Simulating Stock Prices: A Naive Approach
More information can be found in my blog post on this topic.
This simulation uses Monte Carlo simulations where the random movements for the stock price are drawn from intuitively parameterized normal distributions. It's been shown that movements in financial data, in the short-term at least, are not normally disributed. More accurate simulations are provided via geometric Brownian Motion. For this reason, this approach has been labeled naive.
The ideal forecast horizon is 1-10 days. Since the prediction is based of random stock movements the results should not be used as an accurate representation of the future price of a stock. For very long-term horizons (20+ days) the results will be spurious.