Slightly unfortunate premise about the Black Scholes equation

It was the holy grail of investors. The Black-Scholes equation, brainchild of economists Fischer Black and Myron Scholes, provided a rational way to price a financial contract when it still had time to run. It was like buying or selling a bet on a horse, halfway through the race. It opened up a new world of ever more complex investments, blossoming into a gigantic global industry. But when the sub-prime mortgage market turned sour, the darling of the financial markets became the Black Hole equation, sucking money out of the universe in an unending stream.

And because the derivatives markets were based on Black Scholes and we had a financial crisis, thus the financial crisis came from the use (more accurately, misuse)  of Black Scholes.

Except, well, the financial crisis wasn\’t a crisis in derivatives. It was a crisis in housing finance and the securitization of said mortgages. Which aren\’t to the first order, derivatives and which aren\’t priced using Black Scholes.

Ian Stewart is emeritus professor of mathematics at the University of Warwick. His new book 17 Equations That Changed the World is published by Profile (£15.99)

The maths is fine. It\’s the knowledge of the financial world that\’s a little off.

Even where the crisis was arguably about derivatives (ie, where the value of x depends upon the underlying value of y), credit default swaps and AIG, the problem wasn\’t that they had used B-S to value them. It was that they used bull shit to do so and simply never considered the possibility of a fall in the value of y. That is, they didn\’t value them as options, but as insurance contracts that they would never have to pay out on.

9 comments on “Slightly unfortunate premise about the Black Scholes equation

  1. The Black Scholes model is still kinda crazy. It doesn’t seem very realistic that asset prices are continuous and don’t have jumps in

  2. This is a very common misconception – probably not fair to blame the education system seeing as it’s grown adults getting it wrong as well as studenty types, but I’m pretty sure journalism is partly responsible. The media tend to treat the entire world of Finance as esoteric or even alchemic in nature, and when they do try to explain what’s going on to their audience they often make this particular mistake, or one like it.

  3. The B-S model itself may leave something to be desired. But mainly it’s the use that is made of it that is the problem. Rubbish data in, guess what, rubbish price out.

    Same with that Gaussian t-cupola thingy that was used to price CDOs. David Li went into hiding after the financial crash because his formula was being blamed for catastrophic mispricing of CDOs. But there is nothing wrong with the formula itself (except, in my view, in its use of CDS prices as a proxy for default risk – this assumes that there is a perfect market in CDS, which is very far from being the case). The problem was the unrealistic assumptions made in the use of the model. The model itself, when used properly, demonstrates clearly that CDOs are extremely sensitive to correlation risk and the price crashes quickly at higher levels of correlation in the underlying assets. At 50% correlation they are worthless – as we now know.

  4. Doesn’t all these arguments over equations and models just go to show that part of the reason the finance system collapsed is because there were too many brains and not enough sense in the system.

    In other words there words there were lots of mathematics experts coming up with wierd and wonderfull stuff to try and explain a very chaotic system. They did this by looking at the system from the outside (as they weren’t experts in the finance system) rather than from inside by asking the traders who they worked.

    The traders then started using such equations and models rather than common sense and intuition and proper risk and everything went tits-up. Not enough checks and controls in the system because everyone believed the equations and models answered all questions.

    A bit like climate science. Lots of models and equations about something that is intrinsically chaotic.

  5. SBML

    No, I don’t agree. Many of the models in use in the market today are developed in-house by rocket scientists (they call them analysts, but…) working closely with traders. Pricing and risk management models themselves are a source of competitive advantage, after all.

    I stand by my earlier argument that the models themselves are not the problem, it is the wishful thinking in their use. The financial system did not collapse because people were using mathematical models to design and price exotic instruments. It collapsed because they didn’t use those models properly.

  6. Reading the excellent books “Capital Ideas Evolving”, “Capital Ideas” and “Fooled by Randomness” in fairly quick succession, I think I came to understand where these kind of problems arise.

    Its often about Unknown Unknowns, where the equations used, break down under extreme stress, a fact that is almost impossible to model.

    Creating a model of reality is extremely useful, but after a while, we stop remembering that it is a model, that is simplified.

  7. I suspect it is also subject to a variant of Goodhart’s Law. Taking Serf’s point that models are always going to be simplifications, if somebody knows what you are measuring, there is competitive advantage in comparing your assumptions to their assumptions to reality and gaming the differences.

    Anecdata – the most upset I’ve ever seen a senior banker get was when he thought that an employee might have passed modelling information to his wife, who had moved to another bank. It made him utterly irrational (but, as a trader, he didn’t have that far to go.) He was wrong, as well …

  8. SE

    I’m not surprised. Those in-house models are jealously guarded. I was called to account once by a “rocket scientist” for putting one of his algorithms in a computer program that was going to be used by a different department. Mind you, the department in question was trying to manage market risk across the bank, so might have seriously curtailed the activities of the traders he worked for, I suppose……

  9. MyBurningEars: only one correction. I suspect Prof. Stewart, *highly* respected mathematician, would be flattered to be thought young enough to be a student.

    It has to be said that whenever any of us outside math finance mentions Black-Scholes, we make some lame crack about mathematicians bringing down the financial system. (I had cause to earlier this term, introducing my differential equations course.) The math finance people just go quiet. 😀

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