Black Scholes and the formula of doom

Financial Times

It has been argued that one formula known as Black-Scholes, along with its descendants, helped to blow up the financial world.

Well, that got FT Alphaville’s attention this weekend! For a good part of Saturday, the article with the above sentence was among the Most Read on the BBC News website. Not bad for an article about option pricing.

The piece is from Tim Harford’s programme “More or Less” on Radio 4. (Mr Harford is also an FT columnist.)

Our interest was piqued by the above opener… which is a polite way of saying we were intensely skeptical about where this was going.

On the one hand, it’s exciting to see such an article, that is clearly going to try to make some bit of financial markets accessible to a wider audience, be so popular. On the other, did a mathematical formula just get blamed for the financial crisis?! Excuse us, but guns don’t kill people. People kill people.

So what does the article discuss exactly? It’s in part a Myron Scholes bio, complete with the whole Long Term Capital Management (LTCM) episode, and part story about more and more mathematics coming to Wall Street.

Also there’s Professor Ian Stewart who wrote a book called “Seventeen Equations that Changed the World”, and you can probably guess what he thinks by now. (In the book, Black Scholes is itself equation seventeen, the subject of the chapter called “The Midas formula”.)

Here’s a summary: option pricing can be applied in many places, to many problems, Wall Street got more quantitative overall, and the derivatives industry boomed. Like so:

But Black and Scholes weren’t the only kids in the candy store, says Ian Stewart, whose book argues that Black-Scholes was a dangerous invention.

“What the equation did was give everyone the confidence to trade options and very quickly, much more complicated financial options known as derivatives,” he says.

“By 2007 the trade in derivatives worldwide was one quadrillion (thousand million million) US dollars – this is 10 times the total production of goods on the planet over its entire history,” says Stewart. “OK, we’re talking about the totals in a two-way trade, people are buying and people are selling and you’re adding it all up as if it doesn’t cancel out, but it was a huge trade.”

Professor Stewart on LTCM:

Stewart says the lessons from Long-Term Capital Management were obvious. “It showed the danger of this kind of algorithmically-based trading if you don’t keep an eye on some of the indicators that the more conventional people would use,” he says. “They [Long-Term Capital Management] were committed, pretty much, to just ploughing ahead with the system they had. And it went wrong.”

Scholes does not agree:

Scholes says that’s not what happened at all. “It had nothing to do with equations and nothing to do with models,” he says. “I was not running the firm, let me be very clear about that. There was not an ability to withstand the shock that occurred in the market in the summer and fall of late 1998. So it was just a matter of risk-taking. It wasn’t a matter of modelling.”

Interesting. We wonder exactly what the merry band at LTCM had that gave them the confidence to take such large, risky positions…

To the heart of it then:

Ian Stewart claims that the Black-Scholes equation changed the world. Does he really believe that mathematics caused the financial crisis?

“It was abuse of their equation that caused trouble, and I don’t think you can blame the inventors of an equation if somebody else comes along and uses it badly,” he says.

“And it wasn’t just that equation. It was a whole generation of other mathematical models and all sorts of other techniques that followed on its heels. But it was one of the major discoveries that opened the door to all this.”

Warning: it gets a bit romantic…

Black-Scholes changed the culture of Wall Street, from a place where people traded based on common sense, experience and intuition,

No one ever used to just take a punt? Or get in front of a client trade? Really?! But these days it’s changed:

to a place where the computer said yes or no.

Pretty sure someone programmed the computer… Anyways:

But is it really fair to blame Black-Scholes for what followed it? “The Black-Scholes technology has very specific rules and requirements,” says Scholes. “That technology attracted or caused investment banks to hire people who had quantitative or mathematical skills. I accept that. They then developed products or technologies of their own.”

Not all of those subsequent technologies, says Scholes, were good enough. “[Some] had assumptions that were wrong, or they used data incorrectly to calibrate their models, or people who used [the] models didn’t know how to use them.”

Models don’t cause crises. People cause crises.

Discuss.

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