image blog credit risk modeling
August 31, 2020

Introduction to Credit Risk Modeling

Embedded Analytics
Algorithms & Functions

Risk modeling is the analysis of historical risk events and the usage of mathematical and statistical methods to quantify risk. Risk modeling enables organizations in nearly every industry to understand, manage, and minimize risks that are specific to their business. In commercial and consumer finance, organizations use risk models to quantify their risk of loss due to loan default or prepayment. Credit risk modeling plays a crucial role in maintaining profitability for lenders.

In this article, we take a high-level look at credit risk modeling, how it’s used, and various models and algorithms that are commonly used by lending institutions to analyze and manage risk.

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What Is Credit Risk Modeling?

Credit risk modeling is the application of risk models to creditor practices to help create strategies that maximize return (interest) and minimize risk (defaults).

Credit risk models are used to quantify the probability of default or prepayment on a loan. In the case of either default or prepayment, the risk to the lender is a loss of interest revenue.

Credit Risk Factors

Factors that can influence the probability of default include attributes of the borrower, terms and structure of the loan, as well as other factors that can vary from company to company. In the recent paper, Khemakhem, et. al., test several different factors in their risk models for commercial loan defaults. They determined that the key factors in predicting creditworthiness of borrowing companies were:

  • Profitability ratios
  • Repayment capacity
  • Solvency
  • Duration of a credit report
  • Guarantees
  • Company size
  • Loan number
  • Ownership structure
  • Corporate banking relationship (duration)

In their paper on consumer auto loans, Meisenzahl, et. al., confirm a long held belief that auto loan credit performance is correlated with unemployment levels. Based on their credit risk models, they estimated that the “unemployment rate explained about 55% and 66% of the loss performance in prime and subprime auto loan losses, respectively,” and further, that a “100% increase in unemployment rate resulted in a 119% increase in prime loan losses during economic downturns with rising unemployment rates.

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Credit Risk Models and Algorithms

To quantify risk, it usually comes down to estimating a probability or likelihood that a risk event will occur. Having that estimate, and understanding how it is impacted by factors, allows companies to lower risk by adjusting the factors that they can control or by hedging their losses for factors they cannot control

Risk Models and Algorithms for Prediction

Estimating a probability often involves selecting and building a predictive model. The goal of prediction is to accurately predict a target variable.

As we have mentioned, in credit risk models the target variable is often the event of a loan default or the event of a loan prepayment. Historical data on actual loans is used to build or “fit” the risk model, and then the fitted model provides the estimated probabilities at different values of the factors.

There are many types of methods and models for prediction. For binary outcomes such as default/non-default or prepayment/non-repayment, popular predictive models include logistic regression, decision trees, neural networks, Naïve Bayes classifier, and others.

Risk Models and Algorithms for Prediction

Linear regression

Logistic regression

Generalized linear models

Neural networks

Naïve Bayes classifier

Support vector machines

Decision trees, random forest, gradient boosting

Time series

With a fitted predictive model, factor levels on a new loan application can be “run through” the model to predict the probability of default or prepayment. This is part of the process known as “credit scoring”.

Variable Selection and Dimension Reduction

From among a large set of potential factors there are multiple methods to help find the most predictive set to use. These methods range from exploratory tools like charts and summary statistics to sophisticated dimension reduction methods, like principal components and factor analysis.

Methods for Factor Selection and Dimension Reduction

Exploratory data analysis

Regression subset selection models

Variable importance measures in bootstrap aggregation, random forests

Hypothesis tests (e.g., Chi-square tests of association)


Principal component analysis and factor analysis

Finding the best set of variables (or factors) means less cost in terms of measurement and data storage, more accurate predictions, and better understanding of the underlying relationship between the risk and risk factors.

Optimization in Credit Risk Modeling

Mathematical optimization is a class of methods that are often used together with predictive models. In credit risk modeling, while the predictive models estimate the probability of default or prepayment, optimization methods can be used to find the best mix of credit products in a portfolio to keep risk low while achieving a high expected return.

Optimization Methods for Risk Modeling

Linear programming

Quadratic programming

Non-linear programming


Non-negative least squares

Maximum likelihood (Fisher’s scoring)

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Final Thoughts

While important for many industries, risk modeling can be especially useful for financial companies that issue credit or loans. In this blog, we detailed some of the available methods used in credit risk modeling for prediction, factor selection, and optimization.

For those who want to apply credit risk analysis, IMSL provides tested and trusted numerical libraries in C, Java, Fortran, and Python that include many of the models and algorithms we talked about today.

Chat with an IMSL expert today to see how IMSL can help your company quickly add risk modeling to their financial analysis portfolio.

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Additional Resources

Want to learn more about risk modeling? This webinar from Roxy Cramer, PhD Statistician at IMSL, is a must-watch.

Want to learn more about how IMSL can be used for data analysis? These resources are a great place to start.


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