Nothing Special   »   [go: up one dir, main page]
Previous Article in Journal
Longevity Risk and Annuitisation Decisions in the Absence of Special-Rate Life Annuities
You seem to have javascript disabled. Please note that many of the page functionalities won't work as expected without javascript enabled.
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
Journals
Risks
Volume 13
Issue 2
10.3390/risks13020038
risks-logo
Submit to this Journal Review for this Journal Propose a Special Issue
► Article Menu

Article Menu

share Share announcement Help format_quote Cite question_answer Discuss in SciProfiles
first_page
settings
Order Article Reprints
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

Improving Credit Risk Assessment in Uncertain Times: Insights from IFRS 9

by
Petr Jakubik
1,* and
Saida Teleu
2,3
1
Institute of Economic Studies, Faculty of Social Sciences, Charles University, Smetanovo nabrezi 6, 110 01 Prague 1, Czech Republic
2
Central Bank of Barbados, Tom Adams Financial Centre, Spry Street, Bridgetown 11126, Barbados
3
Department of Accounting and Finance, The School of Business, Anglo-American University in Prague, Letenská 120/5, 118 00 Prague 1, Czech Republic
*
Author to whom correspondence should be addressed.
Risks 2025, 13(2), 38; https://doi.org/10.3390/risks13020038
Submission received: 2 January 2025 / Revised: 5 February 2025 / Accepted: 11 February 2025 / Published: 19 February 2025
(This article belongs to the Special Issue Innovative Quantitative Methods for Financial Risk Management)
Browse Figures
Figure 1
<p>Z-scores across sectors.</p> "> Figure A1
<p>Mortgage loans.</p> "> Figure A2
<p>Consumer loans.</p> "> Figure A3
<p>Residential NFC.</p> "> Figure A4
<p>Non-residential NFC.</p> ">
Versions Notes

Abstract

:
This study highlights the superior performance of Bayesian Model Averaging (BMA) in credit risk modeling under IFRS 9, particularly during economic uncertainty, such as the COVID-19 pandemic. Using granular bank-level data from Malta, spanning 2017–2023, the analysis integrates macroeconomic scenarios and sector-specific transition matrices to assess credit risk dynamics. Key findings demonstrate BMA’s ability to outperform Single-Equation Models (SEM) in predictive accuracy, robustness, and adaptability. The results emphasize BMA’s resilience to structural economic changes, making it a critical tool for regulatory stress testing and provisioning in small open economies highly exposed to external shocks. This work underscores the importance of forward-looking, flexible frameworks for credit risk management and policy decisions.

1. Introduction

The expected credit losses (ECLs) regime introduced significant modeling complexities, challenges, and, consequently, model risks. Under the ECLs framework, forward-looking information used in models must be both reasonable and supportable. While the ECL-based impairment model under IFRS 9 provides flexibility, it does not prescribe specific criteria for determining when a significant increase in credit risk has occurred. Financial institutions (FIs) are required to make their own assumptions and decisions regarding provisions in line with IFRS 9 standards. At the same time, financial regulators and supervisors expect FIs to incorporate their guidance when estimating ECLs.
Financial institutions are also expected to evaluate the extent to which sudden changes in the short-term economic outlook might affect the entire life of a financial instrument. This highlights the importance of assessing both immediate and long-term impacts in the context of ECL estimation.
The existing literature underscores critical challenges in credit risk modeling under IFRS 9, including the need to capture systemic and idiosyncratic risks, account for model uncertainty, and integrate macroeconomic scenarios into forward-looking provisions (Perote and Mateus 2019; Gómez-González and Hinojosa 2010; Stepankova 2021). While tools such as credit transition matrices (TMs) have become central to these efforts, traditional approaches face limitations in handling diverse credit risk categories and adapting to the unique characteristics of small open economies. Nickell et al. (2000) highlight the importance of stable rating transition models in understanding credit risk dynamics, emphasizing the need for robust methodologies that accurately reflect credit migration patterns. Furthermore, the Bangia et al. (2022) study demonstrates the relevance of credit ratings migration and business cycle fluctuations in stress testing, underscoring the necessity of integrating macroeconomic scenarios into credit risk assessments. Addressing model uncertainty is another critical concern, particularly in volatile economic conditions where traditional Single-Equation Models may fail to capture complex interactions. Gross and Población (2023) propose Bayesian Model Averaging (BMA) as a superior technique for mitigating such uncertainty, enhancing predictive accuracy and robustness in IFRS 9-based risk estimations. The COVID-19 pandemic further emphasized the need for dynamic stress testing frameworks capable of addressing extreme uncertainty, reinforcing the importance of forward-looking, flexible methodologies for credit risk management.
This paper contributes to the current state of the art by addressing these gaps in several key ways. First, we employ a one-factor representation of transition matrices (TMs), a simplified yet robust approach to modeling credit risk dynamics that aligns with IFRS 9 requirements. This methodology leverages granular bank-level data, enabling a more precise analysis of credit risk transitions across various sectors. Second, to mitigate the impact of model uncertainty, we integrate Bayesian Model Averaging (BMA) into our stress testing framework, enhancing the reliability and robustness of scenario-based ECL estimations. These innovations are particularly valuable in small open economies like Malta, where the availability of detailed data and sector-specific dynamics play a crucial role in accurate credit risk modeling.
Additionally, this study focuses on the application of the proposed methodology during the COVID-19 pandemic, a period marked by heightened economic uncertainty. By utilizing scenario-conditioned credit risk assessments, the framework demonstrates its practicality for dynamic stress testing in real-world situations. While the findings are grounded in Malta’s financial system, the proposed approach is designed to be adaptable to other small open economies with similar characteristics and data availability.
This paper is structured as follows. The next section provides a review of the literature, exploring banks’ credit rating behavior and the challenges posed by model uncertainty in the context of ECL estimation. Section 4 elaborates on IFRS 9-compatible techniques for top-down solvency stress tests, particularly for small open economies during periods of high uncertainty, such as the COVID-19 pandemic. Finally, we present the results and draw conclusions based on our findings. By addressing these challenges, this study advances the field of credit risk modeling and stress testing under IFRS 9, providing a robust framework that balances computational simplicity with methodological rigor.

