# Near-the-money options' range

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.

• Using an absolute range is problematic as it depends on the time-to-maturity. An option that is 1 USD away from the spot of 100 USD would probably be considered at-the-money for long but not for short maturities. A common measure is to use standard deviations - i.e. $\ln \left( K / F_t(T) \right) / \left( \sigma_\text{ATM} \sqrt{T - t} \right)$, where $\sigma_\text{ATM}$ is the forward at-the-money volatility (that you potentially have to interpolate). Notice also the use of the forward instead of the spot. – LocalVolatility Jan 22 '18 at 14:35