American Knock‐In Options Pricing of Mean‐Reverting Stock Model With Floating Interest Rate

ABSTRACT Knock‐in options are a kind of exotic options that are path‐dependent. The options will automatically take effect when the price of the underlying assert reaches a specific limit price. This paper studies an American knock‐in options pricing scheme based on a mean‐reverting stock model, considering the floating interest rate under an uncertain market environment. First of all, ‐paths of uncertain differential equations are utilized to derive the pricing formulas for American call and put options. Then, the real data of the financial market are utilized to obtain the corresponding parameters using uncertain maximum likelihood estimation. Subsequently, a hypothesis test is utilized to assess the adequacy of the stock model in fitting the observed data, and several numerical algorithms are developed to validate the efficacy of the stock model.