Random Walks and Geometric Brownian Motion for Stock Price Simulation
Summary
The article introduces random walks as stochastic paths and explains how the idea relates to the claim that future stock prices cannot be reliably inferred from current prices. Simple up or down steps illustrate a random walk, while drift allows unequal directional tendencies. It discusses arguments and examples around market predictability, including random stock selection, and notes that portfolio composition and risk can affect apparent outperformance. It also points to events and other influences as reasons historical patterns may contain information.
The practical focus is geometric Brownian motion (GBM), which models prices using drift, volatility, and random normal shocks. The article describes estimating parameters from General Motors historical data, simulating paths from a common starting price, and comparing a few simulated paths with actual prices; it suggests generating many paths for risk analysis such as value at risk and expected shortfall. The illustrations do not establish that GBM predicts prices or captures market dynamics reliably. Simulation results depend on the model assumptions and estimated inputs, and the article gives no detailed validation of those assumptions.
Key ideas
- A simple random walk models successive price changes as uncertain steps.
- Drift represents a directional tendency in a process rather than equal up and down chances.
- GBM simulates prices using drift, volatility, and random shocks.
- Multiple simulated paths can support risk measures such as value at risk and expected shortfall.
- The examples illustrate a model and do not demonstrate reliable price prediction.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.