Challenges in Inferring Zero-Coupon Curves from Swap Forwards

Summary

The document describes an attempt to infer a coherent zero-coupon discount curve from a quoted forward swap curve, with the aim of also producing a three-month LIBOR forward curve. The author recognizes that the available observations may not uniquely determine the desired curves and reports trying a Nelson–Siegel parameterization. That approach did not produce a satisfactory LIBOR curve, so the author also tried adding a LIBOR-related relationship to an optimization objective, without success.

No solution or calibration procedure is supplied in the document: it is a question asking for suggestions. It therefore offers no fitted curve, numerical comparison, or evidence that a particular model reproduces the input swap forwards. The setup signals an identification and consistency challenge involving sparse or irregular observations and multiple related rate curves. Any proposed reconstruction would need to specify assumptions, instruments, and curve conventions; the document itself does not resolve those choices or establish that its stated relationships are sufficient for calibration.

Key ideas

• The author seeks discount factors that are consistent with an observed forward swap curve.
• The intended reconstruction also needs to produce a short-term LIBOR forward curve.
• A Nelson–Siegel fit did not yield a satisfactory LIBOR result in the reported attempt.
• Adding a LIBOR-related constraint to an optimization was also unsuccessful.
• The document leaves the curve-identification problem open and provides no validated solution.

Tags

# Retrieve zero coupon curve from forwards


# Retrieve zero coupon curve from forwards












Let's suppose I am given a forward swap curve of a certain maturity (10Y). The curve is not very smooth and is decreasing but whatever. I have the curve : $S(0,t,t+T) = \frac{P(0,t) - P(0,t+T)}{\sum_{k=1...10} P(0,t+k)}$

My goal is to retrieve a sort of coherent zero coupon curve which replicates the forward curve. I am aware that there are not enough points to allow this. But I am just looking for something working.

I have already tried to calibrate a parametric function (Nelson-Siegel) but the problem is to also produce LIBOR3M forward curve at time 0. When I use this method the LIBOR forward curve is not relevent. I've also tried to add a fictive additionnal curve for LIBOR in the optimization $L(0,t) = S(0,t,t+T) - (Swap10Y(0) - Libor3M(0)) = 4(\frac{P(0,t)}{P(0,t+3M)}-1)$ but the optimization is not succesfull

Have you any ideas?

Thank you in advance

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