Credit Risk Models Research Articles

Spectral Expansions for Credit Risk Modelling with Occupation Times

We study two credit risk models with occupation time and liquidation barriers: the structural model and the hybrid model with hazard rate. The defaults within the models are characterized in accordance with Chapter 7 (a liquidation process) and Chapter 11 (a reorganization process) of the U.S. Bankruptcy Code. The models assume that credit events trigger as soon as the occupation time (the cumulative time the firm’s value process spends below some threshold level) exceeds the grace period (time allowance). The hazard rate model extends the structural occupation time models and presumes that other random factors may also lead to credit events. Both approaches allow the firm to fulfill its obligations during the grace period. We derive new closed-from pricing formulas for credit derivatives containing the (risk-neutral) probability of defaults and credit default swap (CDS) spreads as special cases, which are derived analytically via a spectral expansion methodology. Our method works for any solvable diffusion, such as the geometric Brownian motion (GBM) and several state-dependent volatility processes, including the constant elasticity of variance (CEV) model. It allows us to write the pricing formulas explicitly as infinite series that converges rapidly. We then calibrate our models (assuming that GBM governs the firm’s value) to market CDS spreads from the Total Energy company. Our calibration results show that the computations are fast, and the fit is near-perfect.

An Exact Structural Model for Evaluating Credit Default Swaps: Theory and Empirical Evidence

Using structural models for credit default swaps has been difficult. Existing models all adopt shortcuts as approximations. In this article, we provide an accurate and efficient solution to the price of the credit default swap. The main result is a Theorem in section 2. In an empirical study, we show how our model can properly capture credit default swap exposure to interest rate volatility and asset volatility. Furthermore, we apply the new model to study (1) the interactions among market, credit, and interest risks; (2) the consistency with the reduced-form credit risk models; and (3) implications to capital structure arbitrage.

Exchangeable Bernoulli distributions: High dimensional simulation, estimation, and testing

High dimensional simulation of exchangeable multivariate Bernoulli distributions is a challenging and important issue in applications, for example in credit risk models. The main contributions of this paper are, even for high dimensions, algorithms to sample from exchangeable multivariate Bernoulli distributions and to determine the distributions and the bounds of a wide class of indices and measures of probability mass functions. Unlike the algorithms present in the literature the proposed method gives the possibility to simulate also from negatively correlated distributions. Such a method is based on the geometrical structure of the class of exchangeable Bernoulli probability mass functions, which are points in a convex polytope whose extremal points are analytically known. Estimation and testing are also addressed.

Permanent layoff and consumer credit card loss forecasting

PurposeThe unemployment rate (UR) is the leading macroeconomic indicator used in the credit card loss forecasting. COVID-19 pandemic has caused an unprecedented level of volatility in the labor market variables, leading to new challenges to use UR in the credit risk modeling framework. This paper examines the dynamic relationship between the credit card charge-off rate and the unemployment rate over time.Design/methodology/approachThis study uses quarterly observations of charge-off rates on credit card loans of all commercial banks from Q1 1990 to Q4 2020. Univariate, multivariable, machine learning, and regime-switching time series modeling are employed in this research.FindingsThe authors decompose UR into two components – temporary and permanent UR. The authors find the spike in UR during COVID-19 is mainly attributed to the surge in temporary layoffs. More importantly, the authors find that the credit card charge-off rate is primarily driven by permanent UR while temporary UR has little predictive power. During recessions, permanent UR seems to be a stronger indicator than total UR. This research highlights the importance of using permanent UR for credit risk modeling.Originality/valueThe findings in the research can be applied to the credit card loss forecasting and CECL reserve models. In addition, this research also has implications for banks, macroeconomic data vendors, regulators, and policymakers.

Enhancing the predictive performance of ensemble models through novel multi-objective strategies: evidence from credit risk and business model innovation survey data

Enhancing the predictive performance of ensemble models through novel multi-objective strategies: evidence from credit risk and business model innovation survey data

Systematic and Unsystematic Determinants of Sectoral Risk Default Interconnectedness.

