IMEX schemes for a Parabolic-ODE system of European Options with Liquidity Shocks

TL;DR

This paper develops and analyzes implicit-explicit schemes for a coupled parabolic-ODE system modeling European options with liquidity shocks, ensuring positivity and demonstrating high accuracy through numerical experiments.

Contribution

The paper introduces two positivity-preserving IMEX schemes for a degenerate parabolic-ODE system, with theoretical analysis and numerical validation.

Findings

Schemes preserve positivity of solutions.

Numerical results show high accuracy and efficiency.

Richardson extrapolation enhances scheme performance.

Abstract

The coupled system, where one is a degenerate parabolic equation and the other has not a diffusion term arises in the modeling of European options with liquidity shocks. Two implicit-explicit (IMEX) schemes that preserve the positivity of the differential problem solution are constructed and analyzed. Numerical experiments confirm the theoretical results and illustrate the high accuracy and efficiency of the schemes in combination with Richardson extrapolation