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Estimating Bond Futures DV01 from the Cheapest-to-Deliver Bond

Article Quant Q&A · Author: Sithered
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Summary

The note explains how to estimate a bond futures contract’s DV01 from the DV01 of its cheapest-to-deliver (CTD) bond. It gives a conversion-factor adjustment and a small repo-related adjustment: when the net basis is assumed to be zero, the futures DV01 is approximately the CTD DV01 multiplied by one plus repo times the day-count fraction, then divided by the conversion factor.

The example describes a CTD DV01 of 10 cents and says the repo term is a small adjustment. A comment recommends using the forward DV01 rather than a repo-adjusted DV01. The calculation therefore relies on assumptions about the CTD, net basis, repo, and delivery conversion factor; it is an approximation rather than a full treatment of futures basis behavior.

Key ideas

  • The CTD bond’s DV01 is the starting point for estimating the futures contract’s DV01.
  • Adjust the CTD DV01 by the conversion factor and a repo-related term.
  • The stated relationship assumes the net basis remains at zero.
  • A forward DV01 may be preferable to a repo-adjusted DV01.

Tags

FuturesFixed incomeDerivatives pricingRisk management
Full text
# DV01 of bond future from DV01 of CTD


# DV01 of bond future from DV01 of CTD












Is there a way to compute the DV01 of a bond future, from it's underlying cheapest to deliver bond's DV01?

For example, is this correct? : DV01 future = DV01 CTD / conversion factor?

Or any other formula that would give future's DV01?

## Answer by Attack68 (score 4, accepted)

https://quant.stackexchange.com/a/40219

Suppose the CTD DV01 is 10cents. If the CTD yield falls by 1bp then price goes up by 10cents. The price of the future (if the net basis remains at 0) will increase by: $$DV01.Future= (10 \times (1+repo*day.count.frac)) \div conv.factor$$ The repo is a small adjustment.

(See Helins comment about using the forward DV01 instead of repo-adjusted DV01)

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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