Building a USD LIBOR Swap Curve from Spot Rates, Futures, and Swaps

# How to value a long term interest rate swap if the floating leg is USD-LIBOR


# How to value a long term interest rate swap if the floating leg is USD-LIBOR












To value an IRS, you require a spot/zero curve. If I am correct this zero curve will be the USD-LIBOR curve. However, if you have e.g. a 10-year swap that you are trying to value 2 months into the contract, you need the spot rates, beyond 12 months (LIBOR only goes up until 12 months), in order to value the cashflows.

My question is, how would you 'practically' value a swap if you only have the USD LIBOR yield curve up to 12 months?, how is the curve extended?

I read that, for the medium term, Eurodollar Futures can be used, and for the long term swap rates can be used. I am not sure how you would construct the curve using these different rates. Specifically, because a swap curve/rate includes the spread, i.e. Swap curve = Libor + Spread, but I am only looking for the LIBOR part of that curve.

summary of question: I need to price a USD IRS. If I am correct I require a zero curve which is essentially the LIBOR curve I am not sure how to construct the USD libor curve beyond 12 months even if swaps rates can be used to construct the long end of the curve, I'm not sure how this would be done as you would require a USD LIBOR-based Swap curve (cannot use swaps based on different reference/floating rates, since we require the LIBOR curve) and you need to somehow extract the spread.

## Answer by AKdemy (score 1)

https://quant.stackexchange.com/a/66407

A vanilla IRS on USD libor is fixed float with the float variable being 3m Libor. As @KevinT wrote, there is no spread in market quotes. The fixed leg coupon is quoted in a way that the IRS is "fair" at par rate - which means zero cost at initiation.

As of now (before libor cessation), there exists a liquid swap market for 3m libor swaps which will be the main building block in the long end of the curve. Since your swap (assuming you have a standard Libor swap) will have float 3m tenor, the curve must be built in a way to represent accurately the term structure of this specific tenor. This means you do NOT include any other libor tenors.

Generally, the framework will be as follows.

- short end: the 3m Libor spot rate

- mid curve: Futures (or FRAs but for USD mainly futures)

- long end: swaps quotes

Difficulties in building these curves:

- mid curve: you will need to compute convexity adjustment if you use futures

- long end: the market quotes will be dual curve stripped - hence RFR discounted ; that requires you to strip the curves as such as well

On top of this, it is a bit of an art (rather than science) what futures to include, and when to start using swap rates, and what tenors to include, exclude in curve stripping to ensure a reliable and smooth curve (interpolation will also be crucial, especially for non standard tenors and mark to market).

If you want to value these after Libor cessation as well, you will need to think of the fallback rates, or potential zombie Libor rates etc. You can have a look here and here for some details around this.

Overall, getting this right is not trivial if you are not very familiar with curve construction and market conventions (and have access to all the data that is needed). Frequently, if you have access to reliable swap quotes, you will use some of the major vendors like Bloomberg. Fortunately in this case, you will also not need to worry about curve construction (unless you are very sophisticated) because Bloomberg (or any other similar provider) will simply offer this fully automated for you. `ICVS 23` will be the 3m Libor curve (and you can refine the settings to your liking if needed), and `SWPM -FXFL USD` will be the standard template, where you can also add a spread to your floating leg (since it seems you require that).

SWPM would automatically load the appropriate curves (forward and discount), allow you to modify them if needed, and gives you the option of CSA or not. On top of this, you can modify it in (almost) any way that swaps trade in the market.

Lastly, I think the real question (for you) will be what you really need? It is clear that you need to price this. However, what data and tools do you have access to. If none, it may be worth to start asking (yourself) what the best available solutions are (in terms of your budget, usability, reliability). Of course you can do it the hard way and build it all by yourself. In my humble opinion, there are good reasons why Adam Smith already wrote about division of labour. There is no need to reinvent the wheel.