I read that the when parameterising the IV curve we should use delta on the x axis with IV on the y axis. However, we need to be careful about choosing a call delta or a put delta because the strike of a 50 call delta will be different from the strike of a 50 put delta.
Is this because an ATM call has delta > 0.5 and an ATM< -0.5? Thus a call will have a delta of 0.5 below the ATM strike and similarly a put will have a delta of -0.5 above the ATM strike.
Is my reasoning correct?