Smiling at convexity

Information on implied volatilities of swap rates is provided by the market both directly through quotes of swaption smiles and indirectly through prices of constant maturity swaps (CMSs), where a CMS rate is exchanged for a Libor rate plus a spread (referred to as a CMS spread).

Unfortunately, not every swaption in the standard at-the-money matrix also has quotes for away-from-the-money strikes, and when present, the latter are often too few to allow for a robust bootstrap of the whole smile

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