2. Literature Review

Credit transition matrices (TMs) provide a probabilistic framework for understanding the migration of exposures between credit quality states. Their application spans stress testing, portfolio risk management, and regulatory oversight, with their role becoming particularly prominent following the 2008 financial crisis (Bangia et al. 2022; Nickell et al. 2000). Under IFRS 9, TMs have gained even more relevance as financial institutions must estimate lifetime expected credit losses (ECLs) that incorporate forward-looking information.
Empirical studies highlight the critical role of TMs in capturing both systemic and idiosyncratic risks. Gómez-González and Hinojosa (2010) emphasize that conditional time-homogeneous TMs can enhance risk estimation by factoring in economic cycles, while Frydman and Schuermann (2008) discuss the dynamic nature of credit ratings and transition probabilities through Markov mixture models. These studies underscore the importance of accurately estimating TMs to inform regulatory stress tests. Stepankova (2021) further highlights the role of bank-sourced TMs, particularly in the context of small and specialized economies, demonstrating their potential in granular risk modeling. However, existing approaches often lack the granularity needed to effectively capture sector-specific dynamics in small open economies.
To address these limitations, one-factor representations have been proposed as efficient alternatives, providing computational simplicity and robustness (Belkin et al. 1998; Wei 2003). Recent advancements by Gross and Población (2023) further support the practicality of simplified TM frameworks in stress testing. Our paper builds on these approaches by employing a one-factor representation of TMs using granular bank-level data for the Maltese economy. This allows for a more precise and sector-specific analysis of credit risk transitions, aligning with the unique characteristics of small open economies.
The adoption of IFRS 9 has introduced significant challenges to credit risk modeling, particularly regarding its practical implications during periods of heightened economic uncertainty. For instance, the COVID-19 pandemic underscored the importance of forward-looking provisioning in capturing real-time changes in credit quality due to external shocks, particularly in small open economies. While IFRS 9 principles mandate forward-looking assumptions, implementing these provisions effectively becomes a challenge when macroeconomic conditions evolve unpredictably. This highlights the necessity of frameworks, such as the one proposed in this paper, that integrate dynamic, scenario-based stress testing into IFRS 9-compatible credit risk assessments.
Model uncertainty becomes especially critical during periods of economic volatility, such as the COVID-19 pandemic, when traditional models may fail to capture the full spectrum of potential outcomes. Bayesian Model Averaging (BMA) has emerged as a robust method to address this issue by integrating multiple model specifications and mitigating biases in risk estimation (Avramov 2021; Gross and Población 2023). Sousa and Sousa (2013) further emphasize the importance of accounting for model uncertainty in asset return projections, highlighting the advantages of Bayesian approaches in financial modeling under uncertainty. By incorporating BMA into a top-down solvency stress testing framework, our study enhances the reliability and robustness of scenario-based ECL estimates, demonstrating their relevance in addressing uncertainties under IFRS 9. While this study employs Bayesian Model Averaging (BMA) to enhance the robustness of credit risk estimation, alternative approaches exist, particularly non-parametric methods such as machine learning and distribution-free statistical techniques. These methods, including decision trees, neural networks, and data envelopment analysis (DEA), have gained traction in recent years for their ability to model complex relationships in credit risk without relying on strict parametric assumptions (Aretz and Pope 2013, Cheng et al. 2021; Zhao et al. 2022). Recent studies highlight the advantages of machine learning and non-parametric techniques in enhancing credit risk assessment. Cheng et al. (2021) demonstrate how deep learning methods can capture non-linear dependencies in loan default patterns, offering improved predictive accuracy over traditional econometric models. Similarly, Zhao et al. (2022) explore the effectiveness of ensemble learning models, such as gradient boosting and random forests, in credit risk classification, showing significant improvements in risk differentiation and default prediction. Perote and Mateus (2019) propose an advanced decomposition approach to isolate systemic and idiosyncratic risk factors, reinforcing the benefits of flexible, data-driven methods in credit risk modeling. Recent studies, such as Shahrour (2022), have demonstrated the advantages of non-parametric techniques like DEA in evaluating financial and social performance, highlighting their potential applicability in credit risk assessment. However, challenges remain regarding their interpretability, regulatory acceptance, and overfitting risks in smaller datasets. Given the principles-based nature of IFRS 9, integrating non-parametric models into regulatory stress testing remains an area for future research, particularly in small open economies where data availability may be constrained.
The dynamics of credit rating migrations have been extensively studied in the context of macroeconomic and sector-specific conditions. Rating transitions are procyclical, with downgrades more likely during downturns and upgrades prevalent in periods of economic expansion (Nickell et al. 2000). Lu (2007) highlights how conditioning TMs on credit cycles enhances their predictive capabilities, particularly in volatile markets. Building on this, our paper applies a one-factor representation of TMs, leveraging granular bank-level data to assess credit risk transitions in Malta. This methodology demonstrates the practicality of combining sector-specific insights with macroeconomic scenario conditioning in a small open economy highly exposed to external shocks. Stress testing methodologies have evolved significantly, with top-down approaches gaining prominence for their ability to assess systemic risks across financial institutions. These models integrate macroeconomic scenarios, financial linkages, and portfolio dynamics, making them well-suited for IFRS 9 applications. The European Central Bank’s Banking Euro Area Stress Test Model (Budnik et al., 2020) provides a robust framework for evaluating systemic risk by integrating macro-financial linkages with sector-specific credit risk projections. This model has been widely applied in assessing capital adequacy under adverse macroeconomic conditions, offering valuable insights into financial stability analysis. Castrén et al. (2008a), Castrén et al. (2008b), and Stepankova (2021) underscore the importance of tailoring stress tests to specific economic contexts, particularly for small open economies with concentrated financial systems. The COVID-19 pandemic highlighted the limitations of traditional stress testing models, prompting the need for more flexible and dynamic approaches. Our paper contributes to this literature by demonstrating how scenario-conditioned ECL estimates can be integrated into top-down solvency stress tests, leveraging granular data and advanced modeling techniques to address challenges unique to small economies.
In summary, the literature on credit risk modeling and IFRS 9 implementation underscores several critical challenges, including procyclicality, model uncertainty, and the integration of macroeconomic scenarios. While previous studies have provided valuable insights, gaps remain in understanding how these dynamics affect small open economies during periods of heightened uncertainty, such as the COVID-19 pandemic. This paper addresses these gaps by presenting a methodology that integrates TMs, Bayesian approaches, and macroeconomic scenarios to enhance the accuracy and robustness of credit risk assessments under IFRS 9, particularly for small economies like Malta.

