### Mandelbrot's telescope

I'm currently rereading Benoit Mandelbrot's The (Mis)Behaviour of Markets, as preparation for an essay on the option-pricing implications of non-normal distributions of stock prices (ripping stuff, I assure you).

Mandelbrot's basic argument here is that stock price movements don't have the log-normal distribution assumed by the conventional theory underpinning the Black-Scholes-Merton option pricing formulae, but rather a power-law distribution, as the evidence appears to bear out. This means that much of modern finance theory is based on assumptions that are demonstrably wrong. As Mandelbrot (and/or his co-author Richard Hudson) puts in, an a passage I found rather endearing -

Fair comment on the reluctance of economists to change their paradigms (although it does seem as though power-law distributions are now well established in the statistical finance field). But I do think he's being rather generous in his assessment of astronomers...

I interviewed Mandelbrot about his financial work a few years ago. He's probably the most egotistical person I've ever interviewed, but I guess he's entitled to be. And I'll always treasure his explanation of why his work is like a beautiful woman.

Mandelbrot's basic argument here is that stock price movements don't have the log-normal distribution assumed by the conventional theory underpinning the Black-Scholes-Merton option pricing formulae, but rather a power-law distribution, as the evidence appears to bear out. This means that much of modern finance theory is based on assumptions that are demonstrably wrong. As Mandelbrot (and/or his co-author Richard Hudson) puts in, an a passage I found rather endearing -

*If this were astronomy, the argument would have ended long ago. Imagine observatories suddenly finding a new planet where, the standard theory says, none should be. And then another, and another and another. Astronomers, after checking their instruments, would not ignore the data; they would question their understanding of celestial mechanics and a new and fruitful episode in astronomy would dawn. But it does not work that way in economics, even though the equivalent of countless new planetary systems have been recorded.*Fair comment on the reluctance of economists to change their paradigms (although it does seem as though power-law distributions are now well established in the statistical finance field). But I do think he's being rather generous in his assessment of astronomers...

I interviewed Mandelbrot about his financial work a few years ago. He's probably the most egotistical person I've ever interviewed, but I guess he's entitled to be. And I'll always treasure his explanation of why his work is like a beautiful woman.

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