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Why Futures and CTD Forward Prices Share the Delivery-Date Value

Article Quant Q&A · Author: VanillaCall
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Summary

The document addresses an apparent carry mismatch between a bond futures price observed on its last trading day and the cheapest-to-deliver bond’s forward price at the last delivery date. It asks whether the bond forward should instead be valued to the futures contract’s last trading day.

Under the stated assumption that the contract has no optionality, the response says the two compared prices are both expressed in money at the last delivery date. The futures price used after trading ends is therefore already on that delivery-date value basis, so no carry mismatch arises from comparing it with the CTD forward to delivery. This is a concise conceptual answer rather than a detailed derivation. It does not discuss how optionality, financing conventions, delivery choices, or other contract features might affect the comparison.

Key ideas

  • The comparison assumes the futures contract has no optionality.
  • The CTD forward price is valued at the last delivery date.
  • The futures price fixed on the last trading day is also treated as a delivery-date value.
  • On these assumptions, the apparent carry mismatch does not require forwarding the CTD only to the last trading day.

Tags

FuturesFixed incomeCarry
Full text
# Futures vs Forward (Last Delivery or Last Trading Day)


# Futures vs Forward (Last Delivery or Last Trading Day)












For all contracts except the 2-year and 5-year, the last trading day is 7 business days before the end of the contract month.

If we assume there is no optionality, isn't there a mismatch in carry. Futures price is set on the last trading day when it stops trading and that's the price you use until the last delivery date. For the CTD bond, you can calculate the forward to the last delivery date. So what you have is the following:

CTD Forward on last delivery - Conversion Factor * (Futures on last trading day)

There is a mismatch in carry.

Would it be fair to calculate CTD forward to the last trading day to match that of futures?

## Answer by Antoine Conze (score 2, accepted)

https://quant.stackexchange.com/a/49738

Assume there is no optionality. Let $T$ = last delivery date. "CTD Forward on last delivery" is a price in time $T$ money. "Futures on last trading day" is also a price in time $T$ money. There is no mismatch in carry.

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.