Quant
Modeling Equity Market Trends through GBM
Bayesian GBM and HMC for JNJ stock analysis
Overview
A quantitative research project under Professor Jazi using Bayesian Geometric Brownian Motion and Hamiltonian Monte Carlo to estimate and forecast Johnson & Johnson stock behavior.
Problem
Stock prices are noisy, path-dependent, and uncertain over longer horizons. The project studies whether GBM can capture broad movement patterns and how uncertainty expands with forecast length.
Dataset
252 Johnson & Johnson trading observations ingested from Yahoo Finance and transformed into return series for drift and volatility estimation.
Approach
Built the Bayesian GBM formulation, estimated drift and volatility through HMC, and simulated future paths to visualize uncertainty.
Results
Forecasted JNJ prices within a 95% credible interval and 40-day accuracy, estimating drift at 0.1166 and volatility at 0.1460 across 100 stochastic simulations.
Lessons Learned
Quantitative models are strongest when their assumptions and uncertainty are visible. The forecast interval was as important as the point estimate.
Model / Pipeline
The implementation combines R, MCMC, Bayesian Inference, Yahoo Finance API with a repeatable workflow for data preparation, evaluation, and communication.