We present a lattice gas model of financial markets to explain previous empirical observations of the interplay of trends and reversion  . The shares of an asset are modeled by gas molecules that are distributed across a hidden social network of investors. Neighbors in the network tend to align their positions due to herding behavior. The model is equivalent to the Ising model on this network, with the magnetization in the role of the deviation of the asset price from its value. For N independent assets, it generalizes to an O(N) vector model. In efficient markets, the system is driven to its critical temperature  . There, it is characterized by long-range correlations and universal critical exponents, in analogy with the second-order phase transition between water and steam. Using the renormalization group, we show that these critical exponents imply predictions for the auto-correlations of financial market returns. For a simple network topology, consistency with observation implies a fractal dimension of the network of 3.3  and a correlation time of 10 years. While the simple model agrees well with market data on long time scales, it cannot explain the observed market trends over time horizons from one month to one year. In a next step, the approach should therefore be extended to other models of critical dynamics and to general network topologies. It opens the door for indirectly measuring universal properties of the hidden social network of investors from the observable interplay of trends and reversion .
Motivated by empirical observations on the interplay of trends and reversion , a lattice gas model of financial markets is presented . The shares of an asset are modeled by gas molecules that are distributed across a hidden social network of investors. The model is equivalent to the Ising model on this network, whose magnetization represents the deviation of the asset price from its value. It is argued that the system is driven to its critical temperature in efficient markets . There, it is characterized by universal critical exponents, in analogy with the second-order phase transition between water and steam. These critical exponents imply predictions for the auto-correlations of financial market returns. For a simple network topology, consistency with the observed long-term auto-correlations implies a fractal network dimension of 3.3 , and a correlation time of 10 years. To also explain the observed short-term auto-correlations, the model should be extended beyond the critical domain, to other network topologies, and to other models of critical dynamics .
R
We present a lattice gas model of financial markets to explain previous empirical observations of
Motivated by empirical observations on
A
, a lattice gas model of financial markets is presented
D
Neighbors in the network tend to align their positions due to herding behavior.
R
with the magnetization in the role of the
whose magnetization represents the
R
For N independent assets, it generalizes to an O(N) vector model. In efficient markets,
It is argued that
A
in efficient markets
D
long-range correlations and
R
Using the renormalization group, we show that these
These
R
observation
the observed long-term auto-correlations
R
dimension of the network of
network dimension of
A
,
R
While the simple model agrees well with market data on long time scales, it cannot
To also
R
market trends over time horizons from one month to one year. In a next step, the approach should therefore be extended to other
short-term auto-correlations, the model should be extended beyond the critical domain, to other network topologies, and to other
D
and to general network topologies. It opens the door for indirectly measuring universal properties of the hidden social network of investors from the observable interplay of trends and reversion