Numerical analysis of an extended structural default model with mutual liabilities and jump risk

•We analyze a two-dimensional structural default model with interbank liabilities and negative exponential jumps.•We calibrate the model to the market and analyze the impact of jumps on joint and marginal survival probabilities.•We develop a new finite-difference method to solve the multidimensional PIDE, which is second order consistent in both time and space variables.•We prove the von Neumann and l2 stability of the method.•We demonstrate empirically that in the presence of discontinuous terminal and boundary conditions, second order of convergence can be maintained by local averaging of the data and suitable refinement of the timestep close to maturity.