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Since recovery uncertainty results from a number of sources of risk, modelling some of them is not sufficient to capture the overall recovery risk. For instance, we made a number of restrictive assumptions on the valuation of guarantees and support above. In such instances, it is more practical to model the overall recovery risk using expected values plus some distribution around this value. The consequence is that the loss volatility and the loss distribution now depend on the uncertainty of the loss under default. We show how recovery uncertainty influences the loss volatility, before describing the beta distribution, a distribution that seems to fit observed recovery distributions.

Extension of Loss Volatility with Uncertain Lgd

A random loss given default intuitively increases the loss volatility. The value under default is uncertain because of recoveries, and the value under no default is uncertain because of migrations. The loss volatility results from simple calculations under default mode. A simple technique for calculating the increase is to calculate the variance of the random value V as a conditional variance upon another random variable D measuring default or no default³. The formula is:

COVENANTS

Covenants allow for preventive actions. They fit well with active credit management and with a permanent monitoring of risk. The effect is very different from that of collateral and guarantees, because these look more like insurance policies activated only after default occurs. On the other hand, covenants enhance the effect of proactive credit risk management. However, they have no mechanical effects on risk. Their effectiveness depends on many factors such as how constraining they are, the banks attitude and the context.

Covenants serve for avoiding larger losses due to waiting when credit risk increases. Their value would be the difference between asset values net of recovery costs when a breach occurs, and the value without covenants, when a default event occurs later than a covenant breach. The sooner the breach occurs, the higher should be the recovery of lenders. Moreover, covenants and collateral increase the cost of default of the borrower since they make it an obligation to give up the project or the collateral when these still have a significant value. Hence, one path for valuing covenants would be to increase the recovery rate.

Looking at covenants as tools for restructuring before default occurs, their economic value would be to impose a cap on the default risk of the borrower, equivalent to benefiting from a floor on the default probability. It is difficult to go beyond floors on recovery rates and/or floors on default probabilities. Even such simple rules remain hazardous because of a lack of data.