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 ?
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.....
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