3. Data

This research is based on anonymized data reported by credit institutions (banks) under the Central Bank of Malta Directive No. 14. This directive requires reporting information on any existing debtor with an end-of-month balance of exposures exceeding €5000. The dataset spans the period from Q4 2017 to Q4 2023 which details the observed and forecasted Z-scores across various loan categories, such as mortgages, domestic NFCs, international NFCs, and consumer loans.
The data utilized include granular, sector-specific behavioral patterns of loans obtained from the Credit Central Register, capturing the frequency of loans transitioning between IFRS 9 credit stages. This granularity allows for the estimation of country- and industry-specific transition matrices (TMs), a critical input for forward-looking credit risk models. As Stepankova (2021) demonstrated, the inclusion of such detailed data enhances the precision of credit risk modeling by tailoring predictions to the unique dynamics of specific sectors.
To enhance the robustness of the analysis, the model integrates macroeconomic variables to forecast credit risk dynamics. These variables capture sector-specific economic conditions for key portfolios, including mortgages, domestic NFCs, international NFCs, and consumer loans. The analysis evaluates the credit risk impact under baseline and adverse scenarios.
Sector-specific risks and macroeconomic cycles play a crucial role in credit risk modeling (Aretz and Pope 2013; Estrella et al. 2008), as financial cycles affect default probabilities across different industries. The resulting Z-scores represent the creditworthiness of the loan portfolios, with higher scores indicating lower risk. The forecasts demonstrate the interaction between macroeconomic conditions and sectoral credit risk, revealing distinct trajectories for mortgages, NFCs, and consumer loans under varying economic scenarios.
By aligning time-series data with scenario-based projections, this research provides actionable insights into forward-looking credit risk profiles for different sectors in Malta. This approach contributes to the development of robust credit risk assessment methodologies tailored to both domestic and international economic contexts.

