Credit Risk

Credit risk is defined as uncertainty of value due to changes in credit quality. Credit risk in ERM is measured using the CreditMetrics approach which is based on the extended Merton model. Merton’s insight was to recognize that the equity in a firm can be considered as a call option on the firm’s assets. As a result, the value of the firm’s debt can be expressed as the amount of liabilities outstanding reduced by the put option on the assets (the strike being the amount of liabilities). In this option theoretic valuation of debt, bonds become riskier if the return on the underlying equity is weakening, if the maturity is long versus short, if the volatility of the equity is higher rather than lower. The put option reduces the value of debt due to the possibility of default. This basic Merton model can be easily extended to include rating changes (see Section 3.2.1.4).

The Rating Transition Matrix summarizes the historical pattern of migration for bond ratings. For example, a BBB bond may be upgraded or downgraded with the following probability:

Given the range of possible values and probability, we can calculate the variance of the future value of a BBB bond

Merton’s theory of the value of a Firm’s debt

Assumption: credit rating is driven by a firm’s asset value

• Value of a company’s assets determines its ability to pay its debt holders
• Company defaults if its assets fall below certain level in the next year
• Assuming the return of asset value of a company in one year is normally distributed

• CreditMetrics extends the Merton model: there are a series of levels (thresholds) zD , zCCC , zB , zBB …, such that a company’s rating will change if its asset value crosses a level
• CreditMetrics equates the credit migration probability to the area under the curve in order to establish the thresholds of firm values
• If asset thresholds are known, we need to model change in asset value (return)
• From the combination of a credit’s variance and the transition probabilities, ERM is able to derive the risk contribution of a single instrument

• One of the most critical calculations involves the correlation between credit risks
• The link between credit migration and the underlying firm value is established with CreditMetric’s idea
• CreditMetrics assumes that the correlation between obligors’ firm values is equal to the correlation between obligors’ market value of equities. The market values of these equities can be easily observed in the market