Pricing of geometric average Asian option under the sub-diffusion Merton interest rate model

Asian option is an essentially new type of option. In existing option pricing models, the Brownian motion is generally the stochastic driving source of changes in the underlying asset price. This article explores the pricing problem of geometric average Asian option under the sub-diffusive Merton interest rate model. The results obtained the partial differential equations satisfied by the geometric average Asian option via constructing portfolios and utilizing the delta hedging technique. Finally, the findings provide display expressions for the geometric average Asian option under the sub-diffusive Merton interest rate model, combined with boundary conditions and variable substitutions.