So we have an asset whose price follows a GMB:
$dS_t = \mu S_t dt + \sigma S_t d W_t$
and want to know the probability that it drops 5% or more at time $t = 2$, given that $\mu = 0.04$ and $\sigma = 0.2$. I think (thanks Wikipedia) that it should be solved like this:
- first pass is finding the value of $S_2$ (question: how do I compute $W_t$?)
- somehow taking advantage that $S_t$ is log-normally distributed (I'm not sure how to use standard normal CDF tables)
Disclaimer: I know this must be super simple, but have not found the solution and don't know anyone that can help.