Option Price ATM

Call/Put (ATM) = Sigma * S/ sqrt(2*Pi)
                          = Sigma0 * Sqrt(t) * S/sqrt(2*Pi)
                          = 0.4*S*Sigma0*Sqrt(t)

C/S = 0.4*Sigma0*Sqrt(t)

3 Month ATM:

Call/Put = Sigma0 * S / 5 = 0.2 * Sigma0 * S

SPX Call/Put Option ATM with Sigma0 = 20%:

Call/Put = 0.04 * S