Second order finite volume IMEX Runge-Kutta schemes for two dimensional parabolic PDEs in finance (2409.01131v1)

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.