Constructing the Short End of a Multicurve IBOR Forward Curve

Summary

The document discusses how to construct the short end of a six-month IBOR forward curve after a separate discount curve has been bootstrapped. Its central concern is consistency: ordinary deposits may not represent the same tenor as the six-month IBOR curve, potentially producing short-end forwards that do not align with the curve’s underlying rate conventions.

One proposed approach is to infer synthetic short-term six-month IBOR deposits by extrapolating from six-month deposits and forward rate agreements. Another approach is to extrapolate using observed overnight-index-swap versus six-month IBOR basis instruments. The response notes that the choice may have limited effect when the curve is used to project six-month IBOR cash flows, because short periods are already fixed in the described valuation setting. The impact can be greater when the curve is used for discounting, such as for an uncollateralized trade valued under an unsecured funding assumption. No numerical comparison or universal preferred calibration is given.

Key ideas

• A forward curve should be built with instruments consistent with the index and tenor it represents.
• Short-term six-month IBOR rates can be inferred from six-month deposits and forward rate agreements.
• Overnight-index-swap versus IBOR basis instruments offer another possible source for short-end extrapolation.
• The short-end choice may matter more for discounting than for projecting cash flows when the relevant fixings are already set.

Tags

# Building a consistant Forward curve in the multicurve framework


# Building a consistant Forward curve in the multicurve framework












I'm wondering what is the best practice for a consistent Forward Curve construction in the multicurve Framework (cf Bianchetti & Ametrano 2013):

Suppose for example that we have already bootstrapped a discount curve $C_{d}$ and we're building a $6M BOR$ forward curve: what instruments shall we use in the short end of the curve, say from $ON$ to $6M$, to be fully multicurve coherent ?

I've seen implementations where deposits are used, but then wouldn't this lead to "dirty" forwards on the short end since these instruments are not actually based on $6M BOR$ tenor?

Regards

## Answer by Antoine Conze (score 2, accepted)

https://quant.stackexchange.com/a/40322

One possible solution is to build "synthetic" short term 6M IBOR deposits by extrapolating for $T < 6\text{M}$ from the 6M IBOR deposit and 1x7, 2x8, etc. 6M IBOR FRAs as I have seen done in various places, or better by extrapolating from the known 0x6, 1x7, 2x8, etc. OIS-6M IBOR basis as suggested in section 4.4.2 of the paper you are referring to.

In any case you could argue that when valuing a deal indexed on 6M IBOR, any fixing for the rate that covers a period $[T-6\text{M}, T]$ is already fixed when $T < 6\text{M}$ so the choice of short term extrapolation should not have a large impact when the 6M IBOR curve is used as a projection curve. It would have a small impact though when using the 6M IBOR curve as a discount curve, as would be the case say if you're valuing an uncollateralized deal under the assumption that unsecured funding is done at 6M IBOR.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.