Estimating Default Probabilities Research Articles

A new estimation of default probabilities based on non-performing loans

We model the one-year ahead probability of default of Spanish non-financial corporations. While most of the literature defines default based on bankruptcy filings, we define default as having non-performing loans during at least three months in a given year. This broader definition allows to predict firms’ financial distress at an earlier stage, before their financial conditions are too deteriorated. We also carry out two applications of our prediction models: we assess a program implemented by the Spanish government to provide direct aid to firms severely affected by the Covid-19 crisis and we construct credit rating transition matrices.

Estimating default probabilities for no- and low-default portfolios: parameter specification via floor constraints

Abstract For low- and no-default portfolios, financial institutions are confronted with the problem to estimate default probabilities for credit ratings for which no default was observed. The Bayesian approach offers a solution but brings the problem of the parameter assignment of the prior distribution. Sequential Bayesian updating allows to settle the question of the location parameter or mean of the prior distribution. This article proposes to use floor constraints to determine the scale or standard deviation parameter of the prior distribution. The floor constraint can also be used to determine the free parameter γ in the Pluto–Tasche approach.

A bottom-up, reduced form credit risk model approach for the determination of collateralised loan obligation capital

This paper uses a bottom-up, reduced form credit risk model with hazard rate estimated default probabilities to compute various collateralised loan obligation (CLO) tranches' loss probabilities and capital factors. It is shown that with respect to the loss probabilities, credit rated CLO tranches are less risky than comparably rated corporate bonds. In addition, a similar argument can be made that corporate debt loss rates will be on average larger than equally rated CLO tranche loss rates. And, it is shown that the National Association of Insurance Commissioners (NAIC) capital factors are typically larger than value-at-risk based capital factors. The policy implication is that NAIC capital factors distort investment incentives by requiring too much capital for CLOs relative to equally rated corporate debt.

A de-singularized meshfree approach to default probability estimation under a regime-switching synchronous-jump tempered stable Lévy model

The default probability of a publicly-traded company is modeled by a synchronous-jump regime-switching model in the paper (Hainaut and Colwell, 2016). In this investigation, we first generalize the proposed Lévy model to a more general setting of tempered stable processes recently introduced into the finance literature. However, the resulting integro-partial differential operator suffers from a singularity, thus a general framework based on strictly positive-definite functions is proposed as a remedy to de-singularize the operator. We then analyze an efficient meshfree collocation method based on radial basis functions to approximate the solution of the corresponding system of partial integro-differential equations arising from the structural credit risk model. We prove that considering some regularity assumptions, the proposed method automatically de-singularizes the problem in the tempered stable case. Finally, we perform some numerical experiments using the proposed method on some standard examples from the literature which confirm the validity of our theoretical results and the stability of the numerical algorithm.

Macroeconomic conditions, corporate default, and default clustering

This study thoroughly investigates how, and to what extent, macroeconomic conditions interact with corporate default in the US industrial sector from 1980 to 2014. Using an extensive data set of macro-level and micro-level variables, we construct five categories of indicators and measure macroeconomic conditions by investigating co-movements within each category of indicator. We find macroeconomic conditions have bidirectional causal interaction with corporate defaults across different economic regimes, reflecting the existence of feedback causality. Moreover, we find that macroeconomic indicator constructed using the least absolute shrinkage and selection operator (LASSO) approach shows superior explanatory power as well as predictive power for default clustering, indicating that movements of these indicators cause correlated changes in firms' default rates. Overall, our study provides support for literature on default probability estimation from a macroeconomic perspective. • We develop a new approach to capture macroeconomic conditions. • A feedback causality exists between macroeconomic conditions and corporate defaults. • LASSO-selected economic indicators have the best predictive power for default clustering. • The predictive power of economic indicators remains significant during non-recession years. • Early warning signals of default clustering can be identified 3-month ahead.

Enhancing classification performance in imbalanced datasets: A comparative analysis of machine learning models

<abstract><p>In the realm of machine learning, where data-driven insights guide decision-making, addressing the challenges posed by class imbalance in datasets has emerged as a crucial concern. The effectiveness of classification algorithms hinges not only on their intrinsic capabilities but also on their adaptability to uneven class distributions, a common issue encountered across diverse domains. This study delves into the intricate interplay between varying class imbalance levels and the performance of ten distinct classification models, unravelling the critical impact of this imbalance on the landscape of predictive analytics. Results showed that random forest (RF) and decision tree (DT) models outperformed others, exhibiting robustness to class imbalance. Logistic regression (LR), stochastic gradient descent classifier (SGDC) and naïve Bayes (NB) models struggled with imbalanced datasets. Adaptive boosting (ADA), gradient boosting (GB), extreme gradient boosting (XGB), light gradient boosting machine (LGBM), and k-nearest neighbour (kNN) models improved with balanced data. Adaptive synthetic sampling (ADASYN) yielded more reliable predictions than the under-sampling (UNDER) technique. This study provides insights for practitioners and researchers dealing with imbalanced datasets, guiding model selection and data balancing techniques. RF and DT models demonstrate superior performance, while LR, SGDC and NB models have limitations. By leveraging the strengths of RF and DT models and addressing class imbalance, classification performance in imbalanced datasets can be enhanced. This study enriches credit risk modelling literature by revealing how class imbalance impacts default probability estimation. The research deepens our understanding of class imbalance's critical role in predictive analytics. Serving as a roadmap for practitioners and researchers dealing with imbalanced data, the findings guide model selection and data balancing strategies, enhancing classification performance despite class imbalance.</p></abstract>

Probabilistic Overview of Probabilities of Default for Low Default Portfolios by K. Pluto and D. Tasche

This article gives a probabilistic overview of the widely used method of default probability estimation proposed by K. Pluto and D. Tasche. There are listed detailed assumptions and derivation of the inequality where the probability of default is involved under the influence of systematic factor. The author anticipates adding more clarity, especially for early career analysts or scholars, regarding the assumption of borrowers' independence, conditional independence, and interaction between the probability distributions such as binomial, beta, normal, and others. There is also shown the relation between the probability of default and the joint distribution of \sqrt{ϱ}X - \sqrt{1-ϱ}Y, where X, including but not limiting, is the standard normal, Y admits, including but not limiting, the beta-normal distribution and X, Y are independent.

Is bank risk appetite relevant to bank default in times of Covid-19?

The paper aims to analyze the effect of bank risk appetite on banks' default probabilities during the year of COVID-19 in 12 countries while controlling for bank-specific and country-specific effects over time. A System Generalized Methods of Moments (GMM) model of default probabilities is estimated over the periods 2010–2021. This study confirms the ‘risk-mitigation view’, in which banks with higher ESG scores are more prudent in lending and have better relationship management, reducing the probability of bank default. Underperforming banks tend to have a higher portion of risky loans in their credit portfolio and therefore demonstrating a higher default propensity. Bank risk appetite, ESG, asset quality, economic growth, and currency depreciation appear to be material drivers for bank risk. We find that a lower risk appetite ratio (corresponding to higher risk appetite) is associated with higher estimated default probability during the COVID-19 outbreak, identified through interaction with a single time dummy for 2020 (the break-out year of the pandemic).

Decoding Default Risk: A Review of Modeling Approaches, Findings, and Estimation Methods

Default risk permeates the behavior of corporate bond returns and spreads, credit default swap spreads, estimation of default probabilities, and loss in default. Pertinent to this review are salient empirical findings and implications of default process estimation from 1974 to 2021. Both structural and reduced-form models are covered. In structural models, default occurs if the value of assets falls below some threshold obligation. The reduced-form models involve assumptions about the default process combined with recovery in default. Default process estimation and measurements of default probability have improved by exploiting data on defaultable bonds, credit default swaps, tally of default realizations, and options on individual equities. Empirical investigations continue to address the relevance of stochastic asset volatility, jumps in asset values, and modeling of default boundary and firm leverage process.

Low Default Portfolios—A Proposed Rule to Identify Differences between Imprudence, Conservatism, and Exaggeration

Internal models may be used by banks to calculate their regulatory capital for credit risk. There are a variety of methodologies for estimating default probabilities, which leads to major differences in credit provisions and capital requirements. Using either a classical or a Bayesian technique, the computation of default probabilities can be ensured. Reduced form models are a choice. These models, however, might not be used to quantify economic capital because they assume independence among default events. Banks are compelled to employ structural models since defaults in the real world of banking are not solely due to exogenous causes. Because of the diversification effects between credit losses for one obligor and credit losses for other obligors in each bank’s portfolio, total unexpected losses do not equal the sum of individual unexpected losses. Those two types of models—reduced form and structural—are provided in either a theoretical or a numerical format. This paper covers both the classical and Bayesian techniques, with the latter employing a broader set of prior functions that offer considerably different probabilities. Distinguishing between imprudence, conservatism, and exaggeration might be difficult in the context of low default portfolios with scarce data. A realistic rule is proposed for finding the minimum and maximum bounds and therefore assessing the required conservatism margin by comparing classical and Bayesian probabilities.

Benchmark test for calculated default probability values derived from the application of rating-based models

Subject. This article deals with the issues of validation of the consistency of rating-based model forecasts. Objectives. The article aims to provide developers and validators of rating-based models with a practical fundamental test for benchmarking study of the estimated default probability values obtained as a result of the application of models used in the rating system. Methods. For the study, I used the classical interval approach to testing of statistical hypotheses focused on the subject area of calibration of rating systems. Results. In addition to the generally accepted tests for the correspondence of the predicted probabilities of default of credit risk objects to the historically realized values, the article proposes a new statistical test that corrects the shortcomings of the generally accepted ones, focused on "diagnosing" the consistency of the implemented discrimination of objects by the rating model. Examples of recognizing the reasons for a negative test result and negative consequences for lending are given while maintaining the current settings of the rating model. In addition to the bias in the assessment of the total frequency of defaults in the loan portfolio, the proposed method makes it possible to objectively reveal the inadequacy of discrimination against borrowers with a calibrated rating model, diagnose the “disease” of the rating model. Conclusions and Relevance. The new practical benchmark test allows to reject the hypothesis about the consistency of assessing the probability of default by the rating model at a given level of confidence and available historical data. The test has the advantage of practical interpretability based on its results, it is possible to draw a conclusion about the direction of the model correction. The offered test can be used in the process of internal validation by the bank of its own rating models, which is required by the Bank of Russia for approaches based on internal ratings.

Impact of COVID-19 on the Robustness of the Probability of Default Estimation Model

Probability of default (PD) estimation is essential to the calculation of expected credit loss under the Basel III framework and the International Financial Reporting Standard 9. Gross domestic product (GDP) growth has been adopted as a key determinant in PD estimation models. However, PD models with a GDP covariate may not perform well under aberrant (i.e., outlier) conditions such as the COVID-19 pandemic. This study explored the robustness of a PD model with a GDP determinant (the test model) in comparison with that of a PD model with a credit default swap index (CDX) determinant (the alternative model). The test model had a significantly greater ratio of increase in Akaike information criterion than the alternative model in comparisons of the fit performance of models including 2020 data with that of models excluding 2020 data (i.e., that do not cover the COVID-19 pandemic). Furthermore, the Cook’s distance of the 2020 data of the test model was significantly greater than that of the alternative model. Therefore, the test model exhibited a serious robustness issue in outlier scenarios, such as the COVID-19 pandemic, whereas the alternative model was more robust. This finding opens the prospect for the CDX to potentially serve as an alternative to GDP in PD estimation models.

코로나19가 금융 시스템리스크에 미친 영향 (The Effect of COVID19 on Systemic Risk: The Case of Korea)

Korean Abstract: 본 연구는 하향식 스트레스 테스트 방법에 기반하여 코로나19 위기가 한국의 금융 시스템리스크에 미친 영향을 분석하였다. 본 연구에서 감염병 모형을 이용하여 분석한 결과 코로나19 위기의 조기 종식을 위해서는 코로나19 백신개발이 중요한 것으로 예측되었다. 이러한 결과를 바탕으로 본 연구는 코로나19 위기 지속기간에 대하여 시나리오를 설정하고, 시나리오별로 기업부문은 규모 및 업종별로 구분하고 가계부문은 업무종사 형태별로 구분하여 코로나19로 인한 신용위험 증대효과를 추정하였다. 그리고 본 연구는 코로나19 위기에 대응하기 위한 중앙은행의 금리인하 정책으로 인한 금융기관의 이자수익 감소효과도 추정하였다. 다음으로 본 연구는 기업 및 가계부문의 신용위험 및 금융기관의 이자수익 충격을 반영하여 개별 금융회사의 부도확률을 산출하였다. 분석 결과, 은행부문은 코로나19 위기에도 불구하고 안정성을 유지하는 것으로 나타났으나, 일부 상호저축은행 및 국내 생명보험회사들은 코로나19 위기로 인해 위험도가 높아지는 것으로 나타났다. English Abstract: This study examines the effect of Covid19 on Korean financial systemic risks based on a top-down stress test approach. This study employs an epidemiology model and finds that it will be essential to develop effective vaccines for ceasing Covid19 in a timely manner. Based on this finding, this study constructs several scenarios on the duration of the Covid19 crisis and estimates size- and sector-differentiated firm credit risks and occupation-differentiated household credit risks under the scenarios. This study also estimates the effect on interest income shocks to financial institutions of monetary policy changes to respond the Covid19 crisis. This study then estimate default probabilities of individual financial institutions by combining the effects of Covid19 on firm and household credit risks and interest income shocks to financial institutions. This study finds that while the banking sector can remain robust to Covid19 shocks, several savings banks and life insurance companies may be significantly negatively affected.

Credit Scoring – General Approach in the IFRS 9 Context

With the coming into force of the standard IFRS 9 – Financial Instruments, in January 2018, financial institutions passed from an incurred loss model to a forward-looking model for the computation of impairment losses. As such, the IFRS 9 models use point-in-time, estimates of Probability of Default and Loss Given Default and provide a more faithful representation of the credit risk at a given as they are based on past experiences as well as the most recent and forecasted economic conditions. However, given the short-term fluctuations in the macroeconomic conditions, the final outcome of the Expected credit loss models is highly volatile due to their sensitivity to the business cycle. With regard to Probability of Default estimation under IFRS 9, the most commonly methods are: Markov Chains, Survival Analysis and single-factor models (Vasicek and Z-Shift). The development of the score-cards is still the same as in the case of the Internal Ratings Based Probability of Default models, encouraging institutions to use the already available credit rating systems and perform adjustment to the calibration. This paper outlines a non-exhaustive list of quantitative validation tests would satisfy the requirements of the IFRS 9 standard.

Machine learning methods for short-term probability of default: A comparison of classification, regression and ranking methods

Probability of default estimation via machine learning on historical data is widely studied in credit risk modeling. In this work, we investigated the use of machine learning for a finer-grained risk estimation task, namely spot factoring. Here, the goal is to estimate the likelihood that an invoice will be paid in an acceptable timeframe. In this case, risk is more related to the overdueness of an invoice. Based on this observation, we investigate three possible machine learning tasks for estimating this risk: binary classification for a predetermined overdue days cutoff; regression of the overdue days; and learning-to-rank which learns to optimize the risk-related ranking for the full range of instances. We model and evaluate these tasks using real-life spot factoring data. Finally, we perform a profit-driven evaluation that shows that regression models can lead to higher profits and better spread the risk than classification and ranking models for spot factoring.

The Bloomberg Corporate Default Risk Model (DRSK) for Public Firms

The DRSK public model estimates forward-looking real-world default probabilities for publicly traded firms. The model also assigns credit grades based on the estimated default probabilities. The product covers firms in all regions and sectors of operation for which the necessary data is available. The DRSK public model was last updated in 2015. This year we are releasing an updated model which improves on the previous model's performance in a variety of ways. The new model's accuracy ratio is above 92%, adjusted pseudo R-squareds have improved, and performance is more in line with observed historical default rates. We describe the new model, analyze its performance in various ways and compare it to the previous model.

Value-at-Risk and Expected Shortfall approaches for option premiums and the probability of default estimation based on ARMA models

The need to address the issue of risk management has given rise to a number of models for estimation the probability of default, as well as a special tool that allows to sell credit risk – a credit default swap (CDS). From the moment it appeared in 1994 until the crisis of 2008, that the CDS market was actively growing, and then sharply contracted. Currently, there is practically no CDS market in emerging economies (including Russia). This article is to improve the existing CDS valuation models by using discrete-time models that allow for more accurate assessment and forecasting of the selected asset dynamics, as well as new option pricing models that take into account the degree of risk acceptance by the option seller. This article is devoted to parametric discrete-time option pricing models that provide more accurate results than the traditional Black-Scholes continuous-time model. Improvement in the quality of assessment is achieved due to three factors: a more detailed consideration of the properties of the time series of the underlying asset (in particular, autocorrelation and heavy tails), the choice of the optimal number of parameters and the use of Value-at-Risk approach. As a result of the study, expressions were obtained for the premiums of European put and call options for a given level of risk under the assumption that the return on the underlying asset follows a stationary ARMA process with normal or Student's errors, as well as an expression for the credit spread under similar assumptions. The simplicity of the ARMA process underlying the model is a compromise between the complexity of model calibration and the quality of describing the dynamics of assets in the stock market. This approach allows to take into account both discreteness in asset pricing and take into account the current structure and the presence of interconnections for the time series of the asset under consideration (as opposed to the Black–Scholes model), which potentially allows better portfolio management in the stock market.

Correction to: Probability of default estimation in credit risk using a nonparametric approach

Correction to: Probability of default estimation in credit risk using a nonparametric approach

Dynamic Mapping of Probability of Default and Credit Ratings of Russian Banks

Investors are interested in a quantitative measure of banks’ credit risk. This paper maps the credit ratings of Russian banks to default probabilities for different time horizons by constructing an empirical dynamic calibration scale. As such, we construct a dynamic scale of credit risk calibration to the probability of default (PD).Our study is based on a random sample of 395 Russian banks (86 of which defaulted) for the period of 2007-2017. The scale proposed by this paper has three features which distinguish it from existing scales: dynamic nature (quarterly probability of default estimates), compatibility with all rating agencies (base scale credit ratings), and a focus on Russian banks.Our results indicate that banks with high ratings are more stable just after the rating assignment, while a speculative bank’s probability of default decreases over time. Hence, we conclude that investors should account for not only the current rating grade of a bank, but also how long ago it was assigned. As a result, a rising capital strategy was formulated: the better a bank’s credit rating, the shorter the investment horizon should be and the closer the date of investment should be to the rating assignment date in order to minimise credit risk.The scientific novelty of this paper arises from the process of calibration of a rating grade to dynamic PD in order to evaluate the optimal time horizon of investments into a bank in each rating class. In practical terms, investors may use this scale not only to obtain a desired credit rating, but also to identify quantitative measure of credit risk, which will help to plan investment strategies and to calculate expected losses.

The Introduction of a Climate Risk Taxonomy with an Impact Study on the Financial Risks of Climate Change to Corporations.

In this paper we put forward the need to develop a clear understanding of the risks related to climate change for financial institutions. We propose the construction of a taxonomy that can be straightforwardly embedded in the capital framework of banks, insurers and other regulated financial institutions around the world. The approach presented builds on approaches commonly adopted by banks and provides a prudential means to identify and capitalise the relevant risks. We highlight the dangers of potential miss-pricing of risk that could occur under a pure green-taxonomy if risk weights are reduced for assets deemed green. Furthermore we investigate a number of the risks namely asset values (equity) and credit risks for European electrical utility companies and highlight how financial organisations would be able to capture the risks within their current framework. The approach utilises a long term simulation framework from an integrated assessment model that drives company investment choices over the simulation horizon. This approach gives rise to estimates of equity valuation, bond prices, credit ratings and default probabilities that can be used to assess long term credit exposures or potential shifts in current market valuation.