Ch6 Default Risk: Quantitative Methodologies (2)

3. Credit Scoring Models
The structural models do not extend easily to smaller & private companies since they are based on equity information.
Credit scoring has become a widespread technique in banks. Credit scoring techniques focused both on the prediction of failure and on the classification of credit quality.
The most widespread current credit scoring technologies consist of four multivariate scoring models: the linear regression probability model, the logit model, the probit model, & the multiple discrimant analysis model. Features of optimal credit scoring models include:
- Accuracy: low error rates
- Parsimony: the reduction of dimension(explanatory variables)
- Nontriviality: producing interesting results
- Feasibility: running in a reasonable amount of time & using realistic resources
- Transparency & Interpretability: providing high-level insight into the data relationships & trends and understanding where the output of the model comes from

3-1. Fisher Linear Discriminant Analysis
The principal aim of discriminant analysis is to segregate and classify a heterogenous population in homogeneous subsets. Various decision criteria are used to determine a relevant decision rule.
In the case of a credit scoring model, there can be two classes: default and nondefault. Then, we look for the linear combination of explanatory variables which separates the two classes most (maximum distance between the two classes). The most famous appication of discriminant analysis to credit scoring is Altman's Z-score. Explanatory variables used in this model include WC/TA, RE/TA, EBIT/TA, MVE/TL, Sales/TA
Z-score Video Clip: http://www.youtube.com/watch?v=tnADtb-BfFI

3-2. Parametric Discrimination
- Logit, Probit Models
- Parametric discrimant analysis determines a score using a regression.
- The models tend to provide a better fit and have more predictive power than simple linear models

3-3 K-Nearest Neighbor Approach
One of the easiest approaches to obtaining a nonparametric classification. The kNN assesses the similarities between the input pattern x and a set of reference patterns from the training set. A pattern is classified to a class of the majority of its k-nearest neighbor in the training set.

3-4. Support Vector Machine
SVMs separate the various classes of data using a best hyperplane


4. Decision Rules in Credit Analysis
4-1. Minimum-Error Decision Rule
- Using Bayes' theorem: a conditional probability of a firm being in one group or another given its characteristics

4-2. Minimum-Risk Decision Rule
- A class of rules that try to either minimize the probability of misclassification or minimize the loss associated with that error

4-3. Neyman-Pearson Decision Rule
- Type I & Type II Errors.

4-4. Minimax Decision Rule
- A decision rule of minimizing the maximum error or risk.


5. Measures of Performance
5-1. ROC(Receiver Operating Characteristic) evaluates a credit deccision rule by computing the proportion of correctly predicted defaults and the propotion of firms that were predicted to default an did not.

5-2. CAP(Cumulative Accuracy Profile) compares the probabilites of default computed by the classification system to the ranking of observed defaults

5-3. Maximum-Likelihood Decision Rule