Option prices are not formally related to the price of the underlying stock

From the emphasis that is so often placed on formulas that supposedly calculate the "value" of an option, you would think that there must be a formal relationship between the price of a stock and the price of an option on it, but there is not.

Like everything else, the value of an option is whatever someone is willing to pay for it at a particular point in time. If it's hot, it's hot, if it's not, it's not, and an underlying stock and the options on it don't always fall into and out of favor at the same time. Option prices move independently of the price of the underlying stock, and sometimes track the stock surprisingly poorly.

An option valuation calculation might say that an option is undervalued or overvalued, but there is usually a reason. If a company is going into bankruptcy, are you really going to buy call options on the stock just because the Black-Scholes equation says they're undervalued? Of course not! They're undervalued for a good reason. The Black-Scholes equation deliberately omits factors such as this because they are not quantifiable. In this case, though, the bankruptcy is the most important piece of information to know about the company, so the Black-Scholes calculation is utterly worthless even as a guide.

Option prices reflect the expectations of options traders about what the stock is going to do. As soon as a "technical move" looks likely, the options will often move in anticipation of it, to the point that they would be worth after the move has already occurred. If the move doesn't happen, the options drop. If the move does happen, often the option has already made its move, and won't budge any further. If you wait for a signal, others (like the specialist or floor traders) will get there first. If you anticipate a signal, you're going on "nothing".

One of the peculiar ideas I once had was that the only time to buy an option was when it looked as though no signal at all was likely anytime soon. I never followed up on this with any study, but that would be the only time that an option had anywhere near its fair value: when almost no one has any interest in it one way or the other. On the downside, that makes your purchases basically random.

The real fair value of an option is probably its market value.