How to Measure the Atom in Explanation for Short Maturities

When you look at market data, you don't have a continuum of maturities. And in particular, you may find that a power low fits well your finite data term structure for a large range of strikes. So it's very natural and tempting to extrapolate this straight line for all maturities into zero maturity. But maybe one should not jump to conclusions and extrapolate the power low behavior until the zero maturity. It might be that the short term behavior is different.