In this issue of The Journal of Credit Risk we present two research papers and two technical reports.
The first research paper in this issue, "A clusterized copula-based probability distribution of a counting variable for high-dimensional problems", is by Enrico Bernardi and Silvia Romagnoli. In their paper the authors represent the dependence structure of a set of random variables with a particular copula function that they call a clusterized homogeneous copula (CHC). The paper derives an algorithm to implement the extraction of the probability density function of the corresponding counting variable from a CHC. The model is based on the class of CHC that is suitable for dealing with the class of high-dimensional problems in which the probability density function of the counting variable is needed. The authors compare the probability density function obtained with the CHC approach with that obtained with limiting models and Panjer recursion, emphasizing the dimension of granularity and concentration correction introduced into the suggested model.
Our second research paper is "Analytical solutions for the expected loss of a collateralized loan: a square root intensity process negatively correlated with collateral value" by Satoshi Yamashita and Toshinao Yoshiba. This paper proposes a square root process for describing default intensity and a negative correlated affine diffusion process for describing collateral value, and it provides analytical solutions for the expected loss of a collateralized loan. The authors then illustrate the impact of negative correlation between default intensity and collateral value through numerical examples by using the derived solutions, and they find that it can cause the expected loss and the standard deviation of loss to increase, especially when the mean-reversion speed of default intensity is low.
A technical report describes a particular practical technique and enumerates situations in which it works well and others in which it does not. Such reports provide extremely useful information to practitioners in terms of saved time and minimizing duplication of effort. The contents of technical reports complement rigorous conceptual and model developments presented in the research papers. A technical report can be a useful survey article as well.
The first technical report in this issue, "A nonparametric approach to incorporating incomplete workouts into loss given default estimates", is by Grazia Rapisarda and David Echeverry. The main purpose of the paper is to develop an unbiased estimator of loss given default that incorporates partial and total recoveries and that is more efficient than previous such estimators. The methodology used is the nonparametric approach proposed by Kaplan and Mayer, where the authors adapted the reduced and enlarged sample estimator to find two estimators of loss given default - an exposure-weighted one and a default-weighted one - according to the method employed. The authors show that, when there exist partial recoveries in the data, the default-weighted estimator is unbiased and more efficient.
Our second technical report is "Applying the zero-adjusted inverse Gaussian model to predict probability of default and exposure at default for a credit card portfolio" by Rafael Rodrigues Troiani. The paper presents and evaluates the applicability of the zero adjusted inverse Gaussian (ZAIG) model both as a behavior score estimator and as a predictor of credit loss in a loan portfolio. The model presented in this paper targets the measurement of credit risk using information about individuals' behavior history toward the financial institution; therefore, it resembles a behavior score. The model is applied to a credit card portfolio from a Brazilian financial institution. As a behavior score model, the ZAIG model produces results that indicate good performance. As a portfolio loss estimator, the ZAIG model demonstrated a very low level of deviation from the observed loss in both the development and validation samples.
Analytical solutions for the expected loss of a collateralized loan: a square root intensity process negatively correlated with collateral value
Applying the zero-adjusted inverse Gaussian model to predict probability of default and exposure at default for a credit card portfolio
A clusterized copula-based probability distribution of a counting variable for high-dimensional problems