# Is using a Monte Carlo simulation sufficient for predicting probabilities that a stock will hit a certain price by a certain date?

Forgive my ignorance about my question. I understand a Monte Carlo simulation to basically be n times that the truth is checked in some historic data set. For stock prices, if I buy some symbol at say \$100 and I want to predict the probability that the price will reach \$105 within 30 days.

Can I use a MC simulation to look at historic prices and see what the percent gain / loss was over a 30 day period from random starting points and use that to build my probability curve?

Is that too naive or will that yield decent results?

• IMO What you describe in the first part simply amounts to assimilating the probability of occurrence of an event to its historical count. This has nothing to do with Monte Carlo which necessitates sampling out of a distribution. – Quantuple Mar 17 '17 at 9:04
• If you are willing to estimate or guess two parameters: the drift and the variance then you can use the lognormal distribution (which is analytically tractable) to estimate the future range of a stock with a given confidence threshold. See GBM (Geometric Brownian Motion) for more information. – Alex C Mar 17 '17 at 23:59