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Deriving Gross Basis for a Deliverable Bond Futures Contract

Article Quant Q&A · Author: user65739
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Summary

The document checks the gross basis formula for a bond eligible for delivery into a futures contract. It defines gross basis as the bond’s clean price less the futures price multiplied by that bond’s conversion factor. It then asks whether this expression follows from subtracting the futures invoice price from the bond’s dirty price.

The stated dirty price adds accrued coupon interest to the clean price, while the invoice price adds the same accrued interest to the futures price adjusted by the conversion factor. The accrued-interest terms therefore cancel, leaving the clean-price-minus-adjusted-futures-price expression. This is an algebraic identity under the definitions given. The note does not discuss net basis, financing or carry, delivery options, or how to choose among eligible bonds.

Key ideas

  • Gross basis is defined as the deliverable bond’s clean price minus futures price adjusted by its conversion factor.
  • Dirty price equals clean price plus accrued coupon interest under the definitions provided.
  • The invoice price adds accrued interest to the futures price multiplied by the conversion factor.
  • Subtracting invoice price from dirty price cancels the accrued-interest terms.

Tags

Fixed incomeFuturesCommodities
Full text
# Gross Basis - Bond Futures


# Gross Basis - Bond Futures












Just want to confirm - Gross Basis for Bond A, deliverable into a Future:

Gross Basis [A] = Clean Price [A] - Futures Price x CF [A]

where CF [A] = Conversion factor of Bond A.

Is this due to: Gross Basis [A] = Dirty Price [A] - Invoice Price [A]

Where: Dirty Price [A] = Clean Price [A] + Acc Int [from last coupon to now]

Invoice Price [A] = Future Price [A] x CF [A] + Acc Int [from last coupon to now]

simplifying =>

Gross Basis [A] = Clean Price [A] - Futures Price x CF [A]

Thanks

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.