8
$\begingroup$

I've been researching the SABR model and one of the main benefits it seems is that you can obtain a closed for solution of the implied BS volatility in certain cases.

In all the papers I've read, I have not found any proofs/reasoning as to where this solution actually comes from.

Does anyone know/can link me to a derivation of it?

This is the formula I am referring to.

Thanks

$\endgroup$
1
$\begingroup$

It comes from Heat Kernel expansion and differential geometry.

See Theorem 6 and Section 8 of http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1717676&download=yes

$\endgroup$
  • $\begingroup$ The link is broke. Could you please list the exact title and author of the paper, as well as a working link to it? Thank you. $\endgroup$ – Hans Mar 11 '18 at 0:00
0
$\begingroup$

The derivation is in "Managing Smile Risk" by Pat Hagan et al. A copy is here:

http://www.math.ku.dk/~rolf/SABR.pdf

It is not closed form, but rather an approximation based on expansions.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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