I am confused as to why we use Metropolis in financial
Monte Carlo
There are I see two obvious ways of generating a new path
a)Start with current path and use Metropolis to modify with proper sampling.
 This is correct but generates correlated paths which in some cases
with complex measurement (taking longer than generation in time) is
inappropriate. One needs (to use standard techniques) to decorrelate paths
b)Start each path afresh generating S(0) S(1) S(2) etc succesively. This seems to
be fine for distributions now used and gives uncorrelated paths
(S(time t) is underlier price at time t)

So I ask
0)Am I totally screwed up?
1)When is a) (which is more general) actually needed
2)What is best way of estimating correlation in a)
3)Will b) work for simple problems we now do with uncorrelated probabilities
of any particular form.
I believe Miloje agrees that we can improve a) (and I think b)) by
exactly generating points according to given distribution and not
doing Metropolis for each point update.
Thank you