Brokers and web sites offer various IV numbers:
- the IV of each option
- an average IV per expiration
- an average IV for the stock (all options)
Options of the same expiration can have very different values and the values from that expiration can be very different from other expirations.
A volatility smile is when the IV of each option is higher as the option gets further in and out-of-the money. There are also option smirks (IV has either a forward or reverse skew).
They calculate the average implied volatility in different ways. Some just average all of the different IVs. A noted option author weights each individual option's implied volatility by its trading volume and its distance in- or out-of-the-money (at-the- money options receive the most weight). Because of the volatility smile/smirk, IVolatility uses a proprietary weighting of the delta and vega of 4 ATM options per expiration. If you really want a headache, read about the calculation of the CBOE Volatility Index (VIX).
I'd suggest that you use the average implied volatility for an expiration as the input for your formula. I don't know if which method of calculation is most effective though I surmise that it doesn't make much difference because it's just an estimate which changes daily as IV changes.
