Knock-out options pricing formulas in uncertain financial market with floating interest rate

Knock-out options are a kind of path-dependent exotic option. In this paper, we first introduce the uncertain mean-reverting stock model with floating interest rate to depict the price fluctuations of the stock in uncertain financial markets. Following this, our main focus is to investigate the pricing formulas for two types of European knock-out options. Subsequently, stock data with rising and falling trends are selected to calculate the parameters of the model based on the method of moments. Finally, we present numerical examples to verify the validity of the formulas.