I have some ATM swaption volatilities with the following characteristics:

  • (-IBOR) payment frequency: 1M
  • Underlying swap maturities (tail): 1Y, 2Y, 5Y, 10Y, 15Y and 20Y
  • Swaption expiries: 1M, 3M, 6M, 1Y, 2Y 5Y and 10Y.

I would like to compute volatilities for swaptions with shorter swap maturities (tails) (specifically 3M, 6M and 9M).

Is there any model/bibliography that I could check to extrapolate my market vols in such way?


  • 2
    $\begingroup$ Sorry: in which of the dimensions do you want to interpolate: swap tenor (1M,3M,6M,12M) swap maturity (1Y,...,20Y) or swaption expiry - and which data do you have? $\endgroup$ – Kermittfrog Feb 24 at 19:31
  • $\begingroup$ you are misusing the word tenor. Tenor and maturity are usually the same nomenclature, e.g. 2y, 5y, 10y etc. your '1M' is a libor tenor (and useful to make the distinction) but more clearly addressed as floating frequency, $\endgroup$ – Attack68 Feb 24 at 20:05
  • $\begingroup$ Commonly used terminology is expiry and tail (i.e. the tenor/maturity of the underlying swap). Payment frequency is not referred to as "tenor" - I suggest editing your post for clarity. $\endgroup$ – user42108 Feb 24 at 20:06
  • $\begingroup$ @Attack68 thanks for that pointer. In most places I have seen the nomenclature was always a bit different, and tenor/maturity/expiry somehow stuck. But then again, we are in Germany and call a mobile phone a 'handy'. I'll try to stick to floatfreq/tenor/expiry from now on. $\endgroup$ – Kermittfrog Feb 25 at 7:17

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