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"
