Electrodynamical Model of Quasi-Efficient Financial Markets

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 (Cuthbertson, 1996), whilst the practical side of the problem has clear relevance to portfolio management (Elton and Gruber, 1995) and derivative pricing (Hull, 1997). Up till now all market models contain "smart money" traders and "noise" traders whose joint activity constitutes the market (De Long et al., 1990; Bak et al., 1997). 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 "noise". 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 (Ilinski, 1997; Dunbar, 1998). 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 (Ghashghaie et al., 1996, S&P500 (Mantegna and Stanley, 1994) and other stock market indices (Bouchaud and Sornette, 1994; Matacz, 1997).