DV01 of Zero-Coupon Bonds on a Flat Zero-Rate Curve

Summary

The document asks how to calculate the DV01 of one-year and ten-year zero-coupon bonds, each with one million in principal, when the entire interest-rate curve is zero. It reasons that the bond price equals principal at a zero discount rate and that duration equals time to maturity, leading to a ten-to-one comparison in rate sensitivity.

The central lesson is that a zero-coupon bond’s price is its discounted maturity payment, and its DV01 depends on both price and duration. The question raises a useful distinction between discounting at a market yield and using a risk-free rate. However, it does not include an answer or resolve whether the stated formulas and assumptions are appropriate for the intended pricing convention. The comparison is therefore presented as a questioner's derivation, not as a verified result; conventions such as compounding and the exact DV01 definition can also affect the calculation.

Key ideas

• A zero-coupon bond's value is found by discounting its single maturity payment.
• For a zero-coupon bond, duration is tied to its time to maturity.
• The document compares rate sensitivity for bonds with different maturities under a zero-rate curve.
• The calculation depends on the discount rate and the convention used to define DV01.

Tags

# DV01 of 10-Year vs 1-Year Zero-Coupon Bond at 0% Flat Interest Rate Curve


# DV01 of 10-Year vs 1-Year Zero-Coupon Bond at 0% Flat Interest Rate Curve












As the title suggests, what are the DV01s of a 1 million principal zero-coupon bond with 10-year and 1-year TTM with an assumed 0% flat interest rate curve. I understand that the duration for both bonds is just their TTM because all the principal is received at maturity (definition of duration). However, should the current price of the bond be same as the principal because of the 0% flat interest rate curve?

If the previous assumption is correct, this would lead me to a DV01 of the zero-coupon bonds using the formula:

$DV01_{10Y} = Duration * Principal * \frac{\Delta r}{(1+r)^{10}} = 10 * 1mil * \frac{0.0001}{(1+0)^{10}}$

$DV01_{1Y} = Duration * Principal*\frac{\Delta r}{1+r} = 1 * 1mil * \frac{0.0001}{1+0}$

And therefore the DV01 of the 10-year is 10 times that of the 1-year? Honestly, it does make sense to me, but I am just a bit suspicious of the price of the zero-coupon bond being the same as the principal, because it is usually the yield that is being used to discount and not the riskless rate.

PS. If this is too simple, please feel free to vote to close.

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