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While brushing up on my knowledge about the Greeks, I have been struggling coming up with an intuitive, probability-based explanation behind why not only Out-of-the-Money (OTM), but also In-the-Money (ITM) options have low Time/Extrinsic values.

For deeply OTM calls (for example), I can see why the Time Value would be low, because there is an extremely low probability of the underlying's price moving so much as to make the call ITM again. However, this is where my present intuition clearly fails, because when a call is deeply ITM, wouldn't it's Time Value actually be high, since the probability of its underlying's price staying within the ITM zone is high?

I feel like this stack post was getting at the answer, but didn't fully elaborate it.

Would someone be able to explain why OTM + ITM options have low Time Values, or at least discern which facets of basic option pricing I am not grasping?

Thank you in advance.

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In one sentence, time value has to do with the probability of crossing the strike before expiration (whether from below or above). Doesn’t matter whether the crossing results in the option being in the money or not.

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  • $\begingroup$ If a stock, as an underlying, is on its way up clearly (as determined by some analysis), wouldn't it make sense to price that in a Call? I can't imagine the known upside to a growing stock to not be priced in, just because the strike has been crossed into profitable ITM territory. $\endgroup$
    – Coolio2654
    Commented Oct 2, 2019 at 3:11
  • $\begingroup$ No. If there were such a thing as a stock which is “on its way up clearly”, the call option pricing would not be affected. If deep ITM calls were priced higher, it would make better sense just to buy the stock on margin. $\endgroup$
    – dm63
    Commented Oct 2, 2019 at 10:31
  • $\begingroup$ Ok, let me try to phrase my concern this way. An investor A is interested in a stock, which is almost certain to grow 500% within the next month from the current value S to S'. However, since it still has a slight chance of total catastrophe and losing all of its value, he'll try to buy a Call on it - he won't capture all of the 500% upside, but will avoid all the possible downside. $\endgroup$
    – Coolio2654
    Commented Oct 2, 2019 at 16:46
  • $\begingroup$ Now, let's say 10 days pass, the stock has increased 200% (with massive further growth still projected), and the call is long In-the-Money by this point. Investor A wants to sell this Call now. Why would he not price in the fact that the underlying is on a likely meteoric rise? $\endgroup$
    – Coolio2654
    Commented Oct 2, 2019 at 16:46

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