Research on pricing knock-out options in an uncertain financial market

A knock-out option is a type of barrier option in which the option contract is terminated immediately when the underlying asset’s price reaches the predetermined price, i.e., the option is “knocked out” and loses its validity. This research delves into the intricacies of knock-out options within the volatility of an uncertain market. Here, the stock prices are governed by a Liu process, while the interest rates fluctuate in response to market dynamics. The valuation models for European knock-out options are meticulously formulated utilizing the maximum likelihood estimation from the field of uncertain differential equations. To empirically validate these models, a series of computational algorithms are designed and showcased through numerical simulations.