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An Integrated Structural Model for Portfolio Market and Credit Risk

The Gaussian asymptotic single factor model (ASFM) of portfolio credit losses, developed by Vasicek (1987), Finger (1999), Schönbucher (2000), Gordy (2003) and others, provides an approximation for the default rate distribution for a credit portfolio in which default dependence is driven by a single common factor. In a large portfolio of credits, idiosyncratic risk is fully diversified and the only source of portfolio loss uncertainty is the default rate that is driven by the common latent Gaussian factor.

By construction, the ASFM model is a default-mode model meaning that all credits are assumed to either perform or default within the model’s risk measurement horizon. Defaulting credits’ losses are measured by the model. Income earned on nondefaulting credits is not recognized in the Vasicek (and Basel II AIRB) loss distribution estimate.

Credit Metrics popularized mark-to-market (MTM) credit-migration style risk measurement models. The credit-migration class of models generalizes the Vasicek (1987) default-mode model to include the potential for migration of non-defaulting credits among credit quality groups. When these migrating credits are re-priced at the end of the risk measurement horizon, they generate capital gains or losses. The Credit Meterics model uses estimates of credit quality transition matrices and a single latent common factor to drive changes in an obligor’s credit quality and trigger default. The portfolio’s future value distribution includes interest income, MTM gains and losses on non-defaulting credits, and default losses on the portfolio’s positions.

The Credit Metrics approach incorporates correlation among credit quality transitions and defaults, but it does not incorporate market risk. While credits may transition among credit-quality grades, the MTM value of a future cash flow is known and non-stochastic. The end-of-horizon values of performing credits are calculated using credit quality specific implied forward rates that are bootstrapped from the spot yield curves for each credit quality grade used in the model.

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An Integrated Structural Model for Portfolio Market and Credit Risk