A second-order ADI method for pricing options under fractional regime-switching models

Fractional regime-switching option models have recently attracted much attention because they can capture the sudden state movement of the market, and deal with the non-stationary behavior. A second-order numerical scheme is proposed to solve the regime-switching option pricing models with fractional derivatives in space. The sufficient conditions of the stability and convergence of the proposed scheme are studied in details. An alternating direction implicit (ADI) method is implemented to accelerate the computation in every time layer. Numerical experiments are presented to verify the convergence and efficiency of the proposed method, compared with classical Krylov subspace solvers.