6 A model of a financial market
In Follmer et al. (2005), we develop a model of asset price formation. In
that model, the participants in the market can choose between several
forecasting rules. The choice of these speculative rules will determine the
demands of the various agents and determine the evolution of the equilibrium
prices. What is more, these rules turn out to be self-reinforcing. As
more people adopt a particular forecasting rule, that rule becomes more
accurate and, as a result, more people use it. We give a simple example in
which people have a prospect of investing at home or abroad and, what
determines the profits to be made is the exchange rate. We suggest two
types of rules, one type which we refer to as ‘chartist’ that involves extrapolating
from previous prices. The other is based on the idea that individuals
have an idea as to what the ‘fundamental’ or equilibrium value of
the exchange rate is and expect the rate to return to that value and this
type of rule we refer to as ‘fundamentalist’. The participants in the market
are influenced in their choices of rules and hence, in their decisions, by the
yields obtained by their past choices and by, of course, the movements of
the exchange rate. In this model, self-reinforcing changes in the exchange
rate can occur, since as the number of individuals following a rule
increases, the success of that rule also increases and hence, as I have
said, more people tend to follow it. If the rule is an extrapolatory one,
that is ‘chartist’, then the exchange rate will leave its ‘fundamental’ value
and a ‘bubble’ will occur. Switches in, and transmission of, expectation
formation cause this sort of bubble.