Black-Scholes: The maths formula linked to the financial crash (BBC)

[eppur_se_muova]

By Tim Harford
BBC Radio 4, More or Less

It's not every day that someone writes down an equation that ends up changing the world. But it does happen sometimes, and the world doesn't always change for the better. It has been argued that one formula known as Black-Scholes, along with its descendants, helped to blow up the financial world.

Black-Scholes was first written down in the early 1970s but its story starts earlier than that, in the Dojima Rice Exchange in 17th Century Japan where futures contracts were written for rice traders. A simple futures contract says that I will agree to buy rice from you in one year's time, at a price that we agree right now.

By the 20th Century the Chicago Board of Trade was providing a marketplace for traders to deal not only in futures but in options contracts. An example of an option is a contract where we agree that I can buy rice from you at any time over the next year, at a price that we agree right now - but I don't have to if I don't want to.

You can imagine why this kind of contract might be useful. If I am running a big chain of hamburger restaurants, but I don't know how much beef I'll need to buy next year, and I am nervous that the price of beef might rise, well - all I need is to buy some options on beef.

But then that leads to a very ticklish problem. How much should I be paying for those beef options? What are they worth? And that's where this world-changing equation, the Black-Scholes formula, can help.
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more: http://www.bbc.co.uk/news/magazine-17866646

podcast: http://www.bbc.co.uk/podcasts/series/moreorless (Click on the speaker buttons on the RH side of the page to play directly.)




I was going to post this in Science, or Economics, but then decided it deserved to be as widely read as possible ...

[yodermon]

1. Interesting. Max Keiser has been lambasting the Black-Scholes equation on his show for some time now

I was never sure what it was.

[provis99]

2. the movie Margin Call was built around this equation.

or more explicitly, it was built around a statistician at a Wall Street firm discovering the flaw in the equation, and the firm trying to sell all it's holdings before the buyers find out.

[eppur_se_muova]

3. Thanks, now I'm likely to rent that movie. nt

[longship]

4. Ian Stewart is a smart guy

Quoted in the article. It's a good read.

[Lucky Luciano]

5. Everyone in finance knows Black Scholes is flawed,

Last edited Sat Apr 28, 2012, 06:21 PM - Edit history (2)

but it is a good benchmark to start from. It is not like there is this one statistician on Wall Street who was discovering its flaws. The flaws were known from the start.

It assumes securities have a log normal distribution of returns and that the price path is continuous with constant log normal volatility. This is probably a good assumption during most trading hours, but only a few minutes of this assumption being incorrect misprices the option.

People have tried a lot of models where Black Scholes was a starting point to something more complicated like local volatility models, stochastic volatility, stochastic vol with jump diffusion, local stochastic vol. They are all flawed and make assumptions like any model, but improve the original Black Scholes model.

The hardest thing for wall street models to get right is correlation. Correlation is very hard to hedge and anticipate when things go to shit. Like, " how many subprime borrowers should default in this CDO if we know that x number have defaulted in the past.". The correlation of defaults was tough to model. Not enough hard data that was similar in the history of the US with such lax lending standards to properly estimate.

I could go on and on, but...