# How to compute Pr(S>100) when S follows Geometric Brownian Motion?

I have been trying to resolve this problem, under (b), but I cannot find the correct answer. For i=1, my ultimate answer (P=1) deviates from the correct answer (P=0.7580). Please let me know whether my computations are wrong or not.

In blue is the solution according to the solution manual; my computations start at For i=1.

• Start by re-arranging the algebraic variables and "solve" for the normal RV, instead of plugging in the numerical values first. Because it seems as though you've missed moving ln(S_0) to the RHS – Tingiskhan Mar 21 '17 at 17:19

I wrongly assumed that that a random normal variable's distribution was described by its mean and volatility. It is, however, described by its mean and variance.

So for the denominator in the Z computation I now use 0.1 (volatility) instead of 0.01 (the variance, which I had mistaken to be volatility), which results in the right answer.

• Characterising a random variable through (mean, standard deviation) or (mean, variance) is actually exactly the same. But indeed to compute the Z-score you should center the variable then divide the output by that variable's standard deviation not its variance. – Quantuple Mar 22 '17 at 8:42
• you may accept your own answer so that it will not show up again. – Gordon Apr 20 '17 at 18:47