Solvable Stochastic Dealer Models for Financial Markets

TL;DR

This paper presents solvable stochastic dealer models that replicate key empirical laws of financial markets, including power-law price changes, by incorporating simple effects like transaction interval modulation and price forecasting.

Contribution

It introduces a new class of solvable stochastic models that connect microscopic dealer behaviors with market potential forces, enhancing understanding of market dynamics.

Findings

Models reproduce power-law distribution of price changes

Adding effects improves model realism

Quantitative relation with market potential forces established

Abstract

We introduce solvable stochastic dealer models, which can reproduce basic empirical laws of financial markets such as the power law of price change. Starting from the simplest model that is almost equivalent to a Poisson random noise generator, the model becomes fairly realistic by adding only two effects, the self-modulation of transaction intervals and a forecasting tendency, which uses a moving average of the latest market price changes. Based on the present microscopic model of markets, we find a quantitative relation with market potential forces, which has recently been discovered in the study of market price modeling based on random walks.