Numerical methods for a partial differential equation with spatial delay arising in option pricing under hard-to-borrow model

摘要

This paper studies the numerical methods for solving a partial differential equation (PDE) with spatial delay arising in option pricing under hard-to-borrow model. A new expansion approach is introduced to deal with the spatial delay term. Then a modified finite difference method is proposed to discretize the PDEs. Moreover the modified Laplace transform method on the expansion is studied and compared with the time-stepping finite difference method. (C) 2018 Elsevier Ltd. All rights reserved.