Pricing Asian options under the mixed fractional Brownian motion with jumps

The mixed fractional Brownian motion ( mf Bm ) has gained popularity in finance because it can effectively model long-range dependence, self-similarity, and is arbitrage-free. This paper focuses on mfBm with jumps modeled by the Poisson process and derives an analytical formula for valuing geometric Asian options. Additionally, approximate closed-form solutions for pricing arithmetic Asian options and arithmetic Asian power options are obtained. Numerical examples are provided to demonstrate the accuracy of these formulas, which rely on a convenient approximation of the option strike price. The proposed approximation demonstrates significantly higher computational efficiency compared to Monte Carlo simulation.