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Electrodynamical model of quasi-efficient financial market

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Kirill N. Ilinski
Alexander S. Stepanenko

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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}.

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Paper provided by arXiv.org in its series Quantitative Finance Papers with number cond-mat/9806138.

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Date of creation: Jun 1998
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Handle: RePEc:arx:papers:cond-mat/9806138

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  1. P. Bak & M. Paczuski & M. Shubik, 1996. "Price Variations in a Stock Market with Many Agents," Working Papers 96-09-075, Santa Fe Institute.
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  2. J. Bradford De Long & Andrei Shleifer & Lawrence H. Summers & Robert J. Waldmann, . "Noise Trader Risk in Financial Markets," J. Bradford De Long's Working Papers _124, University of California at Berkeley, Economics Department. [Downloadable!]
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