Markov Chain and Fundamental Matrix Solution for Assessing Stock Market Price Variation in UNICEM and BUA PLC

G. L Nwosu; L. E George; I. B Ekeanyanwu

doi:10.56201/wjfir.v10.no2.2026.pg1.16

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Markov Chain and Fundamental Matrix Solution for Assessing Stock Market Price Variation in UNICEM and BUA PLC

G. L Nwosu, L. E George, and I. B Ekeanyanwu

Abstract

Stock market price movements are inherently stochastic and require structured probabilistic models for effective analysis and investment decision-making. This study applies a three-state Markov Chain model and a fundamental matrix solution to examine stock price variations of UNICEM Nigeria PLC and BUA Nigeria PLC using closing price data from the Nigerian Exchange spanning 2022–2025. Transition probability matrices were constructed to capture upward, downward, and stable price movements. The results reveal near-balanced transition probabilities across states, confirming the stochastic and memoryless nature of stock price dynamics. Expected mean rate of return and growth rate analyses indicate that UNICEM exhibits relatively stronger long-term growth stability, while BUA demonstrates slightly stronger short- term upward tendencies. The fundamental matrix solution, derived through eigenvalue and eigenvector analysis, shows that future price movements follow an exponential time-dependent pattern. Numerical simulations further reveal that increasing volatility significantly amplifies future price magnitudes, highlighting volatility as a key determinant of risk exposure and price dispersion. The study concludes that combining Markov chain transition structures with fundamental matrix solutions provides a comprehensive mathematical framework for evaluating short-term transition probabilities and long-term stock price evolution. The findings offer quantitative support for strategic investment planning under stochastic market conditions.

Keywords

Markov ChainFundamental MatrixNigeria Stock ExchangeVolatility

References

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Markov Chain and Fundamental Matrix Solution for Assessing Stock Market Price Variation in UNICEM and BUA PLC

Abstract

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