Pricing Asian Options in Uncertain Stochastic Markets With Jumps

Objective: In practice, the securities industry is characterized by processes exhibiting both randomness and Liu's uncertainty, sometimes called uncertainty. This study proposes Asian option pricing models in uncertain random markets with jumps. Theoretical Framework: This research is based on the concepts of probability, uncertainty, and uncertain stochastic differential equations (USDEs) with jumps. Method: We use an uncertain random stock model with a jump to derive option pricing models in uncertain random markets with jumps. Using USDEs with jumps is a new paradigm in modeling dynamical systems. The solution to the extraordinary type of an uncertain stochastic differential equation (USDE) with jumps examined in this article combines a jump component and the geometric Itô-Liu process. It plays a pivotal role in deriving Asian option pricing formulae under study. Results and Discussion: This study shows that objective randomness and subjective uncertainty are essential in pricing Asian options. Research Implications: The proposed procedures in this branch of knowledge can be used to price Asian options. Originality/Value: This study contributes to the literature by adequately capturing the effects of indeterminacy in pricing Asian options.