Electrodynamical model of quasi-efficient financial market

Abstract

The modelling of financial markets presents a problem which is both theoretically challenging and practically important. The theoretical aspects concern the issue of market efficiency which may even have political implications \cite{Cuthbertson}, whilst the practical side of the problem has clear relevance to portfolio management \cite{Elton} and derivative pricing \cite{Hull}. Up till now all market models contain "smart money" traders and "noise" traders whose joint activity constitutes the market \cite{DeLong,Bak}. On a short time scale this traditional separation does not seem to be realistic, and is hardly acceptable since all high-frequency market participants are professional traders and cannot be separated into "smart" and "noisy". In this paper we present a "microscopic" model with homogenuous quasi-rational behaviour of traders, aiming to describe short time market behaviour. To construct the model we use an analogy between "screening" in quantum electrodynamics and an equilibration process in a market with temporal mispricing \cite{Ilinski,Dunbar}. As a result, we obtain the time-dependent distribution function of the returns which is in quantitative agreement with real market data and obeys the anomalous scaling relations recently reported for both high-frequency exchange rates \cite{Breymann}, S&P500 \cite{Stanley} and other stock market indices \cite{Bouchaud,Australia}.