Asset credit risk model

The first component is the asset credit risk model that contains two main subcomponents:
the credit rating model and the dynamic credit rating model. The credit
rating model calculates the credit riskiness of an asset today while the dynamic
credit rating model calculates how that riskiness may evolve over time. This is
depicted in more detail in Figure 10.4. For example, if the asset is a corporate bond,
then the credit riskiness of the asset is derived from the credit riskiness of the issuer.
The credit riskiness may be in the form of a probably of default or in the form of a
credit rating. The credit rating may correspond to one of the international credit
rating services or the institution’s own internal rating system.

An interesting point is that the credit riskiness of an asset can depend on the
particular structure of the asset. For example, the credit riskiness of a bond depends
on its seniority as well as its maturity. (Short- and long-term debt of the same issuer
may have different credit ratings.) The credit risk does not necessarily need to be
calculated. It may be inputted from various sources or modeled from fundamentals.
If it is inputted it may come from any of the credit rating agencies or the institution’s
own internal credit rating system. For a good discussion of banks’ internal credit
rating models see Treacy and Carey (1998).
If the credit rating is modeled, then there are numerous choices – after all, credit
risk assessment is as old as banking itself. Two examples of credit rating models are
the Zeta model, which is described in Altman, Haldeman, and Narayanan (1977),
and the Lambda Index, which is described in Emery and Lyons (1991). Both models
are based on the entity’s financial statements.

Another well-publicized credit rating model is the EDF Calculator. The EDF model
is based on Robert Merton’s (1974) observation that a firm’s assets are the sum of
its equity and debt, so the firm defaults when the assets fall below the face value of
the debt. It follows that debt may be thought of as a short option position on the
firm’s assets, so one may apply the Black–Scholes option theory.
Of course, real bankruptcy is much more complicated and the EDF Calculator
accounts for some of these complications. The model’s strength is that it is calibrated
to a large database of firm data including firm default data. The EDF Calculator
actually produces a probability of default, which if one likes, can be mapped to
discrete credit ratings. Since the EDF model is proprietary there is no public
information on it. The interested reader may consult Crosbie (1997) to get a rough
description of its workings. Nickell, Perraudin, and Varotto (1998) compare various
credit rating models including EDF.

To accurately measure the credit risk it is essential to know both the credit
riskiness today as well as how that credit riskiness may evolve over time. As was
stated above, the dynamic credit rating model calculates how an asset’s credit
riskiness may evolve over time. How this component is implemented depends very
much on the assets in the portfolio and the length of the time period for which risk
is being calculated. But if the asset’s credit riskiness is not being modeled explicitly,
it is at least implicitly being modeled somewhere else in the portfolio model, for
example in a pricing model – changes in the credit riskiness of an asset are reflected
in the price of that asset.

Of course, changes in credit riskiness of various assets are related. So Figure 10.4
also depicts a component for the correlation of credit rating which may be driven by
any number of variables including historical, econometric, or market variables.
The oldest dynamic credit rating model is the Markov model for credit rating
migration. The appeal of this model is its simplicity. In particular, it is easy to
incorporate non-independence of two different firm’s credit rating changes.
The portfolio model CreditMetrics (J.P. Morgan, 1997) uses this Markov model.
The basic assumption of the Markov model is that a firm’s credit rating migrates at
random up or down like a Markov process. In particular, the migration over one
time period is independent of the migration over the previous period. Credit risk
management models based on a Markov process are implemented by Monte Carlo
simulation.

Unfortunately, there has been recent research showing that the Markov process is
a poor approximation to the credit rating process. The main reason is that the credit
rating is influenced by the economy that moves through business cycles. Thus the
probability of downgrade and, thus, default is greater during a recession. Kolman
(1998) gives a non-technical explanation of this fact. Also Altman, and Kao (1991)
mention the shortcomings of the Markov process and propose two alternative processes.
Nickell, Perraudin, and Varotto (1998a,b) give a more thorough criticism of
Markov processes by using historical data. In addition, the credit rating agencies
have published insightful information on their credit rating and how they evolve over
time. For example, see Brand, Rabbia and Bahar (1997) or Carty (1997).
Another credit risk management model, CreditRiskò, models only two states: nondefault
and default (CSFP, 1997). But this is only a heuristic simplification. Rolfes
and Broeker (1998) have shown how to enhance CreditRiskò to model a finite
number of credit rating states. The main advantage of the CreditRiskò model is that
it was designed with the goal of allowing for an analytical implementation as opposed
to Monte Carlo.

The last model we mention is Portfolio View (McKinsey, 1998). This model is based
on econometric models and looks for relationships between the general level of default
and economic variables. Of course, predicting any economic variable, including the
general level of defaults, is one of the highest goals of research economics. Risk
managers should proceed with caution when they start believing they can predict
risk factors.

As mentioned above, it is the extreme events that most affect the risk of a portfolio
of credit risky assets. Thus it would make sense that a model which more accurately
measures the extreme event would be a better one. Wilmott (1998) devised such a
model called CrashMetrics. This model is based on the theory that the correlation
between events is different from times of calm to times of crisis, so it tries to model
the correlation during times of crisis. This theory shows great promise. See Davidson
(1997) for another discussion of the various credit risk models.