The development of the Black-Scholes option pricing formula is a fascinating story. It is well told in this article by sociologist Donald MacKenzie.

The Black-Scholes-Merton analysis provided a range of intellectual resources for those tackling problems of pricing derivatives of all kinds. Amongst those resources were the idea of perfect hedging (or of a ‘replicating portfolio’, a portfolio whose returns would exactly match those of the derivative in all states of the world); no-arbitrage pricing (deriving prices from the argument that the only patterns of pricing that can be stable are those that give rise to no arbitrage opportunities); and a striking example of the use in economics of Itô’s stochastic calculus

MacKenzie also points out how important the “replicating portfolio” approach to option pricing was in changing the perception of options. Rather than being viewed as unnatural gambles, they were shown to be equivalent to established securities. (Thanks to Daniel Davies for linking to the article.)

There are still people who view financial derivatives as dangerous. Notably Warren Buffett, who wrote that “derivatives are financial weapons of mass destruction, carrying dangers that, while now latent, are potentially lethal.”

*For Discussion*. The Black-Scholes formula seems to provide us with a tool to deal with risk. Is this command over risk real, or an illusion?

## READER COMMENTS

## Bernard Yomtov

## May 31 2003 at 5:18pm

Black-Scholes is technology. Used wisely, and not pushed beyond its limits, it is very valuable.

But when it, or other mathematical methods, is used recklessly it can produce disaster. So while the creation and rational pricing of derivatives can reduce risk, they have great potential for abuse.

A car is a great way to get around, but if you zip along at 100 mph something very bad is likely to happen.

## Bob Coleman

## Jun 1 2003 at 6:38am

Warren Buffet, with a more than five-sigma measured IQ, a photographic long-term memory, and a life-long passion for economics, finance and investing, uses a definition of “risk” that makes sense and is accepted by many economists.

The financial derivatives promoters, who are originally academic careerists, use the word “risk” in a misleading way simply to label a statistical concept. Then they take their misnomer for reality.

Which group and which version of risk would you trust with your retirement money?

For even more abstract theory on the optimum societal allocation of risk-bearing in capital markets, see the work of Kenneth J. Arrow.

## Bernard Yomtov

## Jun 1 2003 at 11:15am

Bob,

It would be easier to respond to your post if you defined what you see as the conflicting definitions of risk involved.

My understanding of risk is variance in the distribution of returns. This is often broken down a number of ways, including distinguishing between systematic and non-systematic risk. Yes, these are statistical concepts, and the definition is not exactly what most people think of as financial risk, which tends to be taken as “risk of loss.” But it is not “misleading,” any more than a physicist’s definition of “weight,” which is not quite the same as the common usage of the word, is misleading.

Both definitions are useful, but it’s important to keep in mind which one is being used in a given discussion.

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