Fundamental concepts of credit risk modelling differ between (1) a credit risk assessment conditional and unconditional on economic conditions, (2) an actuarial versus a mark- to-market consideration of credit risk, (3) expected and unexpected loss of defaultable exposures, and (4) the concepts of risk-adjusted discounting and risk-neutral valuation.
Conditional vs. Unconditional Credit Risk Models
Reflecting the background conditions on credit risk a general framework for modelling credit portfolio risk involves:2
• conditional credit performance
• dependence model of credit risk
• unconditional credit performance
The performance of a credit portfolio as measured in terms of default rate, credit loss, total net revenues or changes in portfolio value over a time interval, fluctuates in time, reflecting the variation of economic background factors that jointly affect the economic prospects of all obligors in the portfolio. Conditional on effective economic conditions, credit performance such as credit defaults of individual obligors, are assumed to be inde- pendent in a period as economic background factors jointly affect the variation of obligors’ credit risk only in time. Conditional credit risk measures account for the effective eco- nomic conditions and represent the credit risk of obligors in a specific period.
The dependence of exposures’ credit risk is typically incorporated by a parametric model of factors that jointly control for an exposure’s credit risk indicating variables. Factors may be of statistical, macro-economic or business-specific nature. The strength of the dependence between the credit risk of single exposures is reflected by the strength of the variation of default rates in time. Credit portfolio models incorporate the dependence of exposures’ credit quality in predicting credit portfolio risk.
The expected unconditional credit performance represents a long-run average of credit performance across the full range of probable economic conditions. A distribution of unconditional credit performance is obtained by aggregating the respective conditional credit performance multiplied with the probability of the conditioning state-of-economy over the range of possible economic conditions. Risk forecasts generated by unconditional models do not explicitly refer to current economic conditions, so that risk parameters involve a through-the-cycle representation. However, risk models used in the banking sectors typically adapt the estimation of through-the-cycle parameters by emphasizing
more recent market conditions, thus taking a hybrid approach concerning the conditioning of risk forecasts.
Through-the-cycle credit risk considerations are not meaningful if a short-term credit risk forecast is required. Instead, conditional credit risk models are forward-looking in nature, as they rely on current or predicted future economic conditions up to the time horizon of the risk forecast. Clearly, the economic conditioning of parameter estimates must coincide with the assumption of the respective risk model application. Conditional risk forecasts are typically performed by macroeconomic factor models as presented in Section 3.4.1. The ability of conditional models to provide adequate forecasts of credit risk is closely related to the accurate prediction of future economic conditions, so that prediction failures or unexpected changes in business prospects result in biased credit risk projections.
Actuarial vs. Mark-to-market based Credit Risk Models
The actuarial concept of credit risk recognition considers a discrete state-space of credit quality that refers to a real-world probability measure. In actuarial models state-specific amounts of exposure and credit loss are typically specified, but no explicit valuation of credit exposures takes place. Mostly a default-only paradigm is implemented, where credit loss is only incurred if a borrower defaults on its contractual obligations, and the effective loss is defined as the difference between the bank’s exposure set in terms of the notional amount of the outstanding claim, and the present value EAD(1-LGD) of expected net recoveries. Since, the actuarial definition of credit loss does not take into account a deterioration of credit quality, unrealized economic losses from an adverse change of mark-to-market values of credit involvements are ignored and may accumulate in credit portfolios.
In the mark-to-market framework, additionally, deteriorations in the credit quality of ex- posures unequal to a credit default are reflected. Credit-risky exposures are explicitly valued using a valuation model that is calibrated either to reproduce market-observed values of credit exposures or to provide mark-to-model values for exposures without ob- servable market indications of the credit risk in question. The value of a credit exposure depends either on a continuous credit-risk-indicating state variable or a discrete multino- mial credit score, such as a rating. Credit performance is defined on the basis of exposures’ change in credit value within a specified period. Rating-based valuation models derive credit values from the rating of an exposure and consider obligor default as a specific rating state.
Expected vs. Unexpected Credit Loss
The expected credit loss EL = P D · EAD · LGD of an exposure is defined by the estimates of the probability of default, the exposure-at-default and the loss-given-default. The unexpected credit loss (UL) of an individual exposure or a credit portfolio is typically
defined as the standard deviation of the (portfolio) credit loss.3 In the determination of
unexpected credit portfolio loss, mutual correlations of default events, exposures and loss rates must be considered for each borrower as well as between borrowers. Expected and unexpected loss typically refer to a one-year time horizon. Obviously, the time horizon and the definition of default must coincide in the estimation of PD, EAD and LGD for loss estimates to be conclusive.
Risk-adjusted Discounting vs. Risk-neutral Valuation
Credit valuation models either involve the risk-adjusted discounting (RAD)4of contractual
cash flows under a real-world probability measure using credit-risk adjusted rates or the risk-neutral valuation (RNV) of defaultable cash flows under a risk-neutral probability measure to determine current and prospective future credit values.
RAD of non-publicly traded credit exposures relies on the classification of exposures with homogenous credit risk characteristics into risk classes and requires discount rates of a class-specific term structures that represents the average credit risk of the class. Risk classes are typically defined on the basis of the rating of exposures or obligors. However, exposures of the same rating grade may vary substantially with respect to the expected LGD of exposures, the migration probabilities or the sensitivity to changes in systematic risk factors, so that valuation errors may arise by using a term structure of discount factors that is homogenous for all exposures of a risk class.
Risk-neutral models may circumvent this short-coming. Risk-neutral valuation (RNV) refers to models of a state- and time-continuous credit risk indicating state variable under a risk-neutral probability measure. From the stochastic properties of this credit risk indi- cating variable risk-neutral survival and default probabilities can be derived that enable, in a complete market setting, the discounting of default state dependent cash flows using a risk-free interest rate. Models that incorporate risk-neutral valuation include structural firm-value models and reduced-form models of an exponential-affine default intensity. The way credit events are triggered constitutes the elementary difference between the two model types.
Structural models incorporate a microeconomic interpretation of the firm, with default only triggered if the value of a firm’s assets is not sufficient to serve its financial obligations. From the dynamics of the firm value risk-neutral probabilities of default and survival are
3 Cf. Ong (1999), p. 113. 4 Cf. Gupton et al. (1997).
calculated that enable the risk-neutral discounting of probability-weighted cash flows.5
In the reduced-form framework, credit default is typically triggered by an exponentially distributed default time with an instantaneous default intensity parameter that has no economic analogy. From the distributional properties of default intensities discount factors that incorporate default risk of an exposure can be derived.
The data used for model estimation substantially affects the appropriateness of both model types. Whereas structural models are more convenient for credit risk applications which are based on macroeconomic and fundamental firm data, intensity models are more suited to a model calibration from market prices of credit risk. A detailed comparison of the competing classes of credit valuation models is given in Section 3.1.
With respect to application issues, RAD and RNV mainly differ in the way discount factors are calculated. RAD models explicitly use market-derived discount factors, whereas RNV is based on parametric models which need to be calibrated to reproduce observed credit spreads, for example in the credit default swaps (CDS) market or the corporate bond markets. RNV models are vulnerable to erroneous specifications and estimation errors and strongly rely on time series of credit market data for the estimation of the model, whereas the non-parametric RAD approach makes minimal use of modelling assumptions but presents estimation problems in the portfolio context.