Actuaries aren’t highly renowned for bouts of creativity. We tend to deal with boring reams of mortality tables. Our theorems are named after famous actuaries of the late 19th century that nobody’s heard of. They’re so boring that I’ve forgotten most of them. There’s one that nearly comes to mind named after someone whose name starts with an H, and the formula has a K in it somewhere. (Or was it the other way around?) Thrilling, truly memorable stuff.
But every now and then, someone comes along and tries to do something about this. Perhaps once every hundred years or so. Usually they fail. But I think a new development in market risk calibration may just cut the grade and bring a new sense of hipness to the actuarial syllabus.
Market risk calibration is all about trying to fit a statistical curve to actual market data (share price movements, interest rate fluctuations, etc). The idea is that if you can match a theoretical distribution to the actual data pretty well, you can predict the future a bit better. Now, simplifying things somewhat, in doing this, you plot the actual data on a graph, stick a licked finger in the air, and come up with a line that goes through the middle. The idea is that the variance between the line, and the actual points.
Obviously, the tricky bits come in because the line isn’t straight, and the way of measuring the variance is complicated. Especially as there are multiple factors involved – and you need to keep the interdependence between them under control. One way of doing this is by combining the impact of the various factors by using a formula called a copula. At this point, I’ll skip past the necessary discussion of rank correlation and cross correlation, and get to the point. There’s a particular type of copula, with a certain level of rank correlation, known as a spider copula. And the name given to the property which determines this is arachnitude. It’s a measure of how extreme the data is – or how many outliers there are. Or, to labour the point a bit, how much the data graph looks like a spider straddling the fit line. Where arachnitude = 1, you have a spider copula.
Now, you may find that just a little bit cheesy (or most probably, a little bit sad), but in my world, that’s about as cool as it gets. Actuaries don’t get it any better than this.
If you’d like to judge how new all this is, Google ‘arachnitude‘ or ‘spider copula‘, and see how few results there are. If you’d like to know more about them, then here’s a presentation (which has a link to the actual paper on page 2).