Building Euribor Forward Curves with Tenor-Specific Instruments
Summary
The document explains how to construct separate three-month and six-month Euribor forward curves when the indices have a basis. Its central guidance is to use instruments tied to the curve’s own tenor: the relevant Euribor fixing, matching forward rate agreements or futures, and swaps referencing that index. For a six-month curve, overnight or one-month Euribor instruments should not supply the first points; the six-month fixing from spot is treated as the initial forward period.
The discussion contrasts this approach with the pre-crisis “one curve” practice, when basis risk between tenors was often treated as negligible and instruments of different tenors could be mixed. It also distinguishes forward curves from the discount curve: an overnight indexed swap curve supplies discount factors, while Euribor curves represent expectations of their respective fixings. The post-crisis framework is presented as market practice, but the text does not detail bootstrapping, interpolation choices, or instrument-specific adjustments.
Key ideas
- Build each Euribor forward curve from instruments referencing its own tenor.
- Use the tenor-specific fixing as the initial point of its forward curve.
- Treat the overnight indexed swap curve as a discount curve, separate from Euribor projection curves.
- Mixing tenors was more accepted when their basis was considered immaterial, but that practice became unsuitable as basis risk mattered.
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# Curve Euribor - Euribor 3M # Curve Euribor - Euribor 3M I'm setting up some Euribor 6M and Euribor 3M curves. So far i have all the data and quotes i need, but i'm having trouble defining the firsts points of the curve. I'm currently using 6M Euribor and 3M Euribor OIS as the first point. My question is, how correct is it if i use O/N Euribor or 1M Euribor on both curves, knowing that there's a basis between the indexes. As an example, for the 6M Euribor these are my two options: - Euribor O/N, Euribor 1M, Euribor 6M, FRAs, Swap Rates. - Euribor 6M, FRAs, Swap Rates. Both options seem correct, but i don't know what is the market convention over this. Thanks for the help. ## Answer by Rostock (score 6, accepted) https://quant.stackexchange.com/a/15478 It is incorrect to use 1m euribor or O/N euribor in a 6m Euribor forward curve. You should only use instruments based on 6M euribor, such as 1x7 FRA, 6x12 FRA or swaps v 6m Euribor, as you have done in your second example. The actual 6m euribor fixing itself can be thought of as a 0x6 FRA out of spot. Before the financial crisis basis between different euribor curves didn't really move and wasn't considered an important risk, so it was standard practice to use euribor instruments of any tenor in the same curve. Hence you can find many old textbooks where futures based on 3m Euribor and swaps v on 6m euribor are used in the same curve, which isn't done nowadays. Incidentally I don't understand the term '3MEuribor OIS' An OIS curve is a separate thing from a euribor Curve. You would build an OIS discounting curve first, then use those discount factors when building your forward curve. In my experience the first point of a 3M euribor forward curve should be the 3m euribor fixing out of spot, and the first point in a 6m euribor forward curve should be the 6m euribor fixing out of spot. ## Answer by Phil H (score 1) https://quant.stackexchange.com/a/15529 Once upon a time, there was the One Curve. It was made of various instruments (Depos, Fixings, Futures, Swaps) and represented the One True Discount Rate for any given term. With that curve, and an appropriate interpolation method, it made sense to talk about expensive days, the curve up to 3m, etc. But that world is long gone. When you create a 3m curve now, you are really trying to calculate expectations of the 3m fixing from your 3m-specific instruments (3m Fixing, FRAs or Futures with adjustment, 3m Swaps), given a known discount curve (built from the instruments specific to the measure, i.e. EONIA for vanilla contracts). So what does that portion of the curve you are constructing really mean? What is the 1w point on a 3m curve? It doesn't matter. It only matters what the 1w to 1w+3m ratio is, because that's what gives you the expectation of the fixing. Or better yet, dispense with factors and make a fixing expectations curve in rate terms, rather than factors.
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