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

ArXiv ID: 2509.10553 “View on arXiv”

Authors: Erina Nanyonga, Juma Kasozi, Fred Mayambala, Hassan W. Kayondo, Matt Davison

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.

Keywords: Illiquidity, Geometric Brownian Motion, Ornstein-Uhlenbeck Process, Markov Chains, Correlation Analysis

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper employs advanced stochastic modeling techniques (Markov chains combined with SDEs like XOU and gBm) requiring significant mathematical theory, but the empirical component is primarily theoretical and simulation-based, lacking the backtest-ready implementation details or heavy data processing typical of production-ready quant strategies.

  flowchart TD
A["Research Goal<br>Model illiquid stock prices & explain<br>apparent low correlation at USE"] --> B{"Data & Inputs"}
B --> B1["USE historical stock data<br>(characterized by price constancy)"]
B --> B2["Simulation data<br>(controlled correlation)"]

subgraph C ["Key Methodology Steps"]
    C1["Combine Models<br>Markov + Exponential O-U + gBm"]
    C2["Compare Models<br>Combined vs. gBm alone"]
    C3["Correlation Measurement<br>via simulation & empirical analysis"]
end

A --> C1
C1 --> C2
C2 --> C3

subgraph D ["Computational Processes"]
    D1["Capture constant prices<br>Markov Chain Component"]
    D2["Capture stochastic dynamics<br>XOU & gBm Component"]
    D3["Measure correlation under<br>varying illiquidity parameters"]
end

C1 --> D1
C1 --> D2
C3 --> D3

D3 --> E["Key Findings & Outcomes"]
E --> E1["Illiquidity decouples prices from<br>risk/return & increases sentiment sensitivity"]
E --> E2["Apparent low correlation is<br>an artifact of illiquidity"]
E --> E3["Verified via simulation:<br>High correlation input yields low measured output<br>under high Markov persistence"]