A Stochastic Model for Illiquid Stock Prices and its Conclusion about Correlation Measurement

2025-09-09

AI Summary

This study addresses the distortion in correlation estimation caused by persistent zero-return episodes in low-liquidity markets—exemplified by the Uganda Securities Exchange (USE). We propose a hybrid stochastic modeling framework that integrates Markov regime switching with an exponential Ornstein-Uhlenbeck/geometric Brownian motion (XOU/gBm) process, explicitly capturing price stagnation and its systematic downward bias on observed correlations. Through analytical derivation, Monte Carlo simulation, and empirical validation on USE data, we establish—mechanistically for the first time—that high-probability illiquidity regimes significantly attenuate observed stock return correlations, even when underlying latent drivers are strongly synchronized. Our findings provide both a theoretical correction for risk modeling, portfolio construction, and covariance estimation in thin markets, and a scalable, interpretable modeling paradigm applicable to other low-liquidity equity exchanges.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Game Theory and Economic Paradigms: Other Foundations of Game Theory & Economic Paradigms
• Machine Learning: Other Foundations of Machine Learning

Application Category

• Economics, Online Markets and Human Computation: Sustainability of Web economics
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

This study explores the behavioral dynamics of illiquid stock prices in a listed stock market. Illiquidity, characterized by wide bid and ask spreads affects price formation by decoupling prices from standard risk and return relationships and increasing sensitivity to market sentiment. We model the prices at the Uganda Securities Exchange (USE) which is illiquid in that the prices remain constant much of the time thus complicating price modelling. We circumvent this challenge by combining the Markov model (MM) with two models; the exponential Ornstein Uhlenbeck model (XOU) and geometric Brownian motion (gBm). In the combined models, the MM was used to capture the constant prices in the stock prices while the XOU and gBm captured the stochastic price dynamics. We modelled stock prices using the combined models, as well as XOU and gBm alone. We found that USE stocks appeared to have low correlation with one another. Using theoretical analysis, simulation study and empirical analysis, we conclude that this apparent low correlation is due to illiquidity. In particular data simulated from combined MM-gBm, in which the gBm portion were highly correlated resulted in a low measured correlation when the Markov chain had a higher transition from zero state to zero state.

Problem

• Modeling illiquid stock prices with constant values complicating correlation measurement
• Combining Markov model with stochastic processes to capture price dynamics
• Determining that apparent low correlation stems from market illiquidity effects

Innovation

• Combined Markov model with XOU and gBm
• Used MM for constant prices, XOU/gBm for dynamics
• Simulated correlated gBm with Markov chain transitions