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Is it possible to bootstrap the new ESTER and SOFR term structures in Quantlib? More in general, does the process work as the usual one? Given these are simple indices that are published on a daily basis I am not sure how the bootstrapping would work since there are no swaps on ESTER for example.

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I'm not sure about ESTER but for SOFR, the FED has stated that the way to get forwards is derive them from SOFR futures.

https://www.federalreserve.gov/econres/notes/feds-notes/indicative-forward-looking-sofr-term-rates-20190419.htm

See section A.2 in this paper:

https://www.federalreserve.gov/econres/feds/files/2019014pap.pdf

The answer looks to be similar for ESTER as well, the hope is by the decommissioning of LIBOR, swap and or futures markets will be liquid enough.

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