Classification of barrier options
  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. 
J. C. Ndogmo