Assessing the financial stability of the banking industry, particularly in credit risk management, has become extremely crucial in times of uncertainty. Given that, this paper aims to investigate the determinants of the interconnectedness of sectoral credit risk default for developing countries. To that purpose, we employ a dynamic credit risk model that considers a variety of macroeconomic indicators, bank-specific variables, and household characteristics. Moreover, the SURE model is used to analyze empirical data. We find the connection between macroeconomic, bank-specific, and household characteristics, and sectoral default risk. The outcomes of macroeconomic factors demonstrate that few macroeconomic determinants significantly influence the sector's default risk. The empirical results of household components reveal that educated households play a substantial role in decreasing sectoral loan defaults interconnectedness and vice versa. While for bank-specific characteristic, we find that greater bank profitability and specialization have substantially reduced loan defaults.

Persistent Crises and Levered Asset Prices

Abstract This paper shows that standard disaster risk models are inconsistent with movements in stock market volatility and credit spreads during disasters. We resolve this shortcoming by incorporating persistent macroeconomic crises into a structural credit risk model. The model successfully captures the joint dynamics of aggregate consumption, financial leverage, and asset market risks, both unconditionally and during crises. Leverage strongly amplifies fundamental shocks by continuing to rise while crises endure. We structurally estimate the model and show that it replicates the firm-level implied volatility curve and its cross-sectional relation with observable proxies of default risk.

Credit Risk Management: Marketing Segmentation, Modeling, Accounting, Analysis and Audit

The relevance of the research is determined by the urgency of implementing the systems of credit risk management in bank activities based on the international accounting and reporting standards. The high level of complexity of the mentioned problem is related to a significant number of credit market segments and a variety of credit forms. The aim of the research paper is to identify the risk level of individual segments in the loan portfolio at the microeconomic level taking into account macroeconomic factors. The research methods used to identify the credit risk are migration matrices, nonlinear approximation, correlation-regression analysis, statistical distributions, and forecasting. The main research results are as follows: credit segmentation of the loan portfolio was performed, a matrix of credit risk sources was constructed, default probability and default losses were quantified to reflect the expected credit losses in accounting, and the audit of construction of credit risk models was performed. The significance of the research results is determined by the possibility to measure the factors of non-stable macroeconomic situation in Ukraine while estimating the risks of functioning of banking establishments. The proposed approaches to solving the problem of credit risk management allow decreasing the volume of non-operating credits and increasing the profitability of the loan portfolio of a bank. It can be considered that the merits of the research are determining the causal relations between the separate components of credit risk, which can be effectively used to neutralize and decrease them. The emphasis was made on the tools of credit risk management represented by marketing segmentation, modeling, accounting, analysis, and audit. The prospects of further studies include clarification of the methodical approaches to credit risk management in part of the separate market segments

A Practical Approach to Development and Validation of Credit Risk Models Based on Data Analysis

A Practical Approach to Development and Validation of Credit Risk Models Based on Data Analysis

On the combination of graph data for assessing thin-file borrowers’ creditworthiness

Thin-file borrowers are customers for whom a creditworthiness assessment is uncertain due to their lack of credit history. To address missing credit information, many researchers have used borrowers’ social interactions as an alternative data source. Exploiting social networking data has traditionally been achieved by hand-crafted feature engineering, but lately, graph neural networks have emerged as a promising alternative. Here we introduce an information-processing framework to improve credit scoring models by blending several methods of graph representation learning: feature engineering, graph embeddings, and graph neural networks. In this approach, we aggregate the methods’ outputs to be fed to a gradient boosting classifier to produce a final creditworthiness score. We have validated this framework over a unique multi-source dataset that characterizes the relationships, interactions, and credit history for the entire population of a Latin American country, applying it to credit risk models, application, and behavior. It also allows us to study both individuals and companies. Our results show that the methods of graph representation learning should be used as complements; they should not be seen as self-sufficient methods, as it is currently done. We improve the creditworthiness assessment performance in terms of the measures of Area Under the ROC Curve (AUC) and Kolmogorov–Smirnov (KS), outperforming traditional methods of exploiting social interaction data. In the area of corporate lending, where the potential gain is much higher, our results confirm that the evaluation of a thin-file company cannot solely consider the company’s own characteristics. The business ecosystem in which these companies interact with their owners, suppliers, customers, and other companies provides novel knowledge that enables financial institutions to enhance their creditworthiness assessment. Our results let us know when and on which population to use graph data and the expected effects on performance. They also show the enormous value of graph data on the credit scoring problem for thin-file borrowers, mainly to help companies with thin or no credit history to enter the financial system.

