Barrier option pricing of mean-reverting stock model in uncertain environment

The barrier options become activated or extinguished only if the underlying asset's price reaches a predetermined level. Options of the former case are the knock-in options, and options of the latter case are the knock-out options. Barrier options are a type of path-dependent options which have a big difference from the path-independent options, such as European options and American options. This paper studies the barrier options based on the mean-reverting stock model in uncertain environment. The four types of European barrier options pricing formulas, which are up-and-in call options, down-and-in put options, up-and-out put options, and down-and-out call options, are derived and the corresponding numerical algorithms are designed to compute the prices of these options. (C) 2019 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.