| Abstract: |
We describe a bottom-up framework, based on the identification of appropriate
order parameters and determination of phase diagrams, for understanding
progressively refined agent-based models and simulations of financial markets.
We illustrate this framework by starting with a deterministic toy model,
whereby $N$ independent traders buy and sell $M$ stocks through an order book
that acts as a clearing house. The price of a stock increases whenever it is
bought and decreases whenever it is sold. Price changes are updated by the
order book before the next transaction takes place. In this deterministic
model, all traders based their buy decisions on a call utility function, and
all their sell decisions on a put utility function. We then make the
agent-based model more realistic, by either having a fraction $f_b$ of traders
buy a random stock on offer, or a fraction $f_s$ of traders sell a random
stock in their portfolio. Based on our simulations, we find that it is
possible to identify useful order parameters from the steady-state price
distributions of all three models. Using these order parameters as a guide, we
find three phases: (i) the dead market; (ii) the boom market; and (iii) the
jammed market in the the phase diagram of the deterministic model. Comparing
the phase diagrams of the stochastic models against that of the deterministic
model, we realize that the primary effect of stochasticity is to eliminate the
dead market phase. |