  For a given level of accuracy in option prices, the paper considers the
problem of deciding when exactly, as one or more of the pricing parameters
change, a barrier option degenerates into a simpler type of option. This
problem is meaningful in the real world where option prices are always
determined within a certain level of accuracy. The problem is reduced to
finding certain critical values of the initial stock price, and this is
achieved through a probability-based approach.
