monte carlo - Usage of Brownian Bridge?

I was recommended to read something about Brownian Bridge. Could someone familiar with BB give some recommendation?

It was mentioned that BB benefits in 2 places

1. 
   

   BB could reduce the simulation paths, this reduces computation effort, especially when the underlying factors are a lot (say 20-30). I noticed that Papageorgiou1 has a paper "The Brownian Bridge Does Not Offer a Consistent Advantage in Quasi-Monte Carlo Integration" (2002). So does this point still hold?

   
   


2. 
   

   BB could reduce the computation effort on path-dependent derivatives. For example, during pricing of a barrier option, a path could be simulated with monthly scenarios of the factors; then BB could be used to estimate the probability of the path "knock-out" of the barrier. Which paper/book would you recommend on this topic?

   
   

Answer

The Papageorgiou paper is presumably referring specifically to quasi-random sequences used in path generation. Researchers had noticed that, in high dimensions, QR sequences tend to have good space coverage for the first couple of dimensions:

but terrible coverage for the latter dimensions:

(Plots here are points 101-200 from a 32-dimensional QR sequence)

One solution proposed was to make sure most variation was from the first few dimensions by taking terminal path values from them, and then "filling in" the path with lower-quality latter dimensions. In practice I believe this has been superseded by scrambling tricks. See this paper for a decent review.

I don't know of a paper covering bridges for "knock-out" probabilities, which is more of a practitioner's trick than an academic's research project, though the computational aspects might well be covered in something like Hull or Shaw. The math is not particularly tricky.