A new Model for Stock Price Movements

A new alternative diffusion model for asset price movements is presented. In contrast to the popular approach of Brownian motion it proposes deterministic diffusion for the modelling of stock price movements. These diffusion processes are a new area of physical research and can be created by the chaotic behaviour of rather simple piecewise linear maps, but can also occur in chaotic deterministic systems like the famous Lorenz system. The reason for the investigation on deterministic diffusion processes as suitable model for the behaviour of stock prices is, that their time series can obey certain stylized facts of real world stock market time series. For example they can show fat tails of empirical log returns in union with varying volatility i.e. heteroscedacity as well as slowly decaying autocorrelations of squared log returns. These phenomena could not be explained by a simple Brownian motion and have been the most criticism to the lognormal random walk. The scope is to show that deterministic diffusion models can explain the occurrence of those empirical observed stylized facts and to discuss the implications for economic theory with respect to market efficiency and option pricing.