Knock-in options of mean-reverting stock model with floating interest rate in uncertain environment

Knock-in options are a type of barrier option that become active when the value of the underlying asset exceeds a predetermined target. This paper investigates knock-in options based on the mean-reverting stock model within an uncertain environment where the interest rate is dynamic and the stock price follows a geometric process. We subsequently provide the price formulas for the European up-and-in call option and European down-and-in put option. Additionally, we apply real data from the financial market and employ moments estimation to derive the optimal parameters of the stock model under bullish and bearish conditions, respectively. Hypothesis testing is subsequently utilized to assess the fitting effect between the model and data. Finally, the numerical experiments are set to verify the validity of the formulas by observing the influence of parameters on the option price.