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In his paper On the distributional distance between the Libor and the Swap market models (and also in his book about IR modeling) D.Brigo says: enter image description here

10, 11, 12 are defined in the end of message. Do I correctly understand that

  1. He simply writes lognormal dynamics in LSM world.

  2. He takes dynamics of forward libors in LFM, translates it to LSM world, expresses Swap rate using these forward rates.

  3. Compares both formulas and finds that it is impossible to derive one from another?

Here are 10,11,12: enter image description here enter image description here enter image description here

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    $\begingroup$ Yea, you got it right. Swap rates and forward rates depend non-linearly on each other, so it would be quite weird to assume that both follow a lognormal distribution. If you try to derive $dS$ from (11) using (10), then there is no way you can end up with (12). $\endgroup$ – Olaf Oct 26 '14 at 13:08

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