Reset option pricing with predetermined levels for uncertain currency models

An option is a kind of financial derivative product with far-reaching influence, and its pricing problem is a high priority of quantitative research in modern finance. A reset option gives holders more choices, so it can bring the holder more profit opportunities. Therefore, this paper analyzes the reset option with predetermined levels on the basis of uncertainty theory. Assuming that the exchange rate is determined by an uncertain differential equation, namely the uncertain currency model, we study the reset option with predetermined levels in an uncertain financial market. Further, according to the principle of identical expected revenue between buyers and sellers, the corresponding pricing formulas of reset options with predetermined levels for an uncertain currency model are proposed. Finally, several numerical examples are designed to verify the rationality of the proposed formulas. The results show that the option price increases monotonically with the number of predetermined levels and the maturity time, which conforms to the actual financial market rules. This model provides a new theoretical method for the pricing of cross-border reset options and has important theoretical value and practical application potential in uncertain financial markets.