Is a bond’s maturity-matched rate equal to its par rate of the same duration?
A maturity-matched rate doesn’t have to be a par rate. It’s simply a rate for the same maturity as the bond you’re considering. You could have maturity matched spot rates, maturity-matched par rates, maturity-matched key rates, and so on.
Where or what is a “maturity-matched rate” derived from?
Whatever the appropriate curve is.
If you have a 10-year bond and you want the maturity-matched spot rate, you look at the spot curve and grab the 10-year spot rate. If you want the maturity-matched par rate, you look at the par curve and grab the 10-year par rate. And so on.
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Perfecto again.