This question emerged from comments in this feed: OIS rate to build Term structure.
I was wondering how the float leg of an IRS will look like in a post-LIBOR world. Assume the following time-line, where we have today ($t$) as the start of the accrual period and $t+3m$ as the payment date for the cashflow:
In a LIBOR world, the time-$t$ fixing is obviously known at $t$ so we know in-advance what amount we are due to pay/receive in 3 months from now. However, if we instead reference a risk-free rate (RFR) in our swap instead of the LIBOR, at $t$ we only know one fixing of the RFR. However, we need to transform it into a 3m term rate, and the question is how practicioners intend to do this.
It appears to me that there are two (three) main methods to compute the cashflow for this 3m accrual period:
- Backward looking: Observe the daily RFRs from $t$ to $t+3m$ and then compound them in-arrears (for example observe the daily SOFR and compute the 3m rate at $t+3m$ as compounded realized daily SOFR, + spread). However, this means the exact cashflow due at time $t+3m$ is not known at $t$ but only at $t+3m$. In my opinion, the IRS would become what today is simply known as OIS.
- Forward looking (scaled): This would take the time $t$ fixing of the RFR (for example SOFR published that morning, + spread) and "scale it" by the appropriate day count to make it a 3m rate.
- Forward looking (compounded): Same as above, but at time $t$, use the compounded RFR between $t-3m$ and $t$ (for example compounded SOFR + spread).
NB: The last option is that a "forward looking" term rate for overnight rates can be derived from the respective futures market, once these are sufficiently liquid/reliable. But I'd like to ignore that case for the moment.
EDIT: This paper (chapter 3) provides a good overview in analytical form: https://ssrn.com/abstract=3308766.