Improved credit default prediction using machine learning and its impact on risk-weighted assets of banks

The use of risk models, especially credit risk models, has been a standard for banks for many years. Banks use models not only for business decision purposes but also for regulatory purposes when comparing their risk with the available regulatory capital. Furthermore, banks need to efficiently allocate their capital in the current competitive and regulatory environments. As part of this process, they develop models to predict the probability of default (PD), which are further used to calculate risk-weighted assets (RWA). This paper gives an overview of how banks calculate RWA for credit risk. We compare the performance of traditional PD models based on logistic regression with a machine learning (ML) algorithm based on gradient boosting. This shows that an improvement in PD model performance by using ML algorithms can also lead to a decrease of RWA, therefore releasing additional capital for the banks. We developed and calibrated PD models based on logistic regression and light gradient boosting machine (GBM) approaches and compared them in terms of discriminatory power and the impact on RWA to prove this statement. This paper shows that the use of ML leads in our case study to an improvement in the model’s discriminatory power of 5 per cent in terms of Gini and releasing RWA of approximately 6.5 per cent.

The Advantage of Case-Tailored Information Metrics for the Development of Predictive Models, Calculated Profit in Credit Scoring.

This paper compares model development strategies based on different performance metrics. The study was conducted in the area of credit risk modeling with the usage of diverse metrics, including general-purpose Area Under the ROC curve (AUC), problem-dedicated Expected Maximum Profit (EMP) and the novel case-tailored Calculated Profit (CP). The metrics were used to optimize competitive credit risk scoring models based on two predictive algorithms that are widely used in the financial industry: Logistic Regression and extreme gradient boosting machine (XGBoost). A dataset provided by the American Fannie Mae agency was utilized to conduct the study. In addition to the baseline study, the paper also includes a stability analysis. In each case examined the proposed CP metric that allowed us to achieve the most profitable loan portfolio.

Covid-19, credit risk management modeling, and government support

We investigate rating and default risk dynamics over the covid-19 crisis from a credit risk modeling perspective. We find that growth dynamics remain a stable and sufficient predictor of credit risk incidence over the pandemic period, despite its large, short-lived swings due to government intervention and lockdown. Unobserved component models as used in the recent credit risk literature appear mainly helpful for explaining the high-default wave in the early 2000s, but less so for default prediction above and beyond growth dynamics during the 2008 financial crisis or the early 2020 covid default peak. Government support variables do not reduce the impact of either growth proxies or unobserved components. Correlations between government support and credit risk are different, however, during the financial and the covid crisis. Using the empirical models in this paper as credit risk management tools, we show that growth factors also suffice to predict credit risk quantiles out-of-sample during covid times.

An analytical GARCH valuation model for spread options with default risk

In this paper, an analytical pricing formula for spread options with credit default risk is derived. Assets are set within discrete-time CAPM markets and Heston–Nandi GARCH processes are adopted for capturing the variance dynamics of asset returns. The proposed model decomposes the risk of all assets into idiosyncratic and systematic parts, and considers the impacts on the default intensity of market fluctuations. A corresponding theoretical framework of discrete-time credit risk modeling in reduced-form is also provided. We incorporate the credit risk and systematic factor into an affine-GARCH valuation model and utilize Fourier transform techniques to obtain the analytic spread option prices. Finally, the empirical results and numerical analysis for different model parameters are displayed.

Euro area banking and monetary policy shocks in the QE era

This paper assesses the effects of monetary policy shocks on the macroeconomy and the euro area banking sector after the global financial crisis. First, financial risk-return indicators of the banking sector based on a compound option-based structural credit risk model are embedded in a large macro-financial quarterly database covering the period 2008Q4–2019Q4. Second, a SFAVAR identifies and estimates the shocks’ responses relating them to the endogenous build-up of banks’ vulnerabilities which are consistent with the internally coherent structure of the credit risk model. By introducing structure in the understanding of banks’ asset-liability management behavior following monetary policy shocks, the research strategy contributes to disentangling results that are often mixed in the empirical literature. The study finds that unconventional monetary policy, in particular the Asset Purchase Program of the European Central Bank, seems to have been more successful than conventional monetary policy in raising output and inflation. The desired boost to bank lending has been muted and loan cyclicality has varied across countries and loan types. The performance of the banking sector following monetary policy shocks can be characterized by a drop in expected return on equity and assets, a relaxation of lending conditions and increased correlation between banks’ assets return and the market return, a mechanism pointing to enhanced risk-taking. While banks’ probabilities of default fall following monetary policy shocks, the price of risk increases. Banks’ net worth rises via higher market capitalization and implied assets value together with lower volatility, despite often incurring more debt. Risk-taking in the banking sector may pose a risk to financial stability, especially if its effects on banks’ vulnerability spread and increase systemic risk. The unintended endogenous build-up of macro-financial vulnerabilities may need to become part of monetary policymaking.

