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I understand that apparently implied volatility of a call option increases as the underlying price of the stock deviates further and further from the moving average. That mostly makes sense, because traders anticipate a return to the mean and as the price strays further away from that more traders will be looking to buy or sell. Do I have that right?

What I don't understand is why this increased volatility on both the low side of the average and the high side make the option more expensive to purchase. On the low side, I see it. The stock is about to rebound and because higher stock prices mean higher option prices (for calls), there is a kind of synergistic effect to the rising price of the option. Why is the same true on the high side? It's clear the stock is about to see a sell-off and so the price of the stock would decrease causing a downward push on the option price.

My question is why does the volatility instead of working in the same direction before, cause an upward push of the price of the option instead? I guess this is good for a holder of the option because the volatility driving the price up is attempting to offset the downward push in price of the option from the stock losing value, but I'm just not understanding the exact rationale behind this.

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You are making a very dangerous assumption when you say:

It's clear the stock is about to see a sell-off and so the price of the stock would decrease causing a downward push on the option price.

It's not clear at all that high-variance stock with spot price above moving average is going to see a sell-off. There could be a myriad of reasons why it will instead continue to go up. While it's true higher variance may knock down the price of the underlying, and therefore the option as well, it may also knock it even higher.

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Option pricing is based on modeling the stock price as a random walk, not a "return to the mean". According to the efficient market hypothesis, it is never "clear" that a stock is "about to rebound" or "about to see a sell-off". Upside and downside risks should always be balanced. They are not necessarily symmetric (e.g., there could be a large chance of a small loss and a small chance of a large gain, leading to option skew), but they are balanced.

One of the factors influencing implied volatility is historical volatility. It is known that when a stock has made a sudden large move up, it is more likely to make a further large move, either up or down, because it is a sign that rapid surprises are occurring. So implied volatility rises for both calls and puts.

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Implied volatility has nothing to do with deviation from the underlying's moving average. If anything, historical volatility might be somewhat akin to that since it is the deviation from the mean (standard deviation) but that's a stretch. Increased IV also has nothing to do with an assumption of reversion to the mean.

At any moment in time, other than volatility, all option pricing variables are known (stock price, stock price, time remaining until expiration, dividend, and risk free rate). The marketplace is an auction and it determines price. The question then is given all of the known variables, what volatility number must be fed into an option pricing model to yield the option's market price? By a process called iteration, this number is the implied volatility.

Investopedia suggests that when a security is in high demand, its price rises as does the IV of its options and when it drops, IV contracts. That isn't true. Any turbulence in the market, real or expected, leads to increased IV. For the former, look at the increased IV of SPY options when the market dropped in February. For the latter, look at the IV of almost every optionable stock prior to an earnings announcement (ignoring very low beta or very low priced stocks) or pending news announcement (for example, clinical trial results for a new drug).

In short, IV is a reflection of option price which is a function of supply and demand. It changes constantly as price changes.

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