Why Swap Spreads Are Quoted Against Treasury or Swap Curves
Summary
The document asks how swap rates relate to a textbook par-rate calculation and why market participants quote spreads against Treasury or swap curves. The response focuses on quoting conventions rather than deriving the swap rate formula. Historically, US government bonds were more liquid than swaps, and dealers often hedged with Treasuries; corporate bond spreads to Treasuries also gave investors a quick, imperfect comparison with government debt of similar maturity.
The answer describes this convention as shaped by market history and changing liquidity. It says swaps have become more liquid in many parts of the curve, and trading them can avoid some repo and bond-specific complications. Benchmark choice still varies by market and issuer: debt spreads are quoted against a reference curve to help investors assess relative value. The explanation is explicitly framed as an informed opinion and does not fully address synthetic replication, discounting conventions, or the modern technical drivers of swap spreads.
Key ideas
- Treasury liquidity and dealer hedging historically encouraged quoting swaps as spreads to Treasuries.
- Corporate issuers use benchmark spreads to help investors compare debt with reference instruments.
- Swap liquidity has increased in many curve segments, affecting prevailing market conventions.
- Benchmark choice varies across markets and issuers.
- The response gives historical context but does not fully derive swap pricing or swap-spread mechanics.
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Full text
# Are Swap Spreads derived the treasury curve?
# Are Swap Spreads derived the treasury curve?
I'm trying to learn more about how swaps are used from a practitioner standpoint, it seems often people will quote spreads to swaps vs treasury curve (which is what I'm more used to).
But also, in CFA Level 2, there is a discussion on valuation of a swap. And the argument goes something as follows:
The value a swap = Fixed Rate Bond - Variable Rate bond.
At initiation you set the value of the swap to 0. So now we have FB = VB. So now we just solve for the fixed rate bond to determine the swap rate. You end up with the formula: $r_{FIX} = \frac{1 - PV_{0,t_n}(1)}{\sum_{i=1}^{n} PV_{0,t_i}(1)}$
It seems swaps are not actually priced like this in the real world? Why is that? If they can be created synthetically through fixed rate bonds, shouldn't they be priced to this?
I was also wondering why people might quote assets to swap spreads, vs quoting to the treasury curve. Are some institutions hedging to swaps so it's more natural to quote vs swap spreads?
## Answer by user68819 (score 0, accepted)
https://quant.stackexchange.com/a/83856
Background is, bonds (especially Us govies) were more liquid than swaps. Dealers therefore, quoted swaps as a spread to tsy (also as they would most likely hedge themselves with tsys, they were also more liquid than bilateral swaps). Also you had corporate issuers, which would be quoted as a spread to Tsys just to be able to give investors, the market, a quick imperfect gauge to how cheap the issue was vs a US govt issue of comparable maturity.
This is now a bit of a fallen tradition. Swaps on most parts of the curve are more liquid, people will trade swaps without the headache of repo, and no idiosyncrasies of the bond you buy, having to roll etc. Its more a phenomenon of how the market developed etc (in my opinion).
If you issue debt and you need to benchmark the debt, you need to show the buyer what the pick up is vs a benchmark. In eur you r benchmark is eur swaps (many issuers), in the US id guess for most its still OTRs.
Mind you, this is a guess, I was wasn't alive when the first swap was dealt.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.