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Bond Futures Roll Costs, Carry, and Delivery Options

Article Quant Q&A · Author: Menny Yedid
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Summary

The document explains why the calendar spread between nearby German government bond futures can differ from zero and why rolling a position has a cost. Ignoring delivery options and margining, a bond future can be approximated as a forward whose fair value reflects the underlying bond price and the cost or benefit of carrying it. The carry comparison includes accrued interest and financing over the contract period.

The spread may also change when the cheapest-to-deliver bond differs between maturities, since the deliverable and its carry can change. Even with the same underlying bond, later delivery entails additional interest accrual as well as additional financing expense. Trading flows can move the spread away from a carry-based fair value; concentrated demand to roll may make the later contract relatively richer. The explanation is qualitative and gives no calculation of the stated spread or a universal estimate of roll cost. Delivery options and margining are excluded from the simplified forward framing, and delivery options may materially affect the spread depending on interest rates.

Key ideas

  • A bond futures calendar spread reflects differences in underlying bond prices and carry across maturities.
  • Carry balances accrued interest against the financing cost of holding the bond.
  • The cheapest-to-deliver bond can differ across contracts and change their relative values.
  • Order flow from concentrated rolling can move a spread away from its carry-based fair value.
  • Delivery options and margining can affect the spread beyond the simplified forward approximation.

Tags

Fixed incomeFuturesCarryExecution
Full text
# what is the cost for rolling 5 year german future?


# what is the cost for rolling 5 year german future?












im looking at the bobl future for september and for december and see 1.8 basis points difference. i wanted to know why there is this gap? and if im holding a position in september and want to roll it to december what is my cost? thank you

## Answer by Helin (score 1)

https://quant.stackexchange.com/a/20664

Ignoring delivery option and margining, then you can treat bond futures like a bond forward. Like any forward contract, fair values of bond forwards are determined by $$ \text{forward price} = \text{spot price} - \text{carry}. $$

The calendar spread is therefore nonzero for several reasons:

- The underlying cheapest-to-delivers might be different, so both spot prices and carries differ for the two contracts;

- Even if the underlyings are identical for both contracts (so the spot price is the same), carries can differ – for the December contract, you'd earn three more months worth of accrue interest, but must also pay three more months worth of financing cost.

Flows and other factors can also drive the roll away from fair value. For example, if a lot of longs decide to roll together, then the back contract (December) will no doubt richen relative to the front contract, cheapening the roll.

Other factors such as delivery options can also play a major role in determining the value of such calendar spreads, depending on the interest rate environment.

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.