ZABR (by Jesper Andreasen and Huge) vs SABR smile

[Aber]

http://janroman.dhis.org/finance/SABR/ZABR Andreasen.pdf

Once again I would like to ask about the ZABR model, I have implemented this is R but I am not sure if this is done correctly.

I have a question which confuses me a lot: IF gamma = 1 and alpha, beta , rho and epsilon ( epsilon is the vol-vol parameter ) is fixed! Will SABR and ZABR then produce the same smile when they both use the SAME alpha, beta , rho and epsilon parameters?

 

[antoinesavine]

For avoidance of doubt I forwarded your question to Brian Huge. His answer is as I expected:

If gamma = 1 then the vol of vol function is the same as in SABR, so in case you use the same approximation or pricing method it will be the same.

Hope this helps.

 

[Aber]

I expected the same, nice to have it confirmed. Thank you.

 

[Aber]

One more question on this subject. This question is more about the intuition rather than technical.... Which consequences does the short time maturity expansion have?

When the vol surface is not flat in Time-to-Mat dimension, does that mean the ZABR approximation of the Implied Vol (equation 8 and 9) are wrong when we price long term derivatives?

Let's take an example

I want to compute the price 30y derivative Y with underlying X:
- I estimate the alpha, beta, rho, epsilon and gamma according to call option market data with underlying X based on IV(implied volatility) computed as in the article
- I simulate for 30y and price derivative Y

How big of a problem is it that the calibration have been based on IV computation which is based on short time maturity?

I hope I have been clear enough so you understand my concerns.