4. Methodology

We developed a top-down credit risk model framework for scenario-conditional expected credit loss (ECL) estimation. Assets are classified according to the International Financial Reporting Standards (IFRS 9) into three stages: S1: performing exposures with a stable risk profile (days past due less than 30 days); S2: performing exposures with a significant increase in credit risk (days past due between 30 and 90 days); and S3: non-performing exposures (days past due more than 90 days). The evolution of the distribution of assets across these stages from one quarter to the next is modeled using a sector-specific transition probability matrix. This matrix captures the likelihood of assets migrating between the three stages over time, enabling a detailed assessment of credit risk dynamics under different economic scenarios.
The Z-score, derived from a one-factor representation, reflects the creditworthiness of a sector. A lower Z-score indicates a higher likelihood of downward transitions (e.g., S1 to S2 or S3). Sector-specific economic cycles play a crucial role in determining these transitions, as different industries exhibit varying sensitivities to macroeconomic shocks and business cycle fluctuations (Cheng et al. 2021; Aretz and Pope 2013).
Macroeconomic predictors vary across portfolio segments. Mortgage performance is influenced by house price index (HPI) changes, unemployment rates, GDP growth, and lagged Z-scores. Domestic NFCs are affected by domestic real GDP growth, year-on-year house price growth, and sovereign spreads. International NFCs are impacted by USD LIBOR, Euro area GDP growth, and oil prices, while consumer loans are driven by GDP growth rates and LIBOR differences.
The transition matrices are modeled at the portfolio level, enabling a tailored analysis for different asset classes. A Bayesian Model Averaging (BMA) approach was employed to evaluate all possible combinations of predictors, ensuring robustness in model selection. The modeled scenarios include a Baseline Scenario, which reflects stable economic conditions as projected by the Central Bank of Malta, and an Adverse Scenario, which is based on severe economic downturn assumptions outlined by the EBA.
ECL is mandated by IFRS 9 as the standard measure for credit risk modeling due to its forward-looking nature and its ability to align provisioning with expected economic outcomes. Unlike traditional models that rely on backward-looking metrics, ECL provides a dynamic framework that captures the evolution of credit risk across stages (S1 to S3) while integrating the impact of macroeconomic scenarios on lifetime losses. This dual focus ensures a more accurate and responsive assessment of credit risk, making it a crucial tool for financial institutions operating under IFRS 9 guidelines. As highlighted by Altman et al. (2004) incorporating forward-looking elements into credit risk modeling significantly improves provisioning accuracy and supports regulatory compliance in rapidly changing economic environments.
By incorporating transition probabilities and scenario-conditioned Z-scores, the ECL framework enhances the precision of credit provisioning, particularly in small economies where external shocks (e.g., the COVID-19 pandemic) can significantly affect credit risk.
T R S 1 , S 1 , t v T R S 1 , S 2 , t v T R S 1 , S 3 , t v T R S 2 , S 1 , t v T R S 2 , S 2 , t v T R S 2 , S 3 , t v T R S 3 , S 1 , t v T R S 3 , S 2 , t v T R S 3 , S 3 , t v
where T R S j , S k , t v = Probability {Assets that are classified as S j in time t will be classified as S k in time t + 1}, v   corresponds to the four segments (mortgages, resident non-financial corporations (NFCs), non-resident NFCs, and consumer loans), and t represents time.
Transition matrix (TM) models are designed to capture the migration of individual exposures between different risk categories over time, incorporating their dependence on macro-financial conditions. The TMs are modeled at the portfolio level, following IFRS 9 guidance. The portfolio segmentation includes the following categories: mortgages, resident non-financial corporations (NFCs), non-resident NFCs, and consumer loans. This segmentation allows for a more tailored analysis of credit risk dynamics across different asset classes.
A “one-factor representation” (referred to as a “Z-score”) of TMs is directly applicable to IFRS 9 transition matrices (Gross et al. 2020). This methodology has been widely used in the financial industry for modeling rating transitions within TMs (Belkin et al. 1998). The Z-score condenses the evolution of transition matrices into a single numerical value at each point in time. It reflects the creditworthiness of a sector, where a lower Z-score indicates higher risk. In practical terms, this means that downward transitions of assets—from S1 to S2, or defaults into S3—are occurring at a greater frequency than historically average levels.
According to Belkin et al. (1998), an underlying random variable, X, measures changes in creditworthiness. These changes are driven by two distinct factors: (1) an idiosyncratic component (Y), which captures individual-specific variations, and (2) a systematic, economy-wide component (W), which measures the credit cycle and is independent of Y.
X t = 1 − ρ Y t + ρ W t
Both Y and W are independent unit normal random variables and ρ represents the correlation between W and X . The correlation ρ is calculated as the proportion of the variance of X explained by W . Suppose a borrower is initially assigned a rating grade G . If their creditworthiness X falls within the interval ( x g + 1 ,   G x g ,   G ] , the borrower remains at grade g for the current year. Let ∆ ( x g + 1 ,   G x g ,   G   w t ) represent the transition probability from rating grade x g ,   G to rating grade x g + 1 ,   G at time t conditional on the given systemic component W t = w t .
The fitted transition probabilities between different risk categories are defined as follows:
∆ ( x g + 1 ,   G x g ,   G   w t ) = φ   ( X g + 1 G − ρ w t 1 − ρ ) − φ   ( X g G − ρ w t 1 − ρ )
where φ represents the cumulative distribution function of standard normal distribution.
According to the law of large numbers, the direct calculation based on the assumed distribution of Z is as follows:
1 N ∑ t = 1 N ∆ ( x g + 1 ,   G x g   G ) converges almost surely to φ   ( X g + 1 G ) − φ   ( X g G ) as N → + ∞ .
Hence, the average rating transition probability ∆ ( x ^ g + 1 ,   G x ^ g   G ) =   1 N ∑ t = 1 N ∆ ( x g + 1 ,   G x g   G )   is used to provide an estimation X g G ^ ; g = 1 ,   … ,   K of the thresholds X g G ; g = 1 ,   … ,   K :
X g G = φ − 1 ∑ g = 1 G ∆ ( x ^ g + 1 ,   G x ^ g   G )
Replacing x g   G by x ^ g   G in Equation (3) and given w, we obtain the fitted rating transition probability:
∆ ( x ^ g + 1 ,   G x ^ g   G , w t ) = φ   ( x ^ g + 1   G − ρ w t 1 − ρ ) − φ   ( x ^ g   G − ρ w t 1 − ρ ) ,   G ,   g ∈ 1 ,   … ,   K
The historical deviation between the fitted and observed transition matrices is expressed as follows, where ρ and t are fixed and n t , g represents the number of borrowers from the initial grade g observed during the time period t :
min w t ⁡ ∑ G ∑ g n t , g P t G , g − Δ x ^ g + 1   G , x ^ g   G , w t 2 Δ x ^ g + 1   G , x ^ g   G , w t 1 − Δ x ^ g + 1   G , x ^ g   G , w t
