Given that the longest tenor for LIBOR in 12M, what rate do we use to discount a cash flow due in, say, 18 months? Some suggest that we use the 12M rates for 1 year and 2 year to interpolate, but these rates assume that there will be a payment at the 12 months point, whereas our cash flow doesn't.
It seems to me that we need to model how the risk premium / spread changes as a function of Tenor (and possibly maturity) and then apply this to calculate appropriate 18M rate. For example, say the difference between 6M rate at 6 month and 12M rate at 1 year is 50bp, then (assuming additive relationship for simplicity of exposition) we would then add this 50bp to the 12M rate at 1 year to arrive at a rate for discounting the cash flow at 18M. (In effect, this assumes that extending the liquidity horizon by 6 months from 1 year to 18 months cost the same a extending it by 6 months from 6 month to 1 year).
However, I haven't really seen this being done / discussed in the literature. How is this done in practice?