Black Scholes Model

It sounds like something that has to do with shoe fashion. “Black Scholes are all the rage in Paris this year!" Only, instead of a bright red sole, theirs is black. And isn’t there a Doctor in there as well somewhere?

Okay, okay…the Black Scholes stock option valuation model is actually a mathematical formula, and a system for coming up with stock option prices.

Example.

Disney is trading at $100 a share today. You, the CIO of the Milwaukee Cardiologists Investment Club, want to buy a call option on Disney with strike price at $120, which won’t expire for about 4 months. How much should that call option cost?

Well, this call option is notably an American style option. Traditional Black Scholes modeling is based on the European style option, which expires only on one day at the end of the period in which the option is alive. So the valuations will be a little bit different depending on your continent. But here we just want to give you the basic gist. The key idea is that, the more volatile the stock, the more volatile should be the call option underlying it. And yes, there are tons of mathematical errors in this model, not the least of which is the fact that past performance of stocks is not necessarily any indication of future performance. But since we have no other way to navigate our future prognostications other than driving a car by looking in the rear-view mirror, then that’s what we have to do.

Essentially, the Black Scholes model takes an average weighting of a stock price over a given duration, and multiplies it by some formula of its volatility.

So...take AT&T. A stock with very low volatility the last several of years. Quotient (a digital coupon company), on the other hand, has been a hoot of a ride for the good, the bad, and the ugly.

You can imagine that a call option priced 20% above AT&T’s price would not be very expensive, because given the low volatility of AT&T stock, the odds that the stock itself breaks out above that 20% line is pretty low. But if you look at Quotient, a price 20% above it seems highly likely, because the stock trades in gaps up and down of a few percentages per day, i.e. the same volatility AT&T has per month.

So if you are the person writing that call option, or selling a call option, which put you on the hook to provide shares at a price roughly 20% above where the stock was currently trading, of course you would charge the call option buyer of Quotient a whole lot more than you would charge the call option buyer of AT&T.

The question that Black Scholes tries to answer is just how much more you would charge for the highly volatile or high-beta Quotient stock option v. that of AT&T.

If you really care about the math, then A) we’re sorry, B) You should probably take a real investing course and go to business school, and C) you may need a hobby. We suggest golf. Or needlepoint.