one probability question, need some help

[jingramm]

I'm stuck on this last one

If S(y), y >= 0, is a geo metric brownian motion with drift rate = .01 and variance = .2
If S(0) = 100, what is the probability that S(10) > 100?

It seems fairly easy but I can't figure out which equation to use, any help would be greatly appreciated

 

[jingramm]

can any of the probability geniuses on this forum help?

I found a similar question on the web but not sure how I should solve mine

Example 4.4.1: The current price of a stock is 100. The stock price follows
a geometric Brownian motion with drift rate of 10% per year and variance
rate of 9% per year. Calculate the probability that two years from now the
price of the stock will exceed 200.

Solution: We need P r[S(2) > 200] = P r[S(2)/100 > 2] or P r[ln{S(2)/S(0)} >
ln 2].

ln[S(2)/S(0)] has a normal distribution with mean (0.1 − 0.09/2)2 = 0.11
and variance (0.09)(2) = 0.18. Therefore

P[ln{S(2)/S(0)} > ln 2] = N(0.6315 − 0.11/sqrt(0.18)) = N (1.3745) = 0.9154.

 

[olds]

The answer is 50/50.
It either is or it isn't.

 

[Juked07]

Without doing any hard calculations, should be close to (slightly more than?) half a standard dev of leeway, so ~75-80%

We'll see how well I did after someone posts the actual answer

Edit: forgot to take sqrt of var, my answer is not a good estimate

 

[eLiu]

I do believe that wikipedia answers this almost directly:
http://en.wikipedia.org/wiki/Geometric_Brownian_motion
i.e., they give you the PDF; now compute CDF

I've never heard of log-normal distributions before, but evaluating S(10) can be handled numerically from here or read off a table or something.