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Well, it isn’t surprising that everyone blames the model that all the bankers are using. But is it really the fault of the formula, or the people using the formula? That is a distinction I believe we have to make.

“I sometimes wonder why people still use the Black-Scholes formula, since it is based on such simple assumptions – unrealistically simple assumptions.” — Fischer Black

Here are the assumptions of the model from The Pricing of Options and Corporate Liabilities:

a) The short-term interest rate is known and is constant through time.

b) The stock price follows a random walk in continuous time with a variance rate proportional to the square of the stock price. Thus the dis- tribution of possible stock prices at the end of any finite interval is log- normal. The variance rate of the return on the stock is constant.

c) The stock pays no dividends or other distributions.

d) The option is “European,” that is, it can only be exercised at maturity.

e) There are no transaction costs in buying or selling the stock or the option.

f) It is possible to borrow any fraction of the price of a security to buy it or to hold it, at the short-term interest rate.

g) There are no penalties to short selling. A seller who does not own a security will simply accept the price of the security from a buyer, and will agree to settle with the buyer on some future date by paying him an amount equal to the price of the security on that date.

Essentially, this model assumes perfect information, stable markets, and no brokers as middle-men to markets. This beautiful equation is nothing but unrealistic. Black and Scholes founded the formula not to make money, but to “find the truth.” Like many other economists, their work is the result of nothing other than their inherent desire to study economics. In fact, when they first initially tested the model, it was nothing more than field testing. They bought some options, and lost money.

Why? The Black-Scholes model is nothing more than a theoretical ingenuity. The performance of Long Term Capital Management, the hedge fund in which Myron Scholes and Robert Merton were on the board of directors, indicates that knowledge of pretty formulas does not necessarily lead to success.

This brings up a big problem: is it the fault of Black-Scholes that the options market has caused much grief for the common man? I think the problem is similar to Einstein’s theories were instrumental in facilitating the development of atomic weapons that kill hundreds of thousands of people, but that by no means suggests he is responsible for the use of the bomb. Similarly, the Black-Scholes model does not in itself prevent irresponsible use. Rather, the user is required to remain diligent and responsible whilst using it. It led to a boom in the establishment of the modern options market, but it by no means promotes irresponsible and unethical trading behavior.

What’s more, in fact, modern traders don’t even use the original Black-Scholes model anymore. They either use advanced derivations or separate models to valuate options. For instance, Goldman Sachs only uses a derivation for the Black-Scholes model for short-term options on long-term bonds.

That being said, the Black-Scholes model is a rather misunderstood model that has been all too often linked with “evil.” Rather, it was just the result of two men and a dream for economic truth. As for its “evil”, I think it may all just be media hype.

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