| Abstract: |
A dynamical model is introduced for the formation of a bullish or bearish
trends driving an asset price in a given market. Initially, each agent decides
to buy or sell according to its personal opinion, which results from the
combination of its own private information, the public information and its own
analysis. It then adjusts such opinion through the market as it observes
sequentially the behavior of a group of random selection of other agents. Its
choice is then determined by a local majority rule including itself. Whenever
the selected group is at a tie, i.e., it is undecided on what to do, the
choice is determined by the local group belief with respect to the anticipated
trend at that time. These local adjustments create a dynamic that leads the
market price formation. In case of balanced anticipations the market is found
to be efficient in being successful to make the "right price" to emerge from
the sequential aggregation of all the local individual informations which all
together contain the fundamental value. However, when a leading optimistic
belief prevails, the same efficient market mechanisms are found to produce a
bullish dynamic even though most agents have bearish private informations. The
market yields then a wider and wider discrepancy between the fundamental value
and the market value, which in turn creates a speculative bubble.
Nevertheless, there exists a limit in the growing of the bubble where private
opinions take over again and at once invert the trend, originating a sudden
bearish trend. Moreover, in the case of a drastic shift in the collective
expectations, a huge drop in price levels may also occur extremely fast and
puts the market out of control, it is a market crash. |