We are surrounded by things that do not work well but are nonetheless widely used. Wire coat-hangers and the US border with Mexico are just two examples. Another, according to Nassim Nicholas Taleb, is the BlackScholes model.

The equation, named after Fischer Black and Myron Scholes, the men who devised it in 1973, is widely seen as the best method available for pricing options and the derivatives based on them. It is often argued that Black-Scholes has provided the basis for the explosion of derivatives trading over the past two decades.

But Mr Taleb, a controversial mathematical trader and author of Fooled by Randomness and The Black Swan, thinks the fundamentals of the equation are plain wrong, that it is not used in practice, and that the revered status of its founders, who were given the Nobel prize for their discovery, is undeserved.

Derivatives have been at the centre of the continuing crisis in credit markets. In particular, what this turbulence has demonstrated is that complex structured products and derivatives can be difficult and at times impossible to value.

Mr Taleb’s assertions, if correct, challenge the very basis for much of quantitative finance – especially those parts based on computer-driven trading that employ complex mathematical and statistical models to exploit price fluctuations. Last August some of the world’s most advanced quantitative traders, including Renaissance Technologies, Goldman Sachs and DE Shaw, lost billions of dollars as their models were flummoxed by sudden unexpected swings in market prices.

Mr Taleb believes Black-Scholes was partly to blame. The model assumes, for example, that the underlying stock can be short-sold and that it is possible to borrow cash at a constant, risk-free interest rate – conditions that were palpably absent last August.

Mr Scholes, the 1997 winner of the Nobel Prize for his work on the equation, does not think Mr Taleb’s theories are up to much. “I don’t want to glorify him by refuting what he says,” said Mr Scholes at a recent conference. He dismisses Mr Taleb as someone who simply “popularises ideas and is making money selling books”, arguing that academics do not take him seriously because he does not cite previous literature.

But Mr Taleb sticks to his guns. “I am simply questioning and my questions are valid. I am not doing this for the money. The fact is other models are not subject to the same unrealistic assumptions behind Black-Scholes, even though it is Black- Scholes that essentially launched the quant revolution.”

At the heart of his objections is the notion that the model does not give you a prediction of an option’s value in practice, as the market and many academics say it does. Rather, it tells you how much you would have to pay for a purely theoretical position.

Replacing Black-Scholes would be no easy matter. In Quantitative Finance 101 in lecture halls around the world, deriving option values using the model is often the first thing you do after brushing up on basic calculus.

But Mr Taleb says that, in practice, many in the market prefer to value options using the work of Louis Bachelier and Edward Thorp, much of which predates the work of Black and Scholes.

One of Mr Taleb’s main objections to Black-Scholes and various other quantitative tools is that they are too backward-looking. Just as it was wrong to assume that all swans were white before the first black species was spotted in Australia in the 17th century, so in markets historical analysis is an inadequate way to judge risk, he says.

Thus the recent past has starkly exposed the limitations of trying to apply models based on historical prices. The problem, according to Espen Haug, an author and a former options trader and academic who has worked with Mr Taleb on recent research papers, is that no matter what model you apply, it does not anticipate every potential disaster, such as the mistaken credit ratings on defaulted subprime debt.

“Finance is an area that’s dominated by rare events and the rules underestimate the impact of an infrequent occurrence,’’ says Mr Taleb. “The tools we have in quantitative finance do not work in what I call the ‘black swan’ domain.’’

Sahbi Jerad, head of dollar options trading at BNP Paribas in New York, points out that a model does not have to reflect reality perfectly to be useful. “What we actually use is a variation on the original Black-Scholes. We like having Black-Scholes as a basis. It gives us a quick and simple tool to assess option values,” he says. “From a practical point of view, we need models for pricing and risk management. Before we use them, traders learn about the limitations and weaknesses of the models and adjust their pricing and risk management strategy accordingly.”

Pablo Triana, director of the Centre for Advanced Finance at the Instituto de Empresa in Madrid, says that academics and practitioners would do well to listen to Mr Taleb and Mr Haug. He says that the beautiful theoretical construct behind the Black-Scholes model offers a good rationale for why options should cost money and how much. But he adds that it is not applicable in real life. “The whole basis of quantitative finance is flawed if it is based on the Black-Scholes derivation, where volatility is essentially fudged,” he says.

Prof Triana believes much academic resistance to criticism of the Black-Scholes model is due to the fact that its loss would undermine other prized certainties, however misplaced, such as faith in the “Greeks”. These are the various symbols – for example, delta, gamma and vega – used to denote the risk of an option trader’s position, or implied volatility. This implied volatility is assumed by many not only to exist but to represent the market’s view of turbulence. This, he says, is not the case.

Mr Taleb concludes that the explosion in options trading is best explained by the technological advances of the computer age – the development of scholastic finance, he argues, is more of a by-product than a cause of the market’s growth. “Once again, lecturing birds on how to fly does not allow one to take subsequent credit,” he says.