I have a fixed-float swap valuation to realize. The floating leg is referenced to SOFR with a 10 days lookback. The first coupon has already started, on 01/09/2023, and ends on 01/12/2023. The first coupon fixing is realized on 15/11/2023.
How do I evaluate the first floating coupon interest rate if I want to evaluate the swap MtM on 01/09/2023 or on a later date? (i.e. before the first fixing is realized).
I understand that for later coupons I can evaluate the floating coupons rate with the help of forward rates (constructed from spot rates that I retrieve from my market data provider bloomberg (490 icvs curve)).
Thanks for your help ! :)