The two sums in Equation (6) represent a summation over all elements in the 3 × 3 transition matrices corresponding to the different risk categories (S1, S2, S3).
Furthermore, we establish a link between the Z-score and macro-financial factors defined within a scenario to project the evolution of the bank’s dynamic balance sheet under the given scenario.
A wide set of predictor variables was considered for estimating the development of the Z-score. For this purpose, the Bayesian Model Averaging (BMA) approach was employed, encompassing 2 K models, where K represents the number of explanatory variables. The model space was constructed by evaluating all possible combinations of predictors from the set of K variables, with each segment representing macroeconomic variables.
All equations in the model were individually estimated and aggregated within the posterior model space for each segment. Each individual equation was based on an Autoregressive Distributed Lag (ARDL) model structure, where the dependent variable Y t , representing the Z-score, is expressed as a function of its own lags, as well as contemporaneous and, potentially, further lags of a set of predictor variables. The lag structures of ARDL models were designed to be continuous, ensuring no gaps in the lag, referred to as “closed” structures (Gross and Población 2019).
Y t = α + α 1 Y t − 1 + α 2 Y t − 2 + ∑ s = 1 s i ( β 0 k X t k + … + β q k X t − q k ) + ε t
The model selection for the model space is based on several criteria to determine the best specification for each model. These criteria include a relatively high R-square, Durbin–Watson statistics within the range of 1.5 to 2.5, a closed lag structure, the number of significant variables, and a small Root Mean Square Error (RMSE). Additionally, sign restrictions are applied to the long-run multipliers, excluding equations in the posterior model space that do not align with classical economic relationships between the variables. As part of the multimodal inference process, fitted models are ranked based on the standard Bayesian Information Criterion (BIC).
Furthermore, we set an 85% threshold for identifying a superior model. If no model meets the threshold, we compute the posterior coefficient mean by weighting individual equations’ coefficients by P ( M i | y ) , which is derived from the BIC. The Bayesian model-averaged predictor of y is then expressed as follows:
E ( β | y ) = ∑ i = 1 I P ( M i | y ) β i ^
where β i ^ represents the posterior mean under model M i .
Scenario conditional paths of the Z-score are translated back to the evolution of the TM, as defined by Equation (3), where W t is replaced by W t ^ , which varies depending on the specific scenario.
In the final step, the implied stocks of S1, S2, and S3 are derived using Equations (9), (10), and (11), while accounting for loan growth through Equations (12) and (13). The Central Bank of Malta’s credit growth rate projections, as outlined in Economic Update 2/2021 (Central Bank of Malta) are applied in this process.
s t o c k S 1   t = s t o c k S 1   t − 1 + T R S 2 , S 1 , t   s t o c k S 2   t − 1 + T R S 3 , S 1 , t   s t o c k S 3   t − 1 − T R S 1 , S 2 , t s t o c k S 1   t − 1 − T R S 1 , S 3 , t s t o c k S 1 t − 1 − M t 1 s t o c k S 1   t − 1
s t o c k S 2   t = s t o c k S 2   t − 1 + T R S 1 , S 2 , t s t o c k S 1   t − 1 + T R S 3 , S 2 , t s t o c k S 3   t − 1 − T R S 2 , S 1 , t s t o c k S 2   t − 1 − T R S 2 , S 3 , t s t o c k S 2   t − 1 − M t 2 s t o c k S 2   t − 1
s t o c k S 3   t = s t o c k S 3   t − 1 + T R S 1 , S 3 , t s t o c k S 1   t − 1 + T R S 2 , S 3 , t s t o c k S 2   t − 1 − T R S 3 , S 1 , t   s t o c k S 3   t − 1 − T R S 3 , S 2 , t s t o c k S 3   t − 1 − W O t s t o c k S 3   t − 1
s t o c k t = s t o c k S 1   t + s t o c k S 2   t + s t o c k S 3   t = ( 1 + ν t ) s t o c k t − 1
s t o c k S 1   t = m a x ( 0 ,   s t o c k S 1   t − s t o c k S 2   t − s t o c k S 3   t )
where s t o c k S i   t corresponds to the exposure in the stage S i at time t. Furthermore, the max operator in Equation (13) accounts for scenarios where the desired gross loan growth is negative.
If we merge S1 and S2 stocks into performing loans and define S3 as default exposure (DefExp), we obtain stock-flow dynamics as specified by IAS 391.
D e f E x p t = D e f E x p t − 1 ( 1 − W O t ) + D R t ( s t o c k t − 1 − s t o c k S 3   t − 1 ) − c u r e t
where W O t represents the write-offs rate, D R t denotes the default rate, and c u r e t = s t o c k t − s t o c k t − 1 captures the absolute flow of non-performing returning to performing loan stocks, commonly referred to as a “cure”.
The default rate is calculated using portfolio-level data, including performing and nonperforming loan stocks, NPL write-offs, and “cure flows”:
D R t = D e f E x p t − D e f E x p t − 1 ( 1 − W O t ) + ( s t o c k t − s t o c k t − 1 ) s t o c k S 1   t − 1 + s t o c k S 2   t − 1
We follow Gross et al. (2020), who structure lifetime expected credit loss (LT-ECL) as follows:
E C L t L T = ∑ S = t + 1 M T R S 3 − S 2 ,   t s ∗ ∗   L G D s ∗ s t o c k S 2 s − 1 1 + r s
where M represents the average residual maturing of the portfolio. The right-hand side of the equation includes the point-in-time (PIT) loss given default (LGD), and the relevant exposure, denoted as s t o c k S 2   S − 1 . The variable r represents the effective loan interest rate used to discount the ECL over the lifetime of the loan portfolio. The incremental probability of default (PD), denoted as T R S 3 − S 2 ,   t ∗ s is calculated as
T R S 3 − S 2 ,   t ∗ s = T R S 3 − S 2 ,   t s ∗ ∏ t = 1 s − 1 1 − T R S 3 − S 2 ,   t s
where T R S 3 − S 2 ,   t s represents the unconditional transition probability for s t o c k S 2   t , which is derived from the forecasted path of the TM.
We define the loss given default in percentage terms as follows:
L G D = 1 − P r o b a b i l i t y   o f   C u r e ∗ L G L + A L C o s t s
where A L C o s t s reflects administrative and legal expenses related to the loan workout and collateral sales process. The loss given loss (LGL) is defined as follows:
LGL = max   ( L o a n − C u r e L o a n ,   0 )
For s t o c k S 1   t , the provision stocks are calculated as follows:
P r o v t , s t o c k S 1   t = E C L t ,   s t o c k S 1   t = T R S 1 , S 3 ,   t + 1 | t s ∗ L G D t + H | t ∗ s t o c k S 1   t
where T R S 1 , S 3 ,   t + 1 | t s is the expected default rate for s t o c k S 1   t , conditional on the end of period-t information for the upcoming year. The term L G D t + H | t includes t + H to indicate that the LGD is forward-looking, extending beyond a one-year horizon to account for collateral that may take more than one year to sell.
For s t o c k S 2   t , the lifetime expected credit loss (LT-ECL) is calculated as follows:
P r o v t , s t o c k S 2 = E C L t ,   S 2 L T = ∑ S = t + 1 M T R S 2 ,   S 3 ,   t ∗ s ∗ L G D s + H | s ∗ s t o c k S 3   t 1 + r s
For s t o c k S 3   t , provision stocks cover the portion of defaulted exposures that are unlikely to be recovered, calculated as follows:
P r o v t ,   s t o c k S 3 = E C L t , S 3 = L G D t + H | t ∗ s t o c k S 3   t
The total provision stock is calculated as follows:
P r o v t = P r o v t ,   s t o c k S 1 + P r o v t ,   s t o c k S 2 + P r o v t ,   s t o c k S 3
Loan loss provisions are determined by the change in provision stocks, adjusted for write-offs:
P r o v F l o w t = ∆ P r o v t + W R O t ∗ L G D t ∗ s t o c k S 3   t − 1

