The long end of the Libor swap curve needs to be constructed from Basis Swaps because there are no other instruments traded. Can please someone explain the concept of Dual Curve Calibration?
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$\begingroup$ you can read Fuji's paper 2010 $\endgroup$– BenedictDec 9, 2019 at 8:45
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$\begingroup$ @Benedict it would be nice if you could summarize this paper as an answer. $\endgroup$– emcorDec 12, 2019 at 10:47
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$\begingroup$ what is LIBOR swap curve ? What is a basis swap ? $\endgroup$– CanardiniDec 17, 2019 at 20:53
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$\begingroup$ @Canardini you are supposed to answer that $\endgroup$– emcorDec 17, 2019 at 21:06
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$\begingroup$ You are the one asking for help. Be more specific $\endgroup$– CanardiniDec 17, 2019 at 21:07
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Actually it is not just the long end of the swap curve it is any part of the curve that needs some form of basis swaps to be calibrated.
A set of curves in any currency usually encompasses the following: { OIS curve, 1M IBOR curve, 3M Ibor curve, 6M Ibor curve } at a minimum.
It is not practical for interbank markets to trade completely bespoke products so the liquid points might be for example: 3M interest rate futures in the first 3Y, then 6M IBOR swaps from 3Y to 50Y at regular intervals.
In order to construct other curves you need to base them reletive to these liquid instruments, so you often have, for example a 6m/3m basis swaps, and 3m/ois basis swaps which allows you narrow down the curves in different sections relative to each other and end up with a consistent set of prices that agree with the normally quoted interbank products.
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$\begingroup$ Can you give a concrete Mathematical example how dual calibration works? I think in case of basis swaps you replace one of the rates by the other rate+spread to calibrate? $\endgroup$– emcorDec 21, 2019 at 11:08