40

# Original thinking in a derivatives market

## How those models work

### Computer says 'no'...

So there is a really interesting and lucrative optimisation problem here in balancing risk and reward, so complex that some outfits use genetic algorithms to crack it. Although efficient, the problem is that the answer "just works", without anyone understanding the underlying problem. And of course this means that when it goes wrong, no-one really knows why.

There are firms selling data on the frequency with which a given type of debt has defaulted, and a bit of regression will give a decent approximation to losses in a given time.

We know that interest rates and defaults correlate, but of course we don't know how rates will move.

So take a rubber band with a weight on one end. Prod it, and the result will look at bit like the way interest rates move over time.

There is a long-term average, of the weight when standing still, and a volatility which is how hard you kick it. The further away from the middle it gets, the more it gets pushed back, so it jumps about more violently the further away from the average it gets. This Vasicek model is in common use, not because the results are brilliant - there are better multi factor models - but because it's easy to code up in C++ or VBA.

The stock market: it's a gas

### In an ideal gas...

Quant finance models are no more "real" than the infinite infinitesimal points in an ideal gas, or the small green peas that we as teenagers were told were electrons moving through a wire, let alone the menagerie of perfectly rigid, frictionless and elastic objects with zero thickness and mass we fought in maths classes.

They allow us to generate an approximation to reality which we can express in mathematics and turn into VBA. Excel is very common, and it's not done very well. Financial VBA is rarely if ever done well , but it is quick. So the basis for working out prices of derivatives is based upon the diffusion of heat through a metal bar, and Paul Wilmott has sold cartloads of books to bankers using partial differential equations lifted from fluid dynamics, and the banks pay good money (£60-120k/\$50-250k) for a very good physics PhD straight from university to become a quantitative analyst.

It's not just physics PhDs. There are thousands of quants in banks and hedge funds with the CQF or a masters in finance. Banks don't yet seem to have cut back employment noticeably, but no one is expecting bonuses to be as good as last year, even for those in areas like FX, which aren't connected.

Collateralised debt obligations can be put together with many different components, for different customer demand, or more cynically to make them look attractive to fund managers and the advisors of high net worth individuals.

The problem is that these black boxes are tough to understand, even if they are explained gently by the bankers. Just because you have the Linux kernel source, doesn't mean you know what it will do. The mathematics of Copulas are sufficiently hard that most banks simply don't expect most people they hire to really understand them at first. It's been clear for a while that some of the banks have been pushing products whose risks are far from clear, unless you are a specialist. However, no investment is risk free, and many money managers are quick to call foul when they've looked at the pretty return graphs, not the dull mathematical caveats.

For more security, it is possible to insure a bond against default, and if you are keeping up, you will recognise that this insurance can also be sold on, so the decrease in risk is balanced by complexity in working out who is actually affected by an event.