American Barrier Option Pricing Formulas for Currency Model in Uncertain Environment

Option pricing problem is one of the central issue in the theory of modern finance. Uncertain currency model has been put forward under the foundation of uncertainty theory as a tool to portray the foreign exchange rate in uncertain finance market. This paper uses uncertain differential equation involved by Liu process to dispose of the foreign exchange rate. Then an American barrier option of currency model in uncertain environment is investigated. Most important of all, the authors deduce the formulas to price four types of American barrier options for this currency model in uncertain environment by rigorous derivation.