Pricing Bond Futures Calendar Spreads with Repo and Switch Optionality

Summary

The document asks what drives the price of a bond futures calendar spread when both contracts share the same deliverable basket and cheapest-to-deliver bond. The accepted answer identifies the forward repo rate implied by term repo rates extending to each contract’s delivery date as the primary factor. Differences in those repo rates can reflect the cheapest-to-deliver bond’s specialness, rather than movements in the money-market rate curve.

The answer also identifies delivery-basket switch risk as a source of optionality when the cheapest-to-deliver bond might change. In that case, the back contract can be more sensitive to changes in implied volatility than the front contract. The suggested analysis separates the spread into forward repo and switch optionality components. It is a concise conceptual explanation; it supplies no pricing formula, quantitative example, or discussion of other market conditions that could matter.

Key ideas

• Forward repo rates to each contract’s delivery date are a main driver of the calendar spread.
• Repo differentials can reflect specialness in the cheapest-to-deliver bond.
• The relevant repo rates are tied to the assumed cheapest-to-deliver bond.
• A possible change in the cheapest-to-deliver bond introduces switch optionality.
• The back contract may be more sensitive to implied volatility when switch risk is meaningful.

Tags

# Bond futures - calendar spread pricing


# Bond futures - calendar spread pricing












I am looking on literature and models on pricing a bond futures' calendar spread. assuming the basket of deliverable bonds is the same and the ctd is the same, what are the factores determining the price of the spread?

Thanks

## Answer by paralogical (score 2, accepted)

https://quant.stackexchange.com/a/8824

In your scenario, the main factor behind the spread would be the forward repo rate implied by the term repo rates on the ctd, one termed to the delivery date of the front contract, the other termed to the back contract. In the current rate environment this will have little to do with the term structure of mm rates. Instead, any difference between the repos will reflect specialness in the ctd. For example, the ctd might be the on-the-run bond (ie, the most recently auctioned bond) now, but it won't be when the back contract becomes the front contract; this will be anticipated in the repo differential.

If there is meaningful probability of switch risk, then the switch optionality will also effect the spread, with the back contract being more sensitive to changes in implied volatility than the front contract.

In summary, you can analyse that spread into forward repo and switch optionality factors.

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.