1
$\begingroup$

I'm wondering how can we check free arbitrage conditions in ATM swaptions surfaces since we only have access to Expiry, Tenor and volatility? Can someone help me please, i didn't find any article about it. N.B:I'm working on python

$\endgroup$

2 Answers 2

6
$\begingroup$

There are no no-arbitrage conditions on ATM vols of swaptions with different expiries/tenors, because the underlying swaps forward rates are different instruments. There are conditions however for these vols to be compatible with specific IR models. For instance when calibrating a Hull & White model on a set of coterminal swaptions, it sometimes happens that the models fails to fit a specific coterminal, because that would require a negative short rate instantaneous variance on the corresponding time bucket. It does not imply that the coterminal vols are not arbitrage free, but rather that the Hull & White model can only fit a limited set of market configurations.

$\endgroup$
1
$\begingroup$

See Johnson, Simon and Nonas, Bereshad, Arbitrage-Free Construction of the Swaption Cube (January 5, 2009). Available at SSRN: https://ssrn.com/abstract=1330869 or http://dx.doi.org/10.2139/ssrn.1330869

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.