[:en]Derivatives[:]
Reduced-form Models
Here is the English version, slightly polished while keeping your original logic and tone:
Credit risk is not easy to diversify, because default risks across different organizations are correlated.
Two types of frameworks are commonly used to explain these correlations: default-intensity-based models and structural models. There is also the Gaussian copula model, which can be viewed as a simplified version of the structural model.
In this note, I will focus on the default-intensity model, also known as the reduced-form model.
This model says that the hazard rates of different organizations are correlated with each other, and this is what creates correlation between defaults.
The key idea is this:
Credit ratings are based on many years of historical statistics. These years include both crisis periods and expansion periods. Therefore, a credit rating usually reflects an average default probability across the cycle.
But the hazard rate is a dynamic measure. It can increase significantly during a crisis.
From this perspective, default correlation becomes intuitive. If a crisis increases the hazard rates of many companies at the same time, then their defaults also become more likely to happen together.
As a reminder, the hazard rate is the conditional probability of default. For example, it is the probability that a company defaults in year 3, conditional on the fact that it did not default during the first two years.
Hazard rates can be estimated statistically from survival and default probabilities. But we can also reverse the logic in the formula:
Therefore, the probability that two organizations default together naturally increases during crisis periods.
See how large the effect can be when we assume only a 10% probability of a crisis:
P.S.
Although this model is mathematically convenient for explaining default correlations, it cannot capture the full range of possible correlations.
The model looks at defaults at a general macro level, but it does not fully capture direct links between specific organizations.
For example:
What happens to one company if another company defaults and that company was its key supplier?
This is one reason why structural models were developed.
I will write about those next.
Adapted from:
Options, Futures, and Other Derivatives — John C. Hull