273Chapter seventeen: A summary a nd concluding comments
irony, behavioral markets, the stock markets, are used as the basis for derivatives, or 
options whose price is determined largely by the operation of algorithms called “models.” 
The original model that created the modern world of options trading was the Black–
Scholes options analysis model, which assumed the “fair value” of an option could be 
determined by entering five parameters into the formula: the strike price of the option, 
the price of the stock, the “risk-free” interest rate, the time to expiration, and the volatility 
of the stock.
The eventual universal acceptance of this model resulted in the derivatives industry we 
have today. To list all the forms of derivatives available for trading today would be to expand 
this book by many pages, and it is not the purpose of this book anyway. The purpose of this 
paragraph is to sternly warn general investors who are thinking of “beating the derivatives 
markets” to undergo rigorous training first. The alternative could be extremely expensive.
At first, the traders who saw the importance of this model and used it to price options 
virtually skinned older options traders and the public, who traded pretty much by the seat 
of the pants or the strength of their convictions, meaning human emotion. But professional 
losers learn fast and now all competent options traders use some sort of model or anti-model, 
or anti-antimodel to trade. True to form, options sellers, who are largely professionals, take 
most of the public’s (the buyers) money. This is the way of the world.
Options pricing models and their importance
After the introduction of the Black–Scholes model, numerous other models followed, among 
them the Cox–Ross–Rubinstein, the Black Futures, and others. For the general investor, the 
message is this: he must be acquainted with these models and what their functions are if 
he intends to use options. Recall, the model computes the “fair value” of the option. One 
way professionals make money off amateurs is by selling overpriced options and buying 
underpriced options to create a relatively lower risk spread (for themselves). Not knowing 
what these values are for the private investor is like not knowing where the present price is 
for a stock; it is a piece of ignorance for which the professional will charge him a premium 
to be educated about. Unfortunately, many private options traders never get educated, in 
spite of paying tuition over and over again. But ignorance is not bliss—it is expensive.
Technology and knowledge works its way from innovators and creative geniuses 
through the ranks of professionals and sooner or later is disseminated to the general public. 
By that time, the innovators have developed new technology. Nonetheless, even assuming 
that professionals have superior tools and technology, the general investor must thoroughly 
educate himself before using options. As it is not the province of this book to dissect options 
trading, though the reader may find references in Appendix B, Resources.
Here it would not be untoward to mention one of the better books on options as a 
starting point for the moderately advanced and motivated trader. Lawrence McMillan’s 
Options as a Strategic Investment is necessary reading. In addition, the newcomer may contact 
the Chicago Board Options Exchange (the CBOE) at http:/ /www.cboe.com , which has 
tutorial software.
Futures on indexes
Futures, like options, offer the speculator intense leverage—the ability to control a 
comparatively large position with much less capital than the purchase of the underlying 
commodity or index. Futures salesmen are fond of pointing out the fact that, if you are 
margined at 5% or 10% of the contract value, a similar move in the price of the index will