Modelling Default Correlations in a Two-Firm Model with Dynamic Leverage Ratios

This article provides a generalized two-firm model of default correlation, based on the structural approach that incorporates interest rate risk. In most structural models default is driven by the firms' asset dynamics. In this article, a two-firm model of default is instead driven by the dynamic leverage ratios, which combines the measure of risks of the firms' total liabilities and assets. This article investigates analytical methods and numerical tools to solve the two-dimensional first passage time problem with time-dependent parameters. We carry out a comparative analysis of the impact of model parameters and provide some insights of their effects on joint survival probabilities and default correlations.