 – Alex C Sep 23 '17 at 12:26