Estimating Forward Swap Roll-Down from a Reconstructed Curve

Summary

The document asks how to estimate the one-year roll-down of forward-starting interest-rate swaps when the available data contain only selected forward swap rates. It defines roll-down as the difference between the current forward-starting rate and the rate for the same swap tenor observed at a shorter forward start, assuming the yield curve remains unchanged. The desired shorter-start rate may not be among the supplied observations.

The response proposes constructing a full swap curve for the observation date from the available forward rates, then using curve fitting and interpolation to infer the missing rate. Once the curve is built, the requested point can be read from it and used in the roll-down calculation. This is a conceptual outline rather than a QuantLib walkthrough or a worked numerical example. It also notes that curve construction is not trivial; the result depends on the available rate coverage and the chosen fitting and interpolation methods.

Key ideas

• Roll-down compares a forward swap rate with the corresponding rate at a shorter forward start.
• The calculation assumes the curve remains unchanged over the roll-down period.
• Available forward rates can be used to construct a swap curve for the observation date.
• Curve fitting and interpolation are needed to estimate rates absent from the input list.
• The answer gives no implementation details or worked example, and curve construction is nontrivial.

Tags

# Roll Down of Forward Starting Interest Rate Swap


# Roll Down of Forward Starting Interest Rate Swap












I have the data for a lot of forwarding starting interest rate swaps. i.e 2Y1Y, 3Y1Y, 5Y1Y, 3Y2Y, 5Y2Y, ... (so different forwarding and maturities).

I would like to calculate the roll down over 1 year for each of them. I don't have other data (Libor, Euribor, etc). What I call a "roll-down" is the difference between xYzY - (x-n)YzY given that the yield curve stays the same. n is the roll-down period. For example, for the 2Y1Y, to get the one-year roll-down I do 2Y1Y - (2-1)Y1Y.

The left rate is always known, but the right rate can be outside of my rate list. So, I need to find its value.

From QuantLib, how could I retrieve this swap rate from all my input data and/or explain the process?

Thanks in advance.

## Answer by dm63 (score 1)

https://quant.stackexchange.com/a/46849

If you have enough forward rates for a given observation date, you should be able to construct a full swap curve for that date. This would involve some curve fitting and some interpolation , so it’s not trivial. However once you’ve done that , you can observe any rate that you like from the curve so you can calculate your roll down.

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