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Specific Risk for Bonds and Credit Risk VaR

Credit risk models address the issue for bond portfolios as for loans. The horizon is a parameter controlled by the banks. Generally, banks measure credit risk with portfolio models on their loans over a horizon of at least 1 year, because of the hold to maturity philosophy. For bonds, the same models apply. Hence, it is possible to capture credit risk over a portfolio of bonds over any horizon. Most of the section on credit risk deals with measuring credit risk VaR over a specified horizon. It makes a distinction between full valuation models that capture all changes in values due to risk migrations and default mode models that capture loss only in the event of default. Full valuation models include KMV Portfolio Manager or Credit Metrics. They apply to credit risk measurement over a portfolio of bonds for any horizon.

Derivative Credit Risk

For over-the-counter derivatives, the hold to maturity view is relevant and modelling exposures provides the time profile of worst-case exposure at future time points until maturity. A common solution consists of summarizing the time profile of potential exposures at risk into a single value, a loan equivalent, or possibly several for various periods. The process applying to banking exposures applies for loan equivalents of derivatives.

This leaves in the shadow the combination of two risks: the default risk and the exposure risk. If default risk and exposure risk are independent, the problem is similar to the modelling of the volatility of combined default risk and recovery risk.