double barrier option pricing formulas of an uncertain stock model

The valuation of options is an essential topic in the financial markets, and barrier options represent a widely utilized category of options that may gain or lose value once the price of the underlying asset hits a specified threshold. a double barrier option includes two barriers, one above and one below the current stock price. it is classified as path dependent due to the fact that the holder’s return is influenced by the stock price’s breach of these barriers. the double barrier option contract defines three specific payoffs, which are contingent upon whether the upper barrier or lower barrier is breached, or if there is no breach of either barrier throughout the option’s duration. in this paper, pricing of the double barrier options when the underlying asset price follows the uncertain stock 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.