#
2007 APS March Meeting

## Volume 52, Number 1

##
Monday–Friday, March 5–9, 2007;
Denver, Colorado

### Session A22: Focus Session: Econophysics

8:00 AM–11:00 AM,
Monday, March 5, 2007

Colorado Convention Center
Room: 108

Sponsoring
Unit:
GSNP

Chair: Victor Yakovenko, University of Maryland

Abstract ID: BAPS.2007.MAR.A22.8

### Abstract: A22.00008 : Using behavioral statistical physics to understand supply and demand*

9:24 AM–10:00 AM

Preview Abstract
Abstract

####
Author:

Doyne Farmer

(Santa Fe Institute)

We construct a quantitative theory for a proxy for supply and
demand curves using
methods that look and feel a lot like physics. Neoclassical
economics postulates
that supply and demand curves can be explained as the result of
rational agents
selfishly maximizing their utility, but this approach has had
very little empirical
success. We take quite a different approach, building supply and
demand curves
out of impulsive responses to not-quite-random trading
fluctuations. Because of
reasons of empirical measurability, as a good proxy for changes
in supply and
demand we study the aggregate price impact function $R(V)$,
giving the average
logarithmic price change $R$ as a function of the signed trading
volume $V$. (If a
trade $v_i$ is initiated by a buyer, it has a plus sign, and vice
versa for sellers; the
signed trading volume for a series of $N$ successive trades is
$V_N(t) =
\sum_{i=t}^{i=t+N} v_i$). We develop a ``zero-intelligence"
null hypothesis that
each trade $v_i$ gives an impulsive kick $f(v_i)$ to the price,
so that the average
return $R_N(t) = \sum_{i=t}^{i=t+N} f(v_i)$. Under the
assumption that $v_i$ is IID,
$R(V_N)$ has a characteristic concave shape, becoming linear in
the limit as $N \to
\infty$. Under some circumstances this is universal for large
$N$, in the sense that
it is independent of the functional form of $f$. While this null
hypothesis gives
useful qualitative intuition, to make it quantitatively correct,
one must add two
additional elements: (1) The signs of $v_i$ are a long-memory
process and (2) the
return $R$ is efficient, in the sense that it is not possible to
make profits with a
linear prediction of the signs of $v_i$. Using data from the
London Stock Exchange
we demonstrate that this theory works well, predicting both the
magnitude and
shape of $R(V_N)$. We show that the fluctuations in $R$ are very
large and for
some purposes more important than the average behavior. A
computer model for
the fluctuations suggests the existence of an equation of state
relating the diffusion
rate of prices to the flow of trading orders.

*In collaboration with Austin Gerig and Fabrizio Lillo. Work supported by Barclays Bank.

To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2007.MAR.A22.8