This is from book Modern Derivatives Pricing and Credit Exposure Analysis page 22
https://www.amazon.com/Modern-Derivatives-Pricing-Exposure-Analysis/dp/1137494832
In an OIS, two parties exchange a fixed coupon (paid annually for longer-dated
swaps and as a single payment at maturity otherwise) against the daily fixed and
compounded overnight rate. Daily compounding means that the rate paid at the
end of period i = 1, . . . ,n is given by
$$R_i = \dfrac{1}{\delta_i}\left[\prod\limits_{k=1}^{n_i}(1+F^{ON}(t_{i,k-1},t_{i,k})\delta_{i,k})-1\right]$$
Here $df^{ON}$ is dicounting factor.
I cannot understand that
Here is the $F^{ON}(t_{i,k-1},t_{i,k})$ the
overnight index rate
(like Fderal funds rate)?What the OIS rate or OIS curve mentioned at last in the formula? I think that it is the swap rate $c_0.$
What is OIS quoting? Do we first have the OIS quoting or first have the overnight index rate quoting in the market? From the final formula we can see that it is not related to the overnight index rate $F^{ON}(t_{i,k-1},t_{i,k}).$ And if we already had a the quoting of OIS rate, then from the relation between OIS and overnight rate, there will be a restriction of series of overnight rate? Or OIS rate is quoted from the forward overnight rate?
Can anyone clarify those of my confusions?