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 approxi...

Abstract The complexity of binary droplet collisions strongly increases in case immiscible liquids with the occurrence triple lines or for high energetic collisions, where strong rim instabilities lead to spattering satellite droplets. To cope such cases, Volume Fluid method is extended by an efficient interface reconstruction, also applicable multi-material cells arbitrary configuration, as we...