Second-order convergent IMEX scheme for integro-differential equations with delays arising in option pricing under hard-to-borrow jump-diffusion models.

The aim of this paper is to develop an implicit–explicit (IMEX) scheme for solving the 2-dimensional (2-D) partial integro-differential equations with spatial delays arising in option pricing under the hard-to-borrow jump-diffusion models. First, a new second-order accurate numerical integration scheme that combines a mesh-dependent expansion and the trapezoidal rule is proposed to handle the integral-delayed term. Then, the IMEX scheme discretizes the integral-delayed term explicitly and the other terms implicitly. The second-order convergence rates for space and time are proved. Numerical examples are consistent with the theoretical results. [ABSTRACT FROM AUTHOR]