I have a question concerning interest yield curves. Many institutions use the Libor-swap rate curve as a yield curve. Let's be precise and say that we want the yield curve to be the curve that gives us the rate at which a well-rated bank can lend money for any tenor. When the tenor is less than 12 months then that's basically the Libor rate of this tenor. But when the tenor is greater than 1 year, then why should this be the swap-rate? Is there a theoretical justification that the swap-rate corresponds really to this rate?
Nobody is saying that the swap rate is used as such in calculations of funding rates. What happens is that the yield curve is constructed using a series of instruments, together with their current market prices.
These instruments are usually short term futures, deposits, ... and swaps. The yield curve is constructed by solving so that each of these instruments returns the current market price. For practical reasons this is usually done by bootstrapping, i.e. trying to find the front of the yield curve to satisfy the shortest maturity and then using that to determine the curve further back.
So swap and swap rates are used mostly because they are the most liquid long-term instrument, but people could choose to calibrate using other instruments if they were quoted on the market.
Recall that an interest rate swap has two legs, one fixed and one floating, each paid by one party to the transaction.
Now, assume you go to a big bank like JPM, and want to borrow $100MM at fixed rate. JPM will have to fund that position, which because it is a big bank it will do at floating interest rates.
But maybe JPM is worried about the effect such interest rate variation has on its Sharpe ratio, so they want to lock in the profits they made from arranging the loan with you. In this case, they will swap fixed for floating and be able to book the profits with certainty (modulo credit risk).
Therefore, the price of your loan was ultimately driven by JPMs cost of a fixed-float swap.