FRN discounted with a Government curve


How do you calculate, for an FRN, the Discount Margin and the Modified Duration if you generate the cash-flows with LIBOR 3M + x bp and discount the cash-flows with the Government Curve (used as the risk-free curve)? LIBOR are nor risk-free.

Seriously what’s your qs ? LIBIR + X, what is X ?
Where does the DISC MARGIN appear ? In the coupon or in the discount rate ?

If you can find answers to the above your query stands solved. These are taught in Level I ( I am not being rude )

I mean, the cash-flows in the FRN is LIBOR + a spread X. Then, using another curve to discount the cash-flows. Here I would like to use a risk-free discount curve = a Government curve + Discount Margin.
In the literature all seems to discount with the same LIBOR curve. But LIBOR after 2008 is not risk-free.

Interbank Swaps are now discounted using OIS (or SOFR, ESTER … the new rates). Before Swaps was discounted with the Swap curve. Same here!

Since FRN are bonds, they should be discounted during a risk-free bond curve, that’s were the Government curve comes in.

LIBOR may be discontinued after this year but not the other ederenxe rates. Why such OIS are used in the first place ?

A. They are customisable
B. OIS rates are readily avl. almost for all maturities
C. They are NEAR risk free

G - Sec. may not be readily avl for the required maturity. Secondly, unless recently issued they may not be liquid as well. So from that perspective reference rates do a better job as disc. factor.

QM is the X spread that the FRN payer must pay. That is pre decided against the Fixed rate