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.