Power-barrier option pricing formulas in uncertain financial market with floating interest rate

Power-barrier option is a typical exotic option formed by attaching some restrictions to the power option, where the power option evolves from standard European option with the strike price and underlying good price attached to some power. Compared with the ordinary options, power-barrier option can provide investors with stable leverage and premium income. Therefore, power-barrier option is more favored by investors. This paper mainly discusses the pricing problems of power-barrier option in uncertain financial market. The fluctuation of stock price is regarded as an uncertain process and the interest rate is floating. The uncertain differential equation is invoked to simulate this fluctuation in an uncertain environment. Then, the clear pricing formulas of power-barrier option are given. Finally, the corresponding numerical examples and a real data example are put forward to illustrate the method.