Asian Option Pricing Formulas for Uncertain Financial Markets Based on the Exponential Ornstein–Uhlenbeck Model

This paper investigates pricing formulas for geometric average and arithmetic average Asian call and put options under an uncertain exponential Ornstein–Uhlenbeck stock model. Employing the α-path technique from uncertainty theory, we derive closed-form integral representations for all four option types and rigorously establish their monotonicity properties with respect to the strike price, interest rate, time to expiration, and initial stock price. A comparative analysis with Liu’s standard uncertain stock model and a discussion of the option Greeks are also provided. Numerical examples are given to illustrate the practical applicability of the proposed formulas.