I basically have one year (2016) of data of vanilla options written on SPX. I was trying to isolate the ATM options, but it is hard to have derivatives having exactly K = S in a given day. For that reason I would select the near-the-money options that correspond to those who have a difference in absolute value less than 0.5 $ between strike price and underlying level. Also such criteria seems to bee too stringent, maybe due to the structure of my dataset.
Is there a reasoning that could allow me to take, for instance, those derivatives that have the above-mentioned absolute difference less than 2 $ or more? I searched about the definition of near-the-money option and the one I have written before seems to be the only one.