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2019-07-20 is a Saturday and 2019-07-21 is a Sunday, so basically you're looking on a 4 day option. Furthermore use ql.Actual365Fixed() to get the same results from the online calculator.

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I think the given python code snippet is composed according to the following steps: $$var(\tau) = \left< |z(t+\tau)-z(t)|^2 \right> \thicksim \tau^{2H}$$ $$\Rightarrow var(...)\thicksim \tau^{2H}$$ $$\Rightarrow std(...) \thicksim \tau^{H}$$ \...

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You can directly use pandas-montecarlo to perform a Monte-Carlo simulation. Code for the same: # Import data import pandas_montecarlo from pandas_datareader import data data = data.get_data_yahoo('AAPL', '2017-01-01', '2018-01-01') # Calculate Returns data['return'] = data.Close.pct_change() # Perform Monte-Carlo Simulation data['return'].montecarlo(sims=...

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