The stock markets are complicated systems and changes in price can appear to be random. However much of what happens in the market can be explained using maths.
Our experts demonstrate how maths can be of use in the market place.
Professor Ian Stewart, believes that many of the decisions that people in the markets have to make about when to buy, and what's a good price, and what will happen in the future appear at first to be more closely related to human psychology or politics than maths but he says, in reality, banks and financial institutions have come to realise that these decisions can be aided by maths. Certain equations appear to be closely related to what the markets do.
"The equations give you some idea of the probabilities, the spread of possibilities, in a sense what the rational decision should be"
Black & Scholes and the Options Markets
According to Ian Stewart the first mathematical equation to really make an impact on the markets was the Black and Scholes equation, an equation used in the options market.
The options market began in the Chicago area, with grain dealing. Farmers were worried about the price of the grain changing during the time that they were actually growing the crop. As a result they started purchasing options. These fix the price and are in effect a promise to deliver the grain to the purchaser at that price in the future. They used this as a way of hedging their bets and protecting themselves against movements in the markets. Then people started trading these options as if they were marketable objects and the options markets were created.
The use of the Black and Scholes equation becomes apparent when you consider the following scenario:
A farmer is selling you wheat. Before he sows the seed you agree the price you will pay him when it is harvested. Three months before the grain is delivered you decide to sell your option to buy the grain, to a third party. How do you decide what it's worth?
Initially you might say it is what ever you can get for it but if you are a bank and you are holding the option as a security you want the right price, which may not necessarily be the price that the market is willing to bear. Black and Scholes came up with a mathematical equation for the probabilities of the price moving in either direction and they worked out what the optimum value in-between was.
What influences the systems?
Setting the rules for the game
How can more specialist mathematical knowledge benefit the markets?
If governments understood the maths within the markets they would be able to interact better says Dr Andy Jackson.
He believes that governments shouldn't intervene in the markets (ie, to prop up currencies) but that they should do what they do well which, Andy Jackson believes, is to set the rules for the markets, shaping the nature of the equilibrium or critical state to which the markets go.
Keeping the systems stable
Adam Smith asked why is it that when everyone is out to satisfy their own greed why does the system remain stable? How are the markets able to remain stable despite the very limited interaction towards a common good.
Dr John Casti believes that if we can understand the structural mechanisms that make the markets stable we will understand a lot of things. He attributes the stability of the markets to the fact that people tend to watch what other people do and then act.
"You tend to have someone that you rely on. You may think they always do the wrong thing."
You've got to look at those traders
What do you learn about the markets if you look at what each individual trader is doing?
Dr John Casti has built an electronic stock exchange to help him to understand the markets by looking at what each individual trader is doing. He has created 60 electronic traders.
At the beginning each trader was given 6 trading rules of their own to use when trading. As trading takes place the electronic traders evaluate the rules they are using and if they see another rule is working better they will shift to that rule in the next period of trading.
If you take out the best trader out of the system and return him a couple of weeks later, encouraging him to use the rules which made him successful before. Almost without fail the trader goes broke. This is because while he was away the market was continuing to evolve and the traders who were in the game were changing the rules. The result is that traders have to keep evolving in order to stay in the game.
Using his electronic stock exchange John Casti was able to demonstrate that the market actually exists on two levels.
If you take a look at say the ftse 100 this is a gross market measure of the whole, and the ftse can move around in a very random way but when you look below the surface what is actually generating these movements are the actions of traders.
It is the interaction between the traders that creates this price movement that appears to be completely random.
"What's generating these [price] movements can be completely deterministic actions of traders"
