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Say I'm considering a long maturity fixed rate swap, for instance 20 years paid semi annually. Now I want to find the fixed rate for this hypothetical swap. I understand that this fixed rate is going to be predicated on discount rates based on the current term structure of the LIBOR yield curve (or whatever reference rate).

Because of the very long maturity of the swap, however, I'll need to have LIBOR discount rates for payments that will be made very far in the future. Now it may be the case that LIBOR rates are only quoted up to 1 year.

So I need the discount rate for the final payment at the end of the swap, in the distant future, to compute the swap fixed rate. However I don't have a LIBOR discount rate for that payment because it isn't quoted up to that maturity.

To compute the swap fixed rate, how do I find the appropriate discount factors beyond what's quoted in the LIBOR curve?

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    $\begingroup$ This question seems very basic. Have you heard of Eurodollar futures? The extend out for several years. Have you seen how comparison of the pricing of two risk free zero coupon bonds of different maturities (say 63 and 60 months) can give insight into future risk free 3 month interest rates 60 months from now? Quarterly interest curves that stretch out for decades are usually constructed by combining information from such disparate sources. HTH. $\endgroup$ – noob2 Jun 22 '16 at 15:47
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You use quoted market swap rates. Once you reach the end of the Eurodollar strip, about 3 years out, swaps are the most liquid source of information about expected future Libor rates. Since swap rates are essentially long-term averages of Libor rates, you have to solve for the implied forward Libor rates (sometimes called "bootstrapping the yield curve", but more commonly now it's a global solving problem).

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