A Stochastic Asset Price Model with Asymmetric and Adaptive Mean Reversion

This thesis develops and empirically evaluates a stochastic framework for modelling financial asset prices that moves beyond the geometric random walk while remaining interpretable and probabilistically coherent. While mean reversion has been widely studied, many existing models rely on return-based dynamics or fixed long-run reference levels that are difficult to reconcile with the adaptive behaviour of market participants.

The central contribution of the thesis is a geometric price-level model in which prices evolve around an adaptive reference level derived from past prices. This reference level is interpreted as a behavioural anchor reflecting recent market consensus. The model allows for asymmetric adjustment dynamics above and below this level, capturing differences in market behaviour during upward and downward deviations. Bayesian inference is used to estimate model parameters, perform model comparison, and generate full predictive distributions.

The framework is first validated using simulation and sensitivity analyses to assess parameter identifiability and inference robustness. It is then applied to a broad cross-section of U.S. equities, where it demonstrates improved explanatory power and predictive performance relative to benchmark models, including the geometric random walk and symmetric mean-reverting alternatives. The resulting probabilistic forecasts are shown to support stable trading strategies under realistic transaction cost assumptions.

The thesis also benchmarks the proposed model against widely used machine learning and deep learning methods using cryptocurrency market data, highlighting the competitiveness of structured stochastic models in predictive and trading settings. In addition, two complementary studies address practical issues in applied financial modelling, focusing on label construction for algorithmic trading and the identification of structural breaks in policy-driven market environments. Together, these contributions highlight the value of adaptive, behaviourally grounded, and probabilistic approaches to financial price modelling.