Multi?step reflection principle and barrier options

This paper examines a class of barrier options, multi-step which can have any finite number barriers level. We obtain general, explicit expression for option prices this type under the Black–Scholes model by deriving reflection principle, that is, boundary-crossing probability Brownian motion. Multi-step options are not only useful in they handle different levels and time steps but also approximate with arbitrary barriers. Moreover, be applied to pricing jump-diffusion models.