Convergence analysis of an IMEX scheme for option pricing under stochastic intensity jump model with mixed fractional Brownian motion

This paper proposes and analyzes an implicit-explicit (IMEX) difference scheme for solving a two-dimensional variable-coefficient partial integro-differential equation (PIDE). The equation arises from option pricing under a stochastic intensity jump model driven by mixed fractional Brownian motion. First, an IMEX scheme is developed to solve the two-dimensional main PIDE along with its associated boundary condition, which is governed by a one-dimensional PIDE. The second-order convergence rate of the scheme is rigorously established for the boundary PIDE in the discrete \(H¹\) -norm and for the main PIDE in the discrete \(L²\) -norm. Finally, numerical experiments are conducted to validate the theoretical results.