Since, as far as I understand, an Overnight Index Rate is a set in arrears, i.e. it is published in the morning after the night to which the rate applies, then I would have thought that we should be take into account convexity adjustment when constructing an OIS curve.
However, I have recently come across the following statement:
"The OIS market trades OIS coupons against fixed or Libor coupons. The key point here is that the market prices are for coupon rates, not the daily index rates that are compounded to calculate the coupon rate. So convexity effects due to unnatural payment dates and compounding are already built into the corresponding tenor-specific forward rate curve for this product type."
I am not sure I understand the argument it that statement.