1202.0606 (Ribin Lye et al.)

Understanding agent-based models of financial markets: a bottom-up
approach based on order parameters and phase diagrams    [PDF]

Ribin Lye, James Peng Lung Tan, Siew Ann Cheong

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.

View original: http://arxiv.org/abs/1202.0606