A Cointegration-Based Stochastic Model for Stock Price Dynamics with Mean-Reverting Market Deviations

Abstract

This paper proposes a novel stochastic framework for modeling stock price dynamics by incorporating a cointegration relationship between observed market prices and underlying fundamental values. Unlike classical models such as Geometric Brownian Motion, the proposed approach decomposes stock prices into two interacting components: a fundamental value following a stochastic growth process and a bounded deviation ratio governed by a mean-reverting Jacobi diffusion. This structure allows the model to capture both long-term equilibrium behavior and short-term market inefficiencies. Theoretical properties including existence, uniqueness, stationarity, and cointegration, are rigorously established. Empirical validation using real stock market data demonstrates that the proposed model outperforms traditional approaches in terms of accuracy and interpretability.natus error sit voluptatem accusantium doloremque laudantium