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I am aware that OIS is the new reference/risk-free rate for collateralized cashflows. OIS is by definition an overnight rate (annualized, I assume). So once I have constructed my OIS yield curve, what does it actually mean as I go along the different tenors.

For example, would the yield at 5yr represent the fair swap rate indexed against the expected overnight lending rates for the next 5 years. How is interest even calculated on the overnight lending? Would it simply be expected rate*(1/360)?

Just curious about how to view OIS rate that is dated beyond overnight, i.e. longer maturity

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When people say OIS swap they mean an exchange of some sort of fixed cash flow and in return the receipt of daily OIS based on the "Fed Effective Rate" (FEDL01 Index on Bloomberg).

The floating side is always fed effective daily (ACT/360). The fixed side can be any schedule you want, but the default I think is ACT/360 (money market).

The PV of the swap should be 0 (otherwise why would anyone engage in the transaction?)

Here's a screen shoot from Bloomberg:

enter image description here

I can get you more details if you need, just let me know.

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