A unified model of distress risk puzzles

We document that (i) debt-to-equity ratios and levered equity betas negatively covary with the market risk premium in distressed firms; (ii) the negative covariance generates negative alphas among those firms. We build a dynamic credit risk model to understand the negative covariance between equity betas and the market risk premium, via endogenous and dynamic debt financing over the business cycles. Because of endogenous debt financing and distress, our model naturally connects the negative failure probability-return relation to the positive distress risk premium-return relation.

Combating Sampling Bias: A Self-Training Method in Credit Risk Models

A significant challenge in credit risk models for underwriting is the presence of bias in model training data. When most credit risk models are built using only applicants who had been funded for credit, such non-random sampling predominantly influenced by credit policymakers and previous loan performances may introduce sampling bias to the models, and thus alter their prediction of default on loan repayment when screening applications from prospective borrowers. In this paper, we propose a novel data augmentation method that aims to identify and pseudo-label parts of the historically declined loan applications to mitigate sampling bias in the training data. We also introduce a new measure to assess the performance from the business perspective, loan application approval rates at various loan default rate levels. Our proposed methods were compared to the original supervised learning model and the traditional sampling issue remedy techniques in the industry. The experiment and early production results from deployed model show that self-training method with calibrated probability as data augmentation selection criteria improved the ability of credit scoring to differentiate default loan applications and, more importantly, can increase loan approval rate up to 8.8\%, while keeping similar default rate comparing to baselines. The results demonstrate practical implications on how future underwriting model development processes should follow.

Credit Strategy Design of Small and Medium-Sized Enterprises

Small and medium-sized enterprises play an important role in promoting social and economic growth, which is an important foundation for the development of China’s national economy. From the perspective of bank interests, this paper uses the invoice data of small and medium-sized enterprises to evaluate their credit risk and formulates corresponding bank credit strategies for these enterprises in different industries and properties. Firstly, the credit risk identification factor system is constructed by using feature engineering, and the quantitative model of enterprise credit risk is built based on back propagation (BP) neural network to predict the default probability of enterprises. On this basis, the k-prototypes clustering algorithm is used to classify enterprises. According to the default probability of each enterprise and the loss rate under different interest rates, a nonlinear programming model, with the maximum expected profit of banks as the goal, is constructed. The simulated annealing algorithm is used to obtain the optimal solution of the credit strategy.

Asymmetric asset correlation in credit portfolios

This study proposes a novel time-varying credit risk model to describe the cyclicality and asymmetry of asset correlation in credit portfolios. Our proposed model is developed based on a GJR-GARCH type volatility and copula-based conditional dependence. We prove that our model outperforms the regulatory model for the U.S. credit portfolios with strong empirical evidence of cyclical and asymmetric asset correlation. Furthermore, we argue that Basel’s criteria of asset correlation may be insufficient during economic downturns.

CREDIT RISK MANAGEMENT CONTROL ON SME SEGMENT: STUDY CASE OF XYZ BANK BRANCH SURABAYA

The study is conducted to explain the suitability of credit risk control management to minimize the non-performing loans at XYZ Bank Branch Surabaya as stipulated by the Basel Accord Committee in Financial Services Authority Regulation No. 18/PJOK.03/2016 about the Implementation of Risk Management for Commercial Banks. Based on the Basel III guidelines, credit risk management includes seven mechanisms. The seven mechanisms are the policy framework, credit risk rating framework, credit risk limits, credit risk modeling, credit risk mitigation, credit audits, and loan review mechanisms. The study uses a qualitative study by the case study approach. The results showed that the control of credit risk management implemented by Bank XYZ Surabaya Branch to minimize non-performing loans to individual debtors in the SME segment had not run effectively. It was primarily about the evaluation of credit risk, which led to the emergence of a new set of risks such as errors in credit risk evaluation, target market losses and ineffective allocation of loan funds, and inadequate strategies for collecting net credit to customers. The study also provides several recommendations for credit risk management as the strategy to reduce the risk of lending to individual debtors in the SME segment at XYZ Bank Branch Surabaya.