A Sophisticated Stochastic Framework for Stock Price Estimation: Theory, Simulation, and Application to
Year: 2026
Type: article
Abstract: Financial markets exhibit complex dynamics including volatility clustering, sudden jumps, regime shifts, and leverage effects. This paper develops a comprehensive hierarchical state-space framework integrating stochastic volatility, jump processes, regime switching, and self-exciting dynamics to capture these phenomena. We provide rigorous theoretical validation through proofs of existence, uniqueness, ergodicity, and estimation consistency. Simulation studies demonstrate strong performance with mean absolute log-price errors of 0.077. Critically, we apply the framework to real AAPL stock data from 2023-2024. Empirical results show the model effectively captures volatility dynamics, identifies market regimes corresponding to known events (banking crisis, Fed policy shifts), detects jumps around earnings announcements, and achieves superior out-of-sample forecasting compared to GARCH and simple stochastic volatility benchmarks, establishing practical utility for financial forecasting and risk management.
Source: Figshare
Authors: Chatterjea, Rajit, Park, Jayson
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7153116992