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How exactly is implied volatility assigned to an option's strike price?
As I understand it, Implied Volatility represents the expected gyrations of an options contract over it's lifetime.  No, it represents that expected movement of the underlying stock, not the option itself.  Yes, the value of the option will move roughly in the same direction the value of the stock, but that's not what IV is measuring. I even tried staring at the math behind the Options pricing model to see if that could make more sense for me but that didn't help. That formula is correct for the Black-Scholes model - and it is not possible (or at least no one has done it yet) to solve for s to create a closed-form equation for implied volatility.  What most systems do to calculate implied volatility is plug in different values of s (standard deviation) until a value for the option is found that matches the quoted market value ($12.00 in this example).  That's why it's called "implied" volatility - the value is implied from market prices, not calculated directly. The thing that sticks out to me is that the "last" quoted price of $12 is outside of the bid-ask spread of $9.20 to $10.40, which tells me that the underlying stock has dropped significantly since the last actual trade.   If the Implied Vol is calculated based on the last executed trade, then whatever algorithm they used to solve for a volatility that match that price couldn't find a solution, which then choose to show as a 0% volatility.   In reality, the volatility is somewhere between the two neighbors of 56% and 97%, but with such a short time until expiry, there should be very little chance of the stock dropping below $27.50, and the value of the option should be somewhere around its intrinsic value (strike - stock price) of $9.18.