2025/03/13 by Yifei Yan, Yan, Yifei, Juan Sosa +3
Decision Sciences · Economics, Econometrics and Finance · #Applications (stat.AP) #Complex Systems and Time Series Analysis #FOS: Computer and information sciences #Financial Risk and Volatility Modeling #Methodology (stat.ME) #Stock Market Forecasting Methods
paper · pdf · doi:10.48550/arxiv.2503.09923
openalex publication_date 2025/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This analysis derives the maximum likelihood estimator and applies Bayesian inference to model geometric Brownian motion, incorporating jump diffusion to account for sudden market shifts. The Bayesian approach is implemented using Markov Chain Monte Carlo simulations on S&P 500 stock data from 2009 to 2014, providing a robust framework for analyzing stock dynamics and forecasting future trends. Exact solutions are obtained for both the standard Geometric Brownian Motion (GBM) model and the GBM model with Poisson jumps. Although both models yield reasonable results and fit the data well, the GBM with Poisson jumps exhibits superior performance, significantly enhancing model fit and capturing more complex market dynamics.