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I'm reading a book on swaps and author mentions in the typical attributes of swaps:

"Discount curve: For present-value calculations (say, to calculate the current market value of the swap), what interest rates will we choose? And because interest rates vary by term, and a yield curve conveys a whole set of rates at once, what yield curve shall we reference for this swap? Note that the discount curve need not be the same as the pricing curve."

What does he refer to when differenciating "pricing" and "discount" curves?

My understanding is that for the floating leg, we just source a yield of a yield curve for the calculation of accruals on coupon dates (aka "pricing" curve).

But then I get lost, would we use another yield curve for discounting (for present swap market value)? Any clarification would be helpful!

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    $\begingroup$ Yes, it sounds lthat in this (not well written) paragraph, "pricing curve" refers to the projection curve (the most common name for the curve used to project an index used to set floating coupons). Sometimes I've also seen it called "coupon curve". On the other hand, "discount curve' is a pretty common name. I've also seen it called "financing curve". In the past, many people assumed that a swap was financed at 3mo libor, i.e. that these 2 curves were the same. But it's not quite accurate, so instead most people now use a "multicurve". $\endgroup$ Jun 7 at 2:40
  • $\begingroup$ Why do they call it "financing curve"? Would this be the same as "funding curve"? Wouldn't this just be the curve used to discount the cash flows for present value purposes. Thank you $\endgroup$
    – F0l0w
    Jun 9 at 4:24
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    $\begingroup$ Yes, that's correct; as Dimitri wrote above, they also commonly call it "discount curve", and this is indeed the curve you'd use to discount the cashflows that you have previously projected by the "projection / coupon" curve. $\endgroup$
    – KevinT
    Jun 9 at 7:01
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    $\begingroup$ yes, I have also seen "funding curve" in some model documents, meaning the same thing as discount curve or financing curve. $\endgroup$ Jun 9 at 10:37

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