How Swap Rates and Long-Term Forward Rates Are Market-Determined
Summary
The document explains that medium- and long-term Libor swap rates are established through market participants’ valuations of future floating-rate cash flows. It addresses why these rates cannot simply be derived from Treasury or corporate yields, and why treating swaps and forward rates as mutually derived creates a circularity.
Its replication perspective is to represent Libor exposure with a series of forward rate agreements funded on a separate funding curve. Swap prices therefore reflect both expected future Libor fixings and counterparty risk under this framework. The explanation emphasizes that Libor had become an index correlated with, but distinct from, actual funding costs. It is a conceptual answer rather than a worked pricing example, and it does not specify market conventions, curve-construction procedures, or how the approach changes across collateral and discounting regimes.
Key ideas
- Swap rates reflect market valuations of future floating-rate cash flows.
- Libor swap prices combine expectations about future fixings with counterparty-risk effects.
- A separate funding curve is used to discount cash flows in the described framework.
- A series of funded forward rate agreements can replicate exposure to Libor fixings.
- Libor fixings may be correlated with funding costs without representing those costs directly.
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Full text
# Where do swap rates and/or long-term forward rates come from? # Where do swap rates and/or long-term forward rates come from? I apologize if this is supposed to be obvious, but ... . Libor spot rates are quoted up to a year, beyond that one can use Eurodollar futures to continue to build the curve. Let's say up to 3 years. Beyond that one can ... well that is what I don't know. Google says "benchmark swaps", but that is the "chicken or egg" problem. Presumbably swap rates can be derived from Libor forward rates and vice versa. But where are they coming from? It can't be Treasuries due to lack of AA credit risk. It can't be corporates. They're not quoted with the BBA (unless I'm wrong). So if you had to trade the first and only swap in the world, where would you get the swap rate for say 5 to 30 years? ## Answer by Phil H (score 7, accepted) https://quant.stackexchange.com/a/4326 The short answer is that Libor swap rates come from the market. They represent a series of cashflows in the future whose value is determined by the fixing, which the market participants have their own valuations of. Since the actual cash flows are now discounted using a separate funding curve, the swap prices embed both a prediction of future fixings and a measure of counterparty risk. Libor no longer represents the actual cost of funding in the market, so Libor instruments involve buying or selling exposure to this Libor fixing index, which is now only correlated to funding costs. You are asking for the arbitrage path/replication basket, for which there is only a series of FRAs funded with your funding curve - nothing else will give you the Libor exposure you need in the resulting basket. Swaps are the market's medium to long term interest rate instrument.
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.