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Maybe this is rather a comment then an answer but three points: GBM is a stochastic model for stock prices. It is used to price derivatives in an arbitrage free setting. In this case you look at a process whose expected return is just the risk free rate (due to no-arbitrage). Forecast this price is trivial. It is debatable how forecastable stock prices ...


There is probably nothing wrong with your code although I did not check it in Mathematica. Normally, Geometric Brownian motion is just a model. Here, you simulate lots of paths and then average over it. The first plot gives something like $$ E(S_t) = S_0*\exp(\mu t) $$ with $S_0$ the initial stock price. However, because of the simulation, you do not get ...

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