What are the correct parameters to enter for an accurate market simulator?

Hi, I am a n00b trying to program some simulators of the main market indexes. So far the codes work, but I might have some issues with the mathematical model. I assumed that a market can be modeled by assuming that each daily movement is the exponential of a random number generated from a normal curve with the mean equal to the logarithm of the average yearly return (calculated by geometric mean) and the standard distribution derived from the historical volatility.
Now the thing is I am not sure Nasdaq-100 parameters are the following:
Logarithm of average daily returns: 0.000654
Standard deviation: 1.25 (assuming that historical volatility annualized is roughly 19)
Are these parameters correct? What do you think?


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