Modeling stock markets through the reconstruction of market processes

TL;DR

This paper investigates the stochastic nature of financial markets by analyzing stylized facts and constructing Markov chain models, demonstrating that such models outperform random walk assumptions in capturing market dynamics.

Contribution

It introduces a Markov chain-based modeling approach for stock markets and provides a generalized algorithm applicable to various alphabet sizes and chain lengths.

Findings

Markov models outperform random walk models in market prediction

Stylized facts like memory effects and power-law behavior are evident in data

The MATLAB code for the model is publicly available on GitHub

Abstract

There are two possible ways of interpreting the seemingly stochastic nature of financial markets: the Efficient Market Hypothesis (EMH) and a set of stylized facts that drive the behavior of the markets. We show evidence for some of the stylized facts such as memory-like phenomena in price volatility in the short term, a power-law behavior and non-linear dependencies on the returns. Given this, we construct a model of the market using Markov chains. Then, we develop an algorithm that can be generalized for any N-symbol alphabet and K-length Markov chain. Using this tool, we are able to show that it's, at least, always better than a completely random model such as a Random Walk. The code is written in MATLAB and maintained in GitHub.