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

TL;DR

This paper introduces a new second-order finite volume IMEX Runge-Kutta method for efficiently solving two-dimensional financial parabolic PDEs with mixed derivatives, ensuring accuracy and stability even with non-regular initial conditions.

Contribution

The paper develops a novel general methodology for second-order IMEX schemes that handle mixed derivatives in 2D financial PDEs, improving stability and accuracy.

Findings

Achieves second-order convergence with non-regular initial conditions

Overcomes tiny time-step restrictions of explicit schemes

Provides accurate, non-oscillatory Greeks approximations

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.