The author has argued before, for example in: 'The Risk Implications of Complex Markets', that the complexity of modern markets could lead to severe unforeseen difficulties; and in particular, that naive attempts to manage risk could actually make things considerably worse under extreme circumstances, such as those currently being experienced. There are three main reasons for this:

• Complexity inevitably leads to a lack of transparency - the system is now so complex that no one has a really good understanding of it. In this context 'efficient' markets tend to be reactive, and, perversely, sometimes appear dangerously irrational.
• We believe that the use of risk management tools to offset and distribute risk may only serve to reduce intermediate levels of risk, and may actually substantially increase extreme risks, without us being aware of it.
• The complex inter-coupling of financial institutions by derivatives and financial risk management instruments may create an environment in which a new phenomenon, which the author has termed 'The Risk Soliton' might be unleashed, with potentially catastrophic consequences.

We have covered the first two of these points elsewhere, and used the example of events at 'LLoyd's of London' in the not too distant past to illustrate them.

One of the points that we have made is that the complex inter-coupling of financial institutions - particularly through the use of derivatives, and in particular, 'credit derivatives' does not always necessarily make the overall system more robust, and we have used the example of a spider's web to illustrate this: if the strands are made too strong, then when an object hits it sufficiently hard, instead of making a hole in the web, it is completely destroyed.

This article is about the third factor, since this is now probably the first time ever that this, perhaps rather frightening theoretical possibility, might actually occur. Unfortunately this is not a straightforward thing to understand, and draws on analogies from physics and nature, based on the behaviour of what are known as 'non-linear systems'.

The transactions that financial institutions undertake with one another often take the form of 'derivatives', often credit derivatives. These are sometimes effectively just insurance policies which provide protection against defaults and other 'credit events'; but in other cases, they are much more complicated.

A key feature of most of these derivatives is that they are fundamentally 'non linear' in nature. This fact is often obscured by the fact that when markets are behaving normally, the process of 'dynamic hedging' is continuously undertaken to control risk in a localised way, so that changes that would otherwise occur due to these non-linear 'convexity effects' are less evident.

We have previously argued that the degree of interconnection between financial institutions is probably a bad thing; here we argue that the type of interconnection could itself be an especially bad thing, for reasons described in the following.

'Waves' occur in many different forms in nature, and are all around us - ranging from sound waves, or waves of light, to the ripples on a pond. In physics, waves are described by a very simple equation, 'the wave equation', which describes, explains and predicts their behaviour. In simple language this equation describes how a small 'ripple' can keep on going - because of how the medium in which the wave is travelling responds to the 'small perturbations' that it makes.

Unfortunately, these are not the only kind of waves that are possible, either in theory, or that are found in nature. There are also non-linear waves that are known as Solitons. These are waves that are driven by the non-linear behaviour of the medium in which they propagate, and are an entirely different animal altogether.

These soliton waves owe their existence and behaviour to non-linearity, i.e. the fact that a 'small perturbation' in an underlying medium can produce a response which is 'curved' - responding increasingly disproportionately.

These strange phenomena have practical uses, for example, in laser fibre-optics, where the strength of a laser beam causes the material in the fibre to behave in a non-linear fashion, and enables 'soliton pulses' to be propagated and sustained over long distances.

Another possible example are huge ocean waves, far larger than ought to be possible due to conventional physical mechanisms - and often thought to be mythical, but whose existence has been confirmed by satellite observations,

So what has any of this got to do with the troubles of the financial system in the current circumstances ?

The answer is that financial engineering has been used to create a highly complex mesh of non-linear interconnections between banks and other financial institutions, which could prove to be an ideal medium for the birth and propagation of a financial Risk Soliton, the ferocity of which we would be ill prepared for.

There is a chance that given the kind of 'shock to the system' that financial markets are currently experiencing, together with the complexity and non-linear coupling between financial institutions, could create a catastrophic non-linear wave of destruction that would spread through the world's financial system; largely travelling through the medium of the credit and other derivatives transactions which bind them together.

So could the fall of Lehman Brothers trigger this, what are the chances of this happening, and what might be done to prevent it ?

In my own view, the fall of Lehman Brothers would not be enough to trigger such an effect, but it certainly makes it more likely, the odds are perhaps only a few percent. In contrast however, today we have heard again that AIG is in trouble, and the collapse of AIG would raise the odds significantly, perhaps to 1 in 10, or greater.

If we escape this time, then we should not forget what has happened, and the world's governments, central banks and regulators should focus their minds on whether fundamental changes need to be made, on a scale which, even a year ago, would have been unthinkable.

The author, Dr Andrew Gray, who is the managing director of RCRT, has a PhD in physics from Cambridge University. He has worked extensively within banks and investment banks in the modelling, pricing and risk-analysis of a range of financial derivatives.

He has also worked extensively in portfolio credit risk management, modelling and analysis, and was formerly the 'Head of Risk-Adjusted Portfolio Analysis', within the group-level risk management function for a major UK banking group.