Convergence rates of the numerical methods for the delayed PDEs from option pricing under regime switching hard-to-borrow models

摘要

The aim of this paper is to study the convergence rates of the finite difference methods (FDMs) for solving the PDEs with spatial delays which arise in the option pricing under regime switching hard-to-borrow models. The PDEs are coupled for different regime states and involve delays in two spatial directions. One of the boundary conditions is implicitly given by an initial-boundary value problem of coupled PDEs which needs to be solved before solving the main equations. This paper proves convergence rates of the FDM based on mesh-dependent expansions for solving the problems. Numerical examples confirm the theory.