Numerical analysis of strategic contingent claims models

We study the numerical properties of a class of models recently introduced to calculate the values of corporate bonds and other corporate liabilities. Starting from a discrete-time extensive form game representing the consequences of financial distress, these “strategic contingent claims models” are associated with a particular free-boundary problem. Here we consider the properties of alternative solution techniques applied to this problem. We discuss four solution techniques of the finite difference type: explicit solutions, explicit solutions of the log transformed model, implicit solutions on a regular grid, and dynamically remeshed implicit solutions. To our knowledge this last method has not previously been employed in financial applications. We find that the use of dynamic remeshing can speed calculation solutions enormously. This opens the way to applying strategic contingent claims models in practical applications.