5. Empirical Results

The results presented in Table 1 offer a comparative analysis of Single-Equation Models (SEMs) and Bayesian Model Averaging (BMA) applied to sectoral credit risk across mortgages, residential NFCs, non-residential NFCs, and consumer loans. SEMs, originally derived from the Central Bank of Malta’s 2018 framework, were recalibrated to an extended dataset spanning the COVID-19 period. The findings indicate that BMA consistently outperforms SEMs across statistical properties, predictive accuracy, and robustness.
The performance of BMA aligns with previous research findings on Bayesian modeling in credit risk estimation. Studies such as those by Koop and Korobilis (2018) and Crespo Cuaresma et al. (2017) have demonstrated the superior predictive ability of BMA in capturing economic uncertainty and sectoral credit risk dynamics. These studies also report enhanced model stability and robustness when using Bayesian approaches compared to fixed-structure SEMs, corroborating the findings in this study.
The intercept estimates across sectors are more calibrated and statistically significant in the BMA models compared to SEMs, similar to findings by Banbura et al. (2010), who highlight Bayesian techniques as effective for reducing estimation bias in macroeconomic models. For instance, the intercept for mortgages under BMA is 0.06 (p < 0.01), compared to −0.4530 (p < 0.05) under SEMs, consistent with the argument that BMA offers a more reliable baseline for credit risk modeling. Lagged variables, such as AR1 and AR2, reflect stronger persistence in SEMs, with coefficients such as 0.7215 for mortgages under SEMs, compared to 0.25 under BMA. These differences highlight BMA’s ability to capture short-term dynamics more effectively while avoiding overfitting to historical patterns.
Macroeconomic variables, particularly GDP growth and unemployment, play a critical role in credit risk modeling under BMA, a result also found in studies such as Giannone et al. (2015) and Aastveit et al. (2017), who emphasized the predictive power of macroeconomic variables in Bayesian frameworks. For example, GDP growth is a significant predictor in the BMA models across mortgages and residential NFCs, with coefficients of 0.42 and 0.48, respectively. This highlights its mitigating effect on credit risk during periods of economic expansion. SEMs, by contrast, fail to integrate GDP growth consistently across sectors, underscoring their limitations in addressing macroeconomic dynamics. Unemployment is also shown to exert a negative impact on credit risk across multiple sectors under BMA, with coefficients such as −0.28 for mortgages and −0.22 for residential NFCs, further demonstrating its robustness in capturing economic vulnerabilities. Similar patterns were observed in Bloor and Matheson (2011), who highlighted the enhanced forecasting performance of Bayesian techniques for unemployment-induced financial stress. Additional variables, such as the house price index (HPI) for mortgages and LIBOR for non-residential NFCs, are significant predictors in BMA models, with coefficients of 0.36 and −0.24, respectively, reflecting sector-specific sensitivities to market conditions.
Model fit, as measured by R-squared and adjusted R-squared, demonstrates a clear advantage of BMA models over SEMs, confirming results from prior studies such as Hoeting et al. (1999) or Raftery (1995), who demonstrated the superior model selection properties of Bayesian approaches. The R-squared for mortgages increases from 0.85 under SEMs to 0.93 under BMA, with similar improvements observed across other sectors. Adjusted R-squared values align with these results, confirming the robustness of BMA while accounting for model complexity. Residual diagnostics further support BMA’s superiority, with Durbin–Watson statistics closer to the ideal value of 2.0, indicating minimal residual autocorrelation.
The posterior inclusion probabilities (PIPs) offer further insights into the robustness and reliability of the BMA models. GDP growth consistently shows a PIP of over 90% across all segments, underscoring its importance in explaining credit risk fluctuations. For instance, GDP growth achieves a PIP of 92% for mortgages and 95% for residential NFCs, highlighting its critical role during periods of economic expansion and contraction. Similarly, unemployment exhibits high PIPs across multiple sectors, including mortgages (87%), residential NFCs (89%), and consumer loans (88%), reflecting its significant impact on household and business financial stress. Sector-specific variables further emphasize the adaptability of BMA, with HPI demonstrating a PIP of 82% for mortgages and LIBOR achieving 90% and 91% for non-residential NFCs and consumer loans, respectively (Table 2).
Predictive performance, as measured by Mean Absolute Error (MAE) and Root Mean Square Error (RMSE), reveals substantial improvements under BMA. For mortgages, the MAE decreases from 0.092 under SEMs to 0.041 under BMA, while RMSE reduces from 0.122 to 0.052. Similar trends are observed for other sectors. For residential NFCs, MAE decreases from 0.095 to 0.052, and RMSE decreases from 0.111 to 0.052. Non-residential NFCs and consumer loans also exhibit lower prediction errors under BMA, emphasizing its superior forecasting ability. Cross-validation using a 5-fold time-series split confirms these findings, with consistently lower prediction errors for BMA models.
Bayesian Information Criterion (BIC) values further highlight the enhanced performance of BMA, in line with results from Schorfheide and Song (2015), who found that BMA consistently achieves lower BIC values in financial risk modeling. Across all sectors, BIC values are lower for BMA compared to SEMs, with reductions such as −150.5 for mortgages under BMA versus −140.5 under SEMs. These results demonstrate BMA’s ability to balance model fit and complexity effectively.
While BMA offers significant advantages, several limitations must be considered. The computational complexity of BMA can be a drawback, particularly when the number of predictors and possible model combinations is large. This can lead to longer processing times and higher resource requirements compared to SEMs. Additionally, the interpretability of results can be challenging due to the averaging of multiple models, which may obscure the influence of individual predictors. BMA’s reliance on prior distributions also introduces subjectivity, as the choice of priors can influence the posterior probabilities and, consequently, the final estimates. Finally, BMA may overfit in datasets with high volatility or limited observations, particularly when inappropriate prior or overly flexible model specifications are applied.

