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You are generating a price series, in time steps $p_{dt},p_{2dt},p_{3dt},...$. I assume? So if you do $\text{Median}\{p_{dt},p_{2dt},p_{3dt},..\}$ then you will get a value biased towards $0$ (for the parameters you gave, and the sample size you have). If you want to look at the distributional characteristics of the price, then you have to do so per each ...


I would suggest you to forecast the series using different models and to determine which one is the best accordingly loss functions such as RMSE, MAPE.. or using the Mincer-Zarnowitz regression . You could also compare one-step forecast versus dynamic forecast. Another way is to compute VaR and observe the model having the lowest failure rate. AIC/BIC ...


Did you try rmgarch package of R ? http://cran.r-project.org/web/packages/rmgarch/index.html http://unstarched.net/r-examples/rmgarch/mgarch-comparison-using-the-hong-li-misspecification-test/


Quantopian provides both the fundamental data (from Morningstar), as well as the backtest platform to reproduce results from the books you mentioned. Here's the introduction to our fundamentals offering: https://www.quantopian.com/posts/fundamental-data-from-morningstar-now-available-for-backtesting (disclosure: I'm the ceo of quantopian)

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