Brownian Bridge

Brownian Bridge is defined as the conditional expected distribution of a standard Brownian Motion given the condition that we know values of Winner process at a starting point and some points. We of course know that this expectations and covariances.
As a mathematical instrument, Brownian Bridge is used when we simulate a extotic product pricing. Concretely, interest rate models are simulated at some discrete-fixed times which are often called "simulation grids". Though we sometimes have to price products whose payoffs do not lie in the simulation grids, we only know information of simulation grids from this calculation. But If we use Bronwian Bridge, we can get a good view of the process at not even simulation grids. Thus by using it, there may happen that we can get a better result.