Complexity theory and the science of finance

Published May 8, 2007

Share

What determines the price of an asset? Like "what is love?", this age-old question has yet to be answered satisfactorily. But unlike love, the value of material assets should be quantifiable.

Let's ignore for a moment debates on the labour theory of value, scarcity, and supply and demand, and consider only prices within modern financial markets. Across the globe, these are mega meeting places of anonymous buyers and sellers.

Without any direct contact, a seller can always find a buyer when the price is right. This process involves some intermediary such as broker or a centralised, possible electronic, exchange. The nature of the trading mechanism has an effect on price formation and is a topic of a relatively young area of research called market microstructure.

For our purposes, we can treat the small-scale details of the market making mechanism as a "black box". Offers to sell and bids to buy are thrown into it and agreed upon prices come out. In this way, the price of an asset is the direct consequence of the interactions between several buyers and sellers.

On a much larger scale, prices must clearly be shaped by macroeconomic factors. But how does this really take place?

There are two key groups of participants in financial markets: those providing the service of market access and those using the service. Service providers include regulators, brokers and various market makers and systems. Service users include personal, public and private interests of investment banks, individuals, investment companies, pension funds, insurance funds, life companies, institutions and the government.

Service users are often referred to as "agents". Agents fall within three broad categories, depending on their behaviour: speculators, hedgers and arbitrageurs. These three groups cover a rich ecology of different behaviours and interests driving financial markets.

Thus, the question of what determines the price of a financial asset is not only answered by trying to look into the trading mechanism "black box". Financial markets are comprised of sets of interacting agents with different and varying agendas, so it requires the understanding of complexity and complex adaptive systems.

There is no widely accepted definition of "complexity" or "complex systems". These terms apply to the interdisciplinary investigation of natural and abstract objects such as ecosystems, communication infrastructures, DNA and the brain.

Complex systems incorporate many autonomous adaptive units that interact in an evolving environment. In ecosystems, the units are animals, while in the brain they are individual cells that function together to control our actions and store memories. It is useful to note that a Boeing 747 is a highly complicated thing, but not a complex system. If you break it up into its individual parts, it will be extremely difficult to put back together, but the parts do not change as you go along, and the reassembled outcome is known and fixed.

Financial markets are complex because purposeful agents compete with each other and adapt their behaviour to improve their performance. At the same time, the collective behaviour of agents has an impact on the financial market as a whole. This may arise through "feedbacks".

The presence of "feedback" implies that the system includes information from its history and responds to it. For example, if the rand drops dramatically against the dollar, many agents may decide to sell rands and buy euros, dollars or pounds. This will cause the value of the rand to drop further and prompt even more selling, and so on. If agents respond simply in this way, the feedback will lead to a crash of the rand value.

In fact, relatively simple feedback like this within automated trading strategies contributed to the crash of the global market in 1987. Agents do learn and markets are often non-stationary. This means that one cannot assume that past statistical properties of the system will remain the same in the future. Moreover, since we cannot rerun history, the system constitutes a "single realisation". This places a limitation on standard statistical techniques.

The system is also coupled to its environment, making it difficult to differentiate between what is self-generated or inside (endogenous) and what is outside (exogenous) the system. Therefore, the entire market is an ecosystem, an interacting and adapting multiagent population influenced by feedbacks on a variable landscape. As a result, the system can cycle through states far from equilibrium (far from the efficient market) and exhibit "extreme behaviour" (market crashes) and "self-organised critical behaviour" (apparently random behaviour on the boundary between order and randomness).

It is not clear what a reasonable theory of complex systems for practical use in finance should be. Clearly, financial markets are not only to be understood for the sake of pension fund investments or profit, they are fascinating examples of complexity theory in interdisciplinary science.

- Diane Wilcox is a lecturer in the department of mathematics at the University of Cape Town and the organiser of the SA Women in Science and Engineering event, A Celebration of Women in Science and Engineering, in August. Tim Gebbie is from Futuregrowth Asset Management

Related Topics: