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Estimating a Zero-Coupon Bond’s Rate Sensitivity with a One-Basis-Point Bump

Article Quant Q&A · Author: miababy
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Summary

The document gives a simple way to estimate the interest-rate sensitivity of a zero-coupon bond. It compares the present value of the bond at the current yield with its present value after increasing the yield by one basis point. The difference is used as the bond’s dollar change for that small rate move, or a local dollar delta under the stated convention.

The example uses a five-year zero-coupon bond with a notional of five million dollars and a starting rate of 2.10%. It reports a value difference of $2,206 after shifting the rate from 2.10% to 2.11%. This illustrates repricing the discounted cash flow rather than applying a separate coupon-based formula. The result depends on the assumed annual compounding and the particular one-basis-point bump; it is an estimate for that move, not a general sensitivity stated in standardized units such as DV01 without specifying sign and convention.

Key ideas

  • A zero-coupon bond’s value is its maturity payment discounted at the prevailing rate.
  • A small rate sensitivity can be estimated by repricing after a one-basis-point yield increase.
  • The example uses a five-year maturity, five-million-dollar notional, and a starting rate of 2.10%.
  • The reported value difference is $2,206 for the specified bump.
  • The estimate depends on the compounding and bump conventions used.

Tags

Fixed incomeRisk management
Full text
# What is the delta of a zero coupon bond?


# What is the delta of a zero coupon bond?












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%.

## Answer by dm63 (score 1)

https://quant.stackexchange.com/a/36154

The delta is (value of bond) - (value of bond if rates go up 1bp) =5mm/(1.0210)^5 - 5mm/(1.0211)^5 =$2206

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