How does an opening gap affect volatility?

[Aston01]

Stock is trading at $100

IV = 32% (0.32)

Daily time frame

$100 x 0.32 = 32 divide by 16 = $2 as the first SD, meaning that the $100 stock could at any given day either go to $102 or $98.

I the situation above assuming a typical daily range of $4 with the current volatility levels the above stock that closed the night before at $100 and the next day gaped up opening at $105. How would I go about determining determining what a 1 standard deviation range based on the new opening price would be ?

 

[dmeista]

apparently you already use some kind of formula to estimate the sd. Why don't you use the same formula with the new implied volatility?