Default rate of corporate debts and their portfolios - Book review of ‘Credit risk modeling using Excel and VBA’

I read this book since credit risk management of collateral loans is key to manage the performance of CLO tranches. In fact, it may be useful for any structured product’s credit analysis.

Individual level

There are two default prediction methods for individual debt: regression analysis and structured method. Regression analysis uses logistic regression and explanatory variables to predict default probability of a borrower. A credit score can be derived during this process to indicate borrower’s ability to repay the debt.

Structured method is based on the option pricing theory. The default probability is equal to the probability that the asset value of a company is lower than its debt value. This method assumes the log normal distribution of asset value, and it requires iteration to find the best fit asset values and their distribution.

Portfolio level

The correlation become the other important factor when evaluating the credit risk in a portfolio. The computation will be explosive if we calculate correlations between all assets in the portfolio. The copula is a good way to solve this problem. It groups different assets and uses common factors to indicate correlations. So we will have less correlations to calculate.

                    

For a portfolio, its default rate will be affected by the common factors and individual factors of assets. The Monte Carlo method can be used to generate these two factors, and if the simulated value is below a default threshold, we consider there is a default. This method is called asset value approach. The Gaussian copula generates the variable with normal distribution, but t-distribution may also be used since it provides more tail risk modeling. With this method, we can also simulate the credit default swap (CDS), and calculate the price of CDS.

Transition matrix

Transition matrices provide the probability of the credit rating change for debts of same ratings. It can be derived from the historical data. Cohort method is a widely used method, but it only considers the year end rating change. So any credit rating change in the middle of a year will not affect the transition matrices.

Hazard method is an upgrade from Cohort method, and it gives weights to the rating change within a year. We first estimate the generator matrix from historical data, then will can get T-year transition matrix with exponential function.

Different years’ transition matrices

The transition matric indicates the probability of rating change for an average year, but the following year may be relatively good or bad. It may be influenced by macroeconomic condition, corporate bond spread, aging effect, etc. Then it may be reasonable to give a shift parameter to the average transition matrix to get a specific year’s transition matrix.

We can also use transition matrices to predict default rate of a portfolio, since any transfer to D-rating indicates a default event.  Poisson regression is introduced to predict the default rate of a portfolio with same credit rating.

Additional content

This book provides the validation of credit rating by evaluating the discrimination and calibration. The other bonus is you can find many VBA code examples on credit risk modeling.