I was hoping someone could help me better grasp the process for deriving the par curve. From my understanding, the forward curve is derived from the spot curve, which is derived from the par curve through bootstrapping. A par rate is the coupon rate the US Treasury would set on a bond hypothetically issued at par today.
So, my question is:
If the par curve is obtained before the spot curve is, and a bond trading at par has its coupon = its YTM, then how does the Treasury actually determine what that coupon should be? If it needs to set a coupon = the YTM of that par bond, where does that YTM come from and how is it determined?
More broadly, I guess I’m a little cloudy on the order of events that determine the bond prices we actually see in the markets. As I understand it, bond prices are arrived at through discounting using treasury spot rates plus a spread for risk (except bonds with options, which use binomial interest rate tree models to arrive at prices). Those spot rates are bootstrapped from the par curve, and the par curve is composed of the coupon rates the US Treasury would hypothetically set on newly issued par bonds. But, by definition a bond trading at par has coupon = YTM, so how does the Treasury determine what that YTM is that it needs to set the coupon equal to to make it = par?
Let me know if there are any issues with my logic. Any help is appreciated. Thanks.