The standard method for simulating final, minimal and maximal values of
Brownian Motion relies on a (discrete) n-step random walk approximation, where
n has to be chosen very large (typically n=100 000) to keep the bias induced
by the approximation "small enough" for certain applications. So if you want
to do MC option pricing of e.g. double barrier options, 5e8 random uniforms
are needed for 5 000 draws of final, minimal and maximal value, which is still
a quite small number of draws in MC applications. I am working on a faster
simulation method and of course I want to compare the speed of the new and
(old) standard method, that's why I needed large numbers of random uniforms. I
thought that the particular application is not of interest for this list, so I
left it out in my initial submission. I apologise, if my submission was
off-topic in this mailing list.
Isn't that usually done by adding rnorm()s and not runif()s?
There are much better algorithms for simulating Brownian motion
barrier-crossing statistics to high accuracy. It's not my field, but one
idea is to use scaled Brownian bridge to infill time when the process is
near a boundary.
Sometimes the R helpers spend a long time answering the wrong question,
which is why it always helps to give the real one.