An asymptotic expansion method for geometric Asian options pricing under the double Heston model

•This paper modifies the double Heston model as a singular and regular perturbed BS model.•This paper derives explicit expressions of the asymptotic expansions for geometric Asian options with fixed and floating strikes under the modified double Heston model 3. The paper provides the convergence of the asymptotic formula.•The paper provides the Greeks of geometric Asian options prices.•The paper calibrates the modified double Heston model to real markets and examines the impacts of the two-factor volatility on geometric Asian option prices with calibrated parameters.