I am trying to understand how the Fix rate on a OIS trade is calculated at trade initiation. I understand this process for a Fixed V LIBOR trade non collateralized ( discount and projection curve are the same ) but get somewhat confused here Particularly in reference to the curve that is used, what are the instruments used to build from, how is it built, is the same curve then used for discounting the cashflows as projection.



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The idea of pricing a Fixed-to-Float IBOR swap is very similar to that of an OIS swap. The only difficulty is determining the present value of the OIS leg since now each payment depends not just on one (in-advance) IBOR fixing but a (daily) compounded OIS rate. That means the final value of an OIS payment is not known until all fixings have occurred. That's where the curve comes in: Depending on the currency, the OIS curve either consists of a mix of outright OIS swaps on the front end (~6 years) and IBORvOIS basis swaps for the long end (combined with IBOR swaps to get a 'fixed' equivalent) or purely outright OIS swaps. An example for the former is USD and for the latter EUR. I haven't seen an OIS curve that uses OIS futures, although they do trade. The method of stripping the curve is similar to any other curve with the additional difficulty of correctly pricing the floating OIS leg.

Example: Say you have a 1y EUR OIS swap with EUR collateral. You project cashflows using the EONIA curve and since you're using EUR collateral you will discount cashflows with the same curve. Now if your collateral were GBP things get more complicated. Because now you not only need to consider EONIA but also SONIA, as well as the basis between EUR and USD, i.e. you'd need a CSA adjusted collateral curve (refer to here for more details). It gets even more tricky if you can choose between a basket of collateral currencies (say USD, GBP and EUR), for an overview refer to here.


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