I'm trying to predict the value of a variable after a specified number of days. I'm assuming it will change each day by a normally distributed random amount.
For example, today the value is 10. Over the past month the std dev of daily changes is 2. What are the odds that, within 20 days, the lowest value will be within a specified range.
Would a monte carlo simulation be an appropriate technique?
I'd run repeated iterations of
start = 10 for d in range(days): start += random.gauss(0, stddev)
After each iteration I'd bin the values.
Does this make sense? Is there a much better way? I've looked at exotic option pricing models, but they seem like overkill and are beyond my ability to implement.