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

Abstract

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.