Is formula (1) correct?
Yes, follows from first definition - floater with deterministic spread is composed (sum) of two components: (1) pure floater and (2) deterministic coupon strip via contractual spread payment.
Is formula (2) correct?
Yes, by taking the derivative of an exponential function.
what other case where duration of floating rate bond not ...
I am a co-author of that paper. You may want to check out FinancePy which is a beta version of a finance library where I have implemented the code for calculating the discount margin. Here is an example Jupyter notebook that reproduces (almost exactly) a Bloomberg example.
I may be missing something, but I think you're overcomplicating it. You don't need discount margin and all that jazz.
The clean price (entered in upper left corner) is 100.311% The face value (entered in the lower right corner) is 1,000 M. So "Principal" (next row below face value) is 1,003,110.00.
Now for the accrued. You see on the left that ...
I don't have enough repuation to commnet, but I think it is a general cashflow discount model for bond pricing, and the formula looks wrong. The last item should be discounting of principal and last period coupon, which should be like this:
PER here refers to coupon payment frequency. FV definitely cannot be divided by frequency.
This is not how most people calculate the yield of a floater.
The way most people calculate the yield of a floater is:
1 for each remaining unset coupon, project the values of the index that will be used (such as 3Mo LIBOR, daily SOFR, SONIA, ESTR, etc - see Forecast 3m LIBOR USD. Budget purpose for example); and project the coupons. For example, if a ...
A floating rate bond trading at par is more like an academic formulation rather than what you would observe in reality.
If there were only one yield curve and the bond has no credit spread, that in theory (on reset dates) the forwards would exactly match the equivalent discount factors and so compounding and discounting at the same rates would offset each ...