Monte Carlo Stock Price Predictor

Uses Geometric Brownian Motion and Monte Carlo Methods for Stock Price prediction

The MATLAB code utilizes Geometric Brownian Motion (GBM) to simulate and predict future stock prices based on historical data. GBM is a mathematical model commonly used in finance to describe the stochastic behavior of asset prices over time. The core of GBM is a stochastic differential equation that accounts for both deterministic growth and random fluctuations in stock prices. Specifically, the equation \( dS_t = \mu S_t \, dt + \sigma S_t \, dW_t \) models the change in stock price \( S_t \) over time \( t \). Here, \( \mu \) represents the average rate of return (drift) and \( \sigma \) denotes the volatility (standard deviation of returns), while \( dW_t \) is a Wiener process representing random noise.

The MATLAB code initializes with historical stock price data, computes daily log returns, and estimates parameters such as volatility and drift from this data. It then performs a Monte Carlo simulation, generating multiple possible future price paths using GBM. Statistical metrics such as mean price, probabilities of price increase/decrease, and extreme price values are calculated from these simulations. The code visualizes historical data alongside simulated price paths to provide insights into potential future price movements, facilitating risk assessment and investment decision-making in financial markets.