Black Scholes Made Easy And Three Ways To Buy Better Call Options
by Dr. Mark Skousen, Chairman, Investment U
Friday, July 14, 2006: Issue #557
If you are going to play in the fastest game in town - stock options trading - you need to understand the implications of the Black Scholes formula for pricing stock options. Invented in 1973 by financial economists Fischer Black and Myron Scholes, this options model will help protect you from losing your shirt in options trading.
First, a little background
The real genius behind Black Scholes is Fischer Black (1938-95), a University of Chicago economist who later worked for Goldman Sachs. In other words, he was a practicing economist, the best of the breed.
I can relate to the troubles he had getting published, because the academic economics profession is in many ways a closed shop that doesn't like economists who get their hands dirty working on Wall Street and in business. Like Black, I've taught at major universities (he at MIT, me at Columbia), only to be held back because of my "commercial" interests.
Black died of cancer in 1995 and was not eligible to receive the 1997 Nobel Prize in Economics, which went to his colleague Myron Scholes, among others, in recognition of their revolutionary work in finance.
And now for the practical side of the Black Scholes model
Putting Black Scholes To Work
What these two economists tried to determine was how option prices work. Obviously, the price of a stock option depends on several factors:
- 1. The underlying price of the company stock
- 2. The exercise (strike) price of the option
- 3. The maturity date of the option contract
- 4. Speculative premium of the option
The Black Scholes formula can be quite intimidating for those unfamiliar with advanced mathematics. The easiest way to understand the implications of Black-Scholes is to look at the curve below, where we use Apple Computer (Nasdaq: AAPL) as an example (from Monday's Investment U: Option Trading Strategies: The World's Fastest Way to Make Money).
We looked at the January $60 call (strike price of $60), selling for roughly $4. Therefore, "A" on the curve represents the price of the call option when we bought it - $4. And "Z" represents the value of the call option when it expires in January - $0.
This scenario, of course, assumes that Apple Computer stock will not change in price between now and January 2007, leaving a $60 call option with no value because shares trade near $53. (Call options grant you the right - but not the obligation - to purchase the shares at the given strike price. In this case, it would cost less to buy the shares at market.)
Obviously, the price of the call option will gradually decline from $4 to $0 in six months. But here's where Black Scholes comes into play The formula tells you that the Apple option is going to essentially "fall off a cliff" in a few weeks' time.
According to Black Scholes, the call option is going to move very little in the first few weeks, but then it's going to PLUNGE way down by 50% to 60% over the next few weeks, and then gradually decline to $0 as the third week in January (the expiration date) approaches.
Conclusion on Black-Scholes
This formula is a warning to all option traders that they must be right both in the direction and timing. Here's what you can do to postpone a collapse in a call option:
- Extend the maturity date of the option
- Go farther "out of the money" with the strike price
- Witness a sharp, quick rally in the stock (or in the case of buying put options, a sharp decline)
Obviously, the third choice is preferable.