Today’s Observer (the Sunday Guardian) has an interesting article about derivatives valuation by Professor Ian Stewart. You’ll probably know Stewart from books he has written with Jack Cohen and Terry Pratchett, and you may remember that for a couple of years I made a living from teaching derivatives valuation, so this is a nice confluence of interests.
Stewart, as I expected, has a good grasp of the mathematics of the Black-Scholes equation, and also does a fine job of presenting the issues to the newspaper-reading public in an accessible manner, though he necessarily simplifies a lot. If he’d just been writing for you lot he could probably have saved a lot of time and words by explaining that Black-Scholes assumes a normal distribution of price fluctuations and in many markets (in particular electricity where I work) that’s very obviously a bad assumption.
The real issue, however, is not in the valuation of individual derivatives, but understanding how those valuations can change with changing market conditions, and how the complex portfolio of instruments owned by a financial institution, and the other institutions with which it trades, can interact to amplify a disaster. There’s also the issue that any form of statistical analysis requires a very large number of instances on which to work. Something that works in stock markets may not work in the much more limited and exotic realm of more complex financial instruments.
Where I mainly disagree with Stewart is where he says, “The world economy desperately needs a radical overhaul and that requires more mathematics, not less.”
I really don’t believe that more mathematics will help. I worked for a company that was at the cutting edge of that sort of work. There’s a lot of research out there, and mostly it was getting ignored. In just about every training course my colleagues and I gave we made the point that understanding the assumptions on which your calculations are based is key to managing risk. This has been obvious ever since Merton and Scholes were involved in the Long Term Capital Management disaster.
The main problem was, and probably still is, that people simply don’t want to listen. It is like trying to tell teenage boys not to drive so fast. Having a better mathematical model isn’t going to help. If people can make silly money in the short term, and get out before everything goes pear-shaped; or rely on a government bail-out because they are “too big to fail”; then we’ll always have this sort of problem.