On Correlation Effects and Default Clustering in Credit Models

We establish Markovian models in the Heath, Jarrow and Morton paradigm where the credit spreads curves of multiple firms and the term structure of interest rates can be represented analytically at any point in time in terms of a finite number of state variables. The models make no restrictions on the correlation structure between interest rates and credit spreads. In addition to diffusive and jump-induced default correlations, default events can impact credit spreads of surviving firms. This feature allows a greater clustering of defaults. Numerical implementations highlight the importance of taking interest rate-credit spread correlations, credit-spread impact factors and the full credit spread curve information into account when building a unified model framework that prices any credit derivative.