Too simple for a final-year project, but OK for a trillion-dollar industry

It is Friday, and I was talking with a colleague on the terrace of the staff club. It was a lovely evening, and for some reason we ended up chatting up about the modelling that is done in places like the City of London. The math they use there is pretty much the same that we and many other physicists having been using since the time of Einstein.

As we understand it, often stock options worth real money, and lots of it, are priced with the help of what is called the Black-Scholes equation. This is a differential equation (i.e., involves rates of changes of quantities) and it is named after Black and Scholes, who invented it.

This equation is actually very simple, you can see it written it down on the Wikipedia page but I can easily describe it in words. It says that in say one day, the change in the value of stock equals the current value of the stock times its average rate of increase or decrease plus a random change. That’s it.

Writing a computer program to calculate solutions to this equation is one of the projects our second-year students can choose to do, as part of a short course on modelling using computers. The equation would be too simple to set its solution as a final-year project.

Yet, apparently huge sums are bet on the basis of predictions of this model, including I guess my (and your) pension. Maybe this is worrying, maybe this is telling me I am in the wrong job. I have to solve much harder equations, and I don’t get paid City-of-London rates.