RBF-FD Based Some Implicit-Explicit Methods for Pricing Option under Regime-Switching Jump-Diffusion Model with Variable Coefficients

In this manuscript, we introduced the radial basis function based three implicit-explicit (IMEX) finite difference techniques for pricing European and American options in an extended Markovian regime-switching jump-diffusion (RSJD) economy. A partial integrodifferential equation (PIDE) yields the values of the European option, which is one of the financial options, and a linear complementary problem (LCP) yields the prices of the American option. To solve the LCP for American option pricing, we combine the suggested techniques with the operator splitting methods. The suggested methods are designed to prevent the use of any fixed-point repetition approaches at each economic stage and time increment. We analyzed the stability of the proposed time discretization methods. We performed numerical experiments and illustrated the second-order convergence and efficiency of the three IMEX numerical techniques (BDF2, CNAB, CNLF) under the extended RSJD model.