Posted by: ardaayvaz | September 25, 2008

Math in Finance – what if it goes wrong?

Hi everyone,

My post is not going to be directly about symmetry or discrete math. However, considering the economic turmoil we are in these days, I thought this article about the Black-Scholes pricing formula that is widely used in finance could be an interesting read:

click here for the article

Prof. Stange mentioned in one of the handouts that the job of mathematician stems from “playing” with mathematical ideas and then formalizing them in the appropriate mathematical language; thus it is an essentially intellectual and abstract endeavor. However, when we try to use mathematical ideas to formalize certain real life events , such as financial markets, the task can have more serious effects. So I think a good question to ask ourselves about this article is if it would be wrong or dangerous when we rely too much on mathematical formulas trying to deal with the complexity of real-life events. Is the mathematics to blame, or over-simplifying by using mathematics? I would appreciate everyone’s comments on the matter.

Arda

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Responses

  1. Because of the attraction of fast money, there are a lot of theories about the stock market, some more or less credible than others. I recently read the book `A mathematician plays the stock market’ by John Allen Paulos, which, incidentally, is where I first learned what it means to short, and only even more recently have I come to understand why it’s frowned upon. (If we think of the market as a giant casino, we may forget that its rise is actually tied to prosperity for everyone.) He mentions a great number of entirely discredited and bizarre mathematical theories for stock-market trends, and claims that we probably cannot use mathematical models to predict it with any great success at all.

    Since I am not very familiar with theories such as Black-Scholes, I can only attempt to answer your question in the abstract. Mathematics, especially statistics, can be used to argue for some action, but in this role it is a tool; it is no more to blame than the hammer we use to build or destroy.

    But is it even an applicable tool? The mere existence of financial markets is a great wonder. We’ve built something that, frankly, we don’t understand, but to which we have handed over an enormous amount of power. Perhaps our error is in thinking the market is mathematical at all. It is, after all, an exercise in human psychology. We should not ‘trust’ mathematics to have our well-being at heart, or to elucidate something to which it may simply not apply.

    One excerpt from Paulos, which I can’t resist repeating here, describes quizzes he administered to his probability class: “I placed a little box at the bottom of each exam sheet and a notation next to it stating that students who crossed the box (placed an X in it) would have ten extra points added to their exam scores. A further notation stated that the points would be added only if less than half the class crossed the box. If more than half crossed the box, those crossing it would lose ten points on their exam scores.” I promise I won’t do this to you… but is there even a mathematical way to analyse this?

    There are fields of mathematics attempting to address these questions, such as complexity theory. But we’re in such a self-referential situation, that the fact of whether we believe (and therefore act upon) a particular theory may determine whether it holds true! How do you even start in such a situation?

    I’m also very interested in everyone’s responses, since many of you know much more about economics and finance than I ever will.

  2. Here’s a mathematician’s take on the question of mathematical responsibility and some discussion there:

    Ars Mathematica’s (math blog) on mathematical responsibility for the current economic crisis.

    (The above is a response to a post about the crisis on
    Not Even Wrong (a string-theory blog).)

  3. Even more interesting comments from mathematicians on the mathematical roots of the problem:

    Good Math Bad Math: Bad Probability and Economic Disaster; or How Ignoring Bayes Theorem Caused the Mess.


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