Par Curve & Spot Curve

I seem to have forgotten how this works, so could someone please clarify if my understanding is right?

Par Yield: Compute by using a theoretical coupon-paying bond (that doesn’t exist in real life), where NPV = FV, the coupon rate = par yield, and the respective spot rates are used for each cash flow. Find par yield.

Spot curve: made up of (primarily) the YTM of on-the-run zero coupon bonds. You can derive this with the help with the par curve relationship above

So for a corporate bond, the discount rate for each cash flow is zn + premium ??

I wrote an article on the par curve, the spot curve, and the forward curve:

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In a nutshell, the par curve gives the YTM for coupon paying bonds, and the spot curve gives the YTM for zero coupon bonds. You can derive the spot curve from the par curve by bootstrapping.

You can discount corporate bonds using the par rate plus a spread; that spread is called the nominal spread. You can also discount the individual cash flows from a corporate bond using the par curve plus a constant spread; that spread is called the Z-spread (or zero-volatility spread).

Amazing as always - thank you! It’s coming back to me :slight_smile: