A prognosis oriented microscopic stock market model

TL;DR

This paper introduces a microscopic stochastic model simulating stock market dynamics based on individual investor forecasts and limit orders, revealing that price differences follow a specific Levy distribution with self-similarity.

Contribution

The model provides a novel microscopic framework for understanding stock price fluctuations driven by investor interactions and forecast-based trading.

Findings

Price difference distribution follows an exponentially truncated Levy distribution.

The model exhibits self-similarity with an exponent mu~5.

Numerical simulations validate the distributional properties.

Abstract

We present a new microscopic stochastic model for an ensemble of interacting investors that buy and sell stocks in discrete time steps via limit orders based on individual forecasts about the price of the stock. These orders determine the supply and demand fixing after each round (time step) the new price of the stock according to which the limited buy and sell orders are then executed and new forecasts are made. We show via numerical simulation of this model that the distribution of price differences obeys an exponentially truncated Levy-distribution with a self similarity exponent mu~5.