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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?


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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.

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