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IV Does not Determine Price
1 project | /r/options | 29 May 2022

If you want to be convinced, here is a repo of BSM implementation in google sheets (https://github.com/BardsWork/bsm-sheets). You can set it up and play around with different IVs, etc. As you can see, the formula explicitly takes IV and will get you a price. It's not 100% accurate but its close enough.