IMEX schemes for a parabolic-ODE system of European options with liquidity shocks

A coupled system, where one is a degenerate parabolic equation and the other has no 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 in time.