Question: Probability of a stock being in a price range

The question is:

 If the stock price today is 100 and the stock has a anual volatility of 12% what is the probability of that stock

being within a price range of [130 - 140] in 5 months time ?
 

Answer:

The 5 months volatility is given by :        vol5 := evalf(.12*sqrt(5/12), 3)  =  0.0774

Which means that

Mean+/-1 stdev  (Probability 0.6826 )                Mean+/-2 stdev  (Probability 0.9544 )                   Mean+/-3 stdev  (Probability 0.9972 )

100*(1+vol5);                                                        100*(1+2*vol5);                                                         100*(1+3*vol5);
100*(1-vol5);                                                         100*(1-2*vol5);                                                           100*(1-3*vol5);

107.7400                                                               115.4800                                                                     123.2200
 92.2600                                                                  84.5200                                                                       76.7800

Which means that that the likelihood of that stock price being between [130 - 140] in 5 months time,

assuming the volatility is constant over time, is very very small.

The problem I am having is to compute the probability though simulation. My algorithm is working ok (I think)  but I get an

probability of around 0.82 after one hundred simulations that the price is between Mean+/-3 stdev  and not a probability 0f 0.9972

I have attached my simulation and would appreciate if anyone could identify my mistake.....

 View 8342_Stock Price Range.mw on MapleNet or Download 8342_Stock Price Range.mw
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