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I'm trying to bootstrap the new F-TIIE curve for mexico. It is an overnight curve which fixings are 1 day forward rates published daily by the central bank of Mexico. On holidays, the last fixing is taken for past dates. It has a settlement day of 1. Does the ql.OvernightIndex object from QuantLib have this kind of behaviour? Thanks!

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That's not the job of ql.OvernightIndex in the library, it's the job of the coupon. The index only tells you the fixing for a given date, if available.

The coupon does the work of accruing the fixing for Friday for the three days until Monday; it currently needs some changes to manage the case in which, like for Mexico, the coupon might start or end on a holiday. It will probably be fixed in release 1.35.

Finally, if by "settlement days" you mean that Wednesday's fixing correspond to the forward rate between Thursday and Friday, that's already implemented. Instead, if by "settlement days" you mean lookback days (i.e., on Wednesday you use Tuesday's fixing), this is proposed in https://github.com/lballabio/QuantLib/pull/1985 and will also be part of release 1.35.

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