My study was in a Mathematical modelling, we studied much about theory, equations, how to resolve equation, how to implement, but we don't understand well where these equations come from.
My question is not difficult, but not easy to be claire, I'll try to explain. It is about the famous Yield Curve built from a set of Treasury coupon Bonds. On most of book, I see that giving a convenable set of bond, determined by its maturities and coupon rate, one can calculate the yield curve from bond's prices, and reversely prices from yield curve. All of those are explained in mathematical formulas, not difficult to understand.
Things that I don't understand, from this equivalence of yield curve and bond's prices, so what exist before, to determine other? Is yield curve quoted, and people calculate bond's prices from this, or reversely?
I have in my mind 2 scenarios
- The government when issued bonds, they determine every things, bond's coupon rate, bond price, and also the yield curve built in these set (so they quote the bond price?). Each time new bonds are issued, new prices added, yield curve change, people update these new yield curve to use as interest rate risk-free for other calculation. In this scenario, is the government who fully determine the interest rate (yield curve). Also by this scenario, i understand why it is call risk-free since everything are controlled by government, so do its liability.
- The government issue bonds, but do not determine the price. It is then slapped into the market. Traders then buys and sells, these actions determine the bonds prices below the balance demand-offer. These prices so are determined and quoted by the market. So the yield curve equivalently has to change each time bond's prices change. This scenarios help me to see that the yield curve then mirror the economic condition of the market, since it is determined by the market. But also in this scenarios, i don't understand how it can still be called "risk-free" when it is completely random.
Can someone with experiences in the market explain me how that works, from issuer of the bond, what he does, how bonds pass to the market (which market?), how prices is determined, and in this case how use the corresponding yield curve?
If there are a reference links, books (pdf) that also help me a lot.