The assessment of default risk is also critical in the valuation of corporate bonds and credit derivatives such as basket-default swaps.
There is an important distinction between default risk under the actual probability measure and that under the risk-neutral probability measure. Typically, a decision to lend would be assessed using the former, where risk is assessed in terms of the probabilities of actual default occurrences. Decisions relating to pricing would be assessed under the latter.
Credit ratings
Ratings are based on factors such as the agency’s assessments of the firm. It will then go through public information and meet with the debt issuer to obtain further information. Ratings might be carried out independently of the firm, with ratings revealed on a confidential basis to the agency’s clients.
Recently, institutions have developed their own risk rating systems. These produce estimates of the probability of loan default. Many also produce estimates of the loss given default. Combined with information about exposure at default, this allows a bank to estimate the expected loss on a loan.
Contingent claims approaches
Some approaches to default risk utilise the contingent claim approaches that build on the limited liability rule that allows shareholders to default on their obligations provided that all the firm’s assets are handed over to creditors.
The firm’s liabilities are contingent claims issued against its assets. Default occurs at maturity when the value of the firm’s assets falls short of the value of its liabilities. Such default risk can be modelled using regular option pricing methods.
Credit migration approaches
Some classes of models are built on a credit migration or transition matrix. This examines the probabilities of any given credit rating changing to any other over the horizon period. These probabilities are assessed from historical default data and will suggest whether a firm with any given rating is likely to retain that rating by the end of the horizon period.
The best-known migration model, the CreditMetrics model, considers the forward value of a loan at the end of the horizon period for each possible end-horizon credit rating. Values are found by discounting the loan’s cash flows at a rate equal to the risk-free end-horizon forward rate, with an estimate of the credit spread for that rating. The combination of transition probabilities and end-horizon loan values enables the modeller to apply value-at-risk (VaR) analysis and obtain the credit VaR as the loan value minus the relevant quantile of the distribution of forward loan values.
Default and migration probabilities are unlikely to remain constant over time and there is a need for an underlying structural model to tie these to more fundamental economic variables. CreditMetrics uses the Merton model to tackle this, making simplifications to obtain probabilities from the joint distribution of the equity returns of obligor firms. An alternative solution is offered by the CreditPortfolioView model, which relates probabilities to macroeconomic variables.
Intensity models of default risk
This system models default as an exogenous process that occurs randomly in accordance with a fitted intensity or hazard function. These models are empirical and don’t embody any economic theory of default. They make no attempt to relate default risk to capital structure or make assumptions of the causes of default.
Since intensity-based models are based on debt prices, they can reflect complex default term structures better than some other approaches. However, corporate bond markets can prove illiquid, making pricing data inaccurate.
General problems and future objectives in default risk modeling
All models of default risk have their weaknesses, particularly their exposure to model risk. It can be difficult to discriminate between models, making it impossible to determine which model is the “best”. Even within the confines of a model there exists the parameter risk, which is calibrated rather than estimated. As calibration requires judgement, it introduces error. Evidence suggests estimates of default probabilities are also likely to be sensitive to key parameter values, such as volatilities and correlations.
The recent financial crisis has exposed the weaknesses of credit models in the starkest possible terms. Their sensitivity to key parameters and their failure to take adequate account of market conditions have been shown to be very serious problems indeed.
This article is an edited version of
an entry in the “Encyclopedia of Quantitative Risk Analysis and
Assessment”, Copyright © 2008 John Wiley & Sons Ltd. Used by
permission.
