Cross- and Autocorrelation in Multi-Period Credit Portfolio Models

For the risk assessment of credit portfolios single-period credit portfolio models are by now widely accepted and used in the practical analysis of loan respectively bonds books in the context of capital modeling. But already Finger (2000) pointed to the role of inter-period correlation in structural models and Thompson, McLeod, Teklos and Gupta (2005) strongly advocated that it is ‘time for multi-period capital models’. With the emergence of structured credit products like CDOs the default-times/Gaussian-copula framework became standard for valuing and quoting liquid tranches at different maturities, Bluhm, Overbeck and Wagner (2002). Although it is known that the standard Gaussian-copula-default-times approach has questionable term structure properties the approach is quite often also used for the risk assessment by simply switching from a risk-neutral to a historical or subjective default measure.

From a pricing perspective Andersen (2006) investigates term structure effects and inter-temporal dependencies in credit portfolio loss models as these characteristics become increasingly important for new structures like forwardstart CDOs. But the risk assessment is also affected by inter-temporal dependencies. For the risk analysis at different time horizons the standard framework is not really compatible with a single-period correlation structure; Morokoff (2003) highlighted the necessity for multi-period models in that case. Long-only investors in the bespoke tranche market with a risk-return and hold-to-maturity objective have built in the past CDO books with various vintage and maturity years, based only on a limited universe of underlying credits with significant overlap between the pools. A proper assessment of such a portfolio requires a consistent multi-period portfolio framework with reasonable inter-temporal dependence. Similarly, an investor with a large loan or bond book, enhanced with non-linear credit products, needs a reliable multi-period model with sensible inter-temporal properties as both bond or structured investments display different term structure characteristics.