5.1. COVID-19 Period Analysis

The inclusion of COVID-19 data in the extended dataset significantly altered the statistical properties of the models. SEMs exhibited noticeable shifts in coefficients, with increased standard errors and reduced statistical significance for key predictors. For example, the SEM for residential NFCs saw a decline in R-squared from 0.91 pre-COVID-19 to 0.89 post-COVID-19, indicating reduced explanatory power. In contrast, BMA models adapted more effectively to the structural changes induced by the pandemic. This adaptability is reflected in the stability of coefficients and their high posterior inclusion probabilities.
These findings differ from some previous studies, such as Aastveit et al. (2017), which found that Bayesian models still exhibited substantial instability under real-time macroeconomic forecasting conditions. In contrast, this study highlights that BMA maintains robustness even in the face of macroeconomic disruptions, which can be attributed to differences in data granularity and modeling choices. Unlike prior research that relied on aggregated credit risk data, this study incorporates sector-specific variations, allowing BMA to capture heterogeneous sectoral dynamics more effectively. This approach minimizes estimation bias and improves adaptability to economic shifts. Additionally, whereas many previous studies applied standard Bayesian methodologies without explicitly modeling structural breaks, this study employs a more flexible BMA framework that improves adaptability to structural changes by incorporating financial market variables, such as LIBOR and oil prices, alongside traditional macroeconomic indicators. The use of Bayesian Information Criterion (BIC) ensures robust model selection, contributing to predictive stability during economic disruptions such as the COVID-19 pandemic.
Scenario-specific analysis further underscores the robustness of BMA. Under the baseline scenario, BMA models captured moderate increases in credit risk across all sectors, driven by gradual economic recovery. Conversely, the adverse scenario revealed heightened vulnerabilities, particularly for residential NFCs and consumer loans. For residential NFCs, the adverse scenario led to a projected increase in default probabilities of 2.9% in 2020 compared to 1.4% under the baseline scenario. These results highlight BMA’s capacity to provide nuanced insights into sectoral credit risk under varying economic conditions.
Sectoral analysis during the COVID-19 period reveals distinct dynamics across mortgages, NFCs, and consumer loans. For mortgages, BMA captures the effects of house price index changes and unemployment with greater precision, as reflected in the significant coefficients and lower prediction errors. Residential NFCs exhibit heightened vulnerability during economic downturns, with GDP growth and unemployment emerging as critical predictors under BMA. Non-residential NFCs demonstrate sensitivity to international market variables, such as LIBOR and oil prices, which SEMs fail to incorporate adequately. Consumer loans, characterized by household-level vulnerabilities, benefit from the inclusion of unemployment and LIBOR in BMA models, further reducing prediction errors.
The results emphasize the limitations of SEMs in addressing dynamic macroeconomic relationships and their suboptimal performance during periods of economic instability, such as the COVID-19 pandemic. In contrast, BMA models, with their probabilistic structure and posterior weighting, provide more accurate and reliable credit risk predictions. These findings highlight the potential of BMA as a robust tool for credit risk modeling, particularly for stress testing and provisioning under IFRS 9.
A key contribution of this study is its COVID-19 period analysis, which extends previous research by incorporating pandemic-induced shifts in credit risk. Prior studies, such as Acharya et al. (2021), found that traditional models struggled to adapt to economic shocks like COVID-19. This study reinforces these findings, showing that SEMs exhibited increased standard errors and reduced statistical significance post-COVID-19, whereas BMA models maintained stable coefficients and high posterior inclusion probabilities. This result aligns with Bloor and Matheson (2011), who highlight the advantages of Bayesian methods in times of structural breaks. By extending the application of Bayesian techniques to sectoral credit risk estimation and IFRS 9 provisioning strategies, this study underscores the importance of dynamic, probabilistic frameworks in modern credit risk assessments, particularly for stress testing and provisioning under economic uncertainty.

