Option pricing is a fundamental issue in financial markets, and barrier options are a popular type of options that can become valuable or worthless when the underlying asset price reaches a predetermined level. A double barrier option consist two barriers, one situated above and the other below the prevailing stock price. This particular option is categorized as path dependent because the return for the holder is influenced by the stock price’s breach of the two barriers. The double barrier option contract stipulates three specific payoffs, depending on whether the up-barrier or down-barrier is touched, or if there is no breach of either barrier during the entire duration of the option. In this paper, pricing of the double barrier options when the underlying asset price follows the exponential Ornstein-Uhlenbeck model is investigated, and also pricing formulas for different types of double barrier options (knock-in and knock-out) are derived by α-paths of uncertain differential equations in the uncertain environment.
Abbasi et al. (Sun,) studied this question.