Credit risk pricing model

The next major component of the model is the credit risk pricing model, which is
depicted in detail in Figure 10.5. This portion of the model together with the market
risk model will allow the credit risk management model to calculate the relevant
return statistics.
The credit risk pricing model is necessary because the price of credit risk has two
components. One is the credit rating that was handled by the previous component,
the other is the spread over the riskless rate. The spread is the price that the market
charges for a particular credit risk. This spread can change without the underlying
credit risk changing and is affected by supply and demand.
The credit risk pricing model can be based on econometric models or any of the
popular risk-neutral pricing models which are used for pricing credit derivatives.
Most risk-neutral credit pricing models are transplants of risk-neutral interest rate
pricing models and do not adequately account for the differences between credit risk
and interest rate risk. Nevertheless, these risk-neutral models seem to be popular.
See Skora (1998a,b) for a description of the various risk-neutral credit risk pricing
models.
Roughly speaking, static models are sufficient for pricing derivatives which do not
have an option component and dynamic models are necessary for pricing derivatives
which do have an option component. As far as credit risk management models are
concerned, they all need a dynamic credit risk term structure model. The reason is
that the credit risk management model needs both the expected return of each asset
as well as the covariance matrix of returns. So even if one had both the present price
of the asset and the forward price, one would still need to calculate the probability
distribution of returns.
So the credit risk model calculates the credit risky term structure, that is, the yield
curve for the various credit risky assets. It also calculates the corresponding term
structure for the end of the time period as well as the distribution of the term
structure. One way to accomplish this is by generating a sample of what the term
structure may look like at the end of the period. Then by pricing the credit risky
assets off these various term structures, one obtains a sample of what the price of
the assets may be.
Since credit spreads do not move independently of one another, the credit risk
pricing model, like the asset credit risk model, also has a correlation component.
Again depending on the assets in the portfolio, it may be possible to economize and
combine this component with the previous one.
Finally, the choice of inputs can be historical, econometric or market data. The
choice depends on how the portfolio selection model is to be used. If one expects to
invest in a portfolio and divest at the end of the time period, then one needs to
calculate actual market prices. In this case the model must be calibrated to market
data. At the other extreme, if one were using the portfolio model to simply calculate
a portfolio’s risk or the marginal risk created by purchasing an additional asset, then
the model may be calibrated to historical, econometric, or market data – the choice
is the risk manager’s.