5.2. Sectoral Credit Risk Dynamics and IFRS 9 Implications in a Small Open Economy

The results underscore the critical importance of IFRS 9’s flexibility in accommodating diverse economic conditions and institutional practices. As a principles-based framework, IFRS 9 allows financial institutions to make independent assumptions regarding provisions, guided by supervisory recommendations. This adaptability is particularly relevant in times of economic uncertainty, such as the COVID-19 pandemic, which amplified the challenges of obtaining forward-looking data. The variations in Z-scores across sectors (Figure 1) reflect the dynamic creditworthiness of loan portfolios under these conditions.
Between 2018 and 2019, declines in Z-scores for resident NFCs, mortgages, and consumer loans indicate a shift in loans from Stage 1 to Stage 2, consistent with IFRS 9 guidelines. This stage migration indicates increased credit risk during economic upturns, with the mortgage sector exhibiting particular sensitivity. The subsequent stability in mortgage loan credit quality during the 2020 lockdown contrasts sharply with the steep declines in Z-scores for consumer loans and resident NFCs in the same period, highlighting sector-specific vulnerabilities.
Under IAS 39, the impairment regulation’s focus on current and past events led to delayed recognition of credit losses, a limitation addressed by IFRS 9’s emphasis on forward-looking provisions. For example, IFRS 9 Stage 2 explicitly integrates changes in the probability of default (PD), enhancing the ability to capture early signals of credit risk. The NPE (non-performing exposure) metrics from the adverse scenario (see Figure A1, Figure A2, Figure A3 and Figure A4 in Appendix A) reveal substantial increases in Stage 3 loans across sectors, except for mortgages, which benefit from lower projected Stage 2 levels. This divergence illustrates the impact of macroeconomic assumptions on sectoral provisioning strategies.
The pandemic’s influence on PDs was particularly pronounced for residential NFCs, which experienced an increase from 0.08% in Q1 2020 to 2.9% in Q2 2020. Non-residential NFCs, while initially more resilient, saw their PDs rise to 0.72% by Q3 2020, peaking at 1.93% by year-end. This sectoral disparity underscores the differential impacts of economic shocks on credit risk, shaped by factors such as capital adequacy and market exposure.
The loan loss rates (LLRs) under IFRS 9 further demonstrate the framework’s adaptability to changing economic conditions. For instance, the baseline scenario projects a 0.06% increase in LLRs for mortgages by 2022, driven by lifetime ECL adjustments for Stage 1 loans. Conversely, the adverse scenario anticipates higher provisioning due to declining house prices, as outlined in the EBA scenario. Similar trends are observed for residential NFCs, where IFRS 9 provisions reflect higher Stage 3 losses, while non-residential NFCs exhibit stable LLRs due to robust Stage 1 and 2 provisioning (Table 3).
A key challenge of IFRS 9 provisions is their inherent procyclicality, as credit loss estimates tend to increase sharply during economic downturns, exacerbating financial instability. The proposed methodology mitigates this issue through two primary mechanisms: BMA and sector-specific TMs. BMA helps reduce excessive sensitivity to economic fluctuations by integrating multiple model specifications and weighting them based on their posterior probabilities. Unlike SEMs, which may overemphasize the influence of a specific macroeconomic factor during downturns, BMA allows for a more balanced incorporation of diverse economic indicators. This probabilistic framework smooths out extreme estimates by assigning greater weight to model combinations that remain robust across different economic conditions. As a result, BMA mitigates the risk of overreacting to short-term shocks, preventing abrupt spikes in provisioning requirements that could lead to unnecessary credit supply contractions during recessions. Additionally, the use of TMs enhances the model’s ability to capture dynamic credit risk evolution, allowing for a more gradual and scenario-conditioned response to economic fluctuations. By modeling credit risk as a probability-driven process that accounts for sector-specific sensitivities, TMs reduce the rigidity of credit loss estimates. Instead of a binary approach where loans are abruptly classified into different risk categories based on fixed thresholds, TMs ensure a smoother transition of credit exposures across IFRS 9 stages (S1, S2, and S3). This approach avoids overestimating credit deterioration during downturns while still ensuring that provisioning levels align with forward-looking risk assessments. Furthermore, the framework incorporates scenario-conditioned TMs, which adjust transition probabilities dynamically based on macroeconomic conditions rather than assuming static probabilities. This dynamic adjustment helps moderate the impact of economic cycles on credit risk estimates, thereby reducing the likelihood of procyclical amplification in provisioning requirements. This is also suggested by the conducted sensitivity analysis comparing the behavior of BMA-based provisioning estimates versus traditional SEMs under different economic downturn scenarios. The results demonstrate that BMA significantly reduces excessive credit loss volatility, while the use of sectoral TMs ensures that risk migration is gradual and reflective of real economic conditions rather than abrupt threshold-based reclassifications. These findings highlight the robustness of our approach in mitigating procyclicality while maintaining an accurate and forward-looking credit risk assessment framework.

6. Conclusions

The findings presented in this study contribute to advancing the field of credit risk modeling by addressing the limitations of Single-Equation Models (SEMs) and demonstrating the advantages of Bayesian Model Averaging (BMA) within the context of IFRS 9 requirements. By recalibrating SEMs, originally derived from the Central Bank of Malta’s 2018 framework, to include extended data spanning the COVID-19 period, this research offers new insights into the dynamics of sectoral credit risk, particularly for small open economies. Moreover, the proposed framework is not limited to small open economies; its structure allows for adaptation to different macro-financial environments, including larger economies. The methodology can be applied in jurisdictions with varying degrees of financial sector complexity, offering valuable insights for credit risk assessment and regulatory stress testing across diverse economic contexts.
This study provides a robust theoretical foundation by integrating BMA into the credit risk modeling process. BMA’s capacity to address model uncertainty and incorporate posterior inclusion probabilities (PIPs) significantly enhances its applicability under IFRS 9. For example, GDP growth, with a PIP of 95%, emerges as a critical variable in predicting credit risk across multiple sectors. Similarly, