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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.

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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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  • $\begingroup$ I see how to do this for non-forwarded starting swaps. You build/adjust a curve, then you can find any point of this curve. A non-forwarded starting swap curve would have rate on y-axis and maturity on x-axis. But for forwarded starting swap do we have to work with a 3d curve (forwarding on z-axis)? I don't succeed to figure out this $\endgroup$ – ZottoZ Jul 29 at 13:00
  • $\begingroup$ For example you can chain together some forward swaps to get all the forward rates: 1y1y, 2y1y, 3y2y, 5y5y, 10y10y for example. (I selected these because the end date of each rate matches the start date of the next one). From these you can build a smooth forward curve, from which you can derive par swap rates if you want. $\endgroup$ – dm63 Jul 29 at 13:05
  • $\begingroup$ Does it make sense to build a curve such that y=rate value and x=Forward+Maturity? So, in your example, I have on the x-axis 2, 3, 5, 10, 20. Then if I want the 3y1y, I look for the corresponding points on the curve having 3+1=4 on the x-axis? $\endgroup$ – ZottoZ Jul 29 at 14:04
  • $\begingroup$ Yes you could do that $\endgroup$ – dm63 Jul 29 at 15:50

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