Option Pricing Model

Let's say you have a stock that trades for $10, with minimal historical volatility of about 11% (which corresponds to a roughly 10 cent change, either up or down, every other day; as in: $10 to $10.10 or $9.90, then back to $10, and so on... for a whole year). A pretty reliable stock no doubt!

According to the Black-Scholes option pricing model, a $11 call with a year to expiration should trade for next to nothing at roughly $0.13 (the exact price depends on a few other variables that don't matter much – let's keep it simple by glossing over things like interest and dividends).

One day, there's terrible news about the company. Its stock plunges an unprecedented 10% in one trading session, hitting a 52-week low of $9. Surely, that's also bad news for the value of your call options? Well, no! According to the standard model, your call options have almost doubled in price to $0.24. Not that bad you think!

If instead the price hits $8, the same counter-intuitive outcome happens, the "value" of your options double to $0.50, even though they are getting further and further away from being in-the-money. Somewhere around $5 is where the "value" of your options maxes out at around $0.88.

Of course, this illogical conclusion is dependent on the assumption that your historical volatility (as measured here with a 60-day or 90-day realized volatility) will mimic perfectly your future volatility. In other words, the assumed increase in implied volatility is what is "causing" your call options to increase in value while moving away from the strike price of $11. That assumption is tenuous at best, and the option markets will probably diverge from the theoretic pricing given to us by the Black-Scholes pricing model.

However, this B-S model (no pun intended) is used in a number of applications, like executive option valuation and pricing company warrants, most of which are priced mechanically for tax, compensation and compliance reasons. So these wonky results do have real-world impacts!

The bottom line is trust your judgment: if you own a call option, don't rejoice when the stock price takes a nosedive, no matter what your account statement says! Similarly, when holding put options, you aren't better off when the price of the stock skyrockets and your options go deeply out-of-the-money. Common sense should triumph over option pricing models. Underwater isn't a good place to be no matter what the math says!

Just beware, these financial formulas have assumptions that are too easily violated!