Second Order Finite Volume IMEX Runge-Kutta Schemes for Two Dimensional Parabolic PDEs in Finance

Abstract

[Abstract]: We present a novel and general methodology for building second order finite volume implicit-explicit Runge-Kutta numerical schemes for solving two dimensional financial parabolic PDEs with mixed derivatives. The methods achieve second order convergence even in the presence of non-regular initial conditions. The IMEX time integrator allows to overcome the tiny time-step induced by the diffusive term in the explicit schemes, also providing accurate and non-oscillatory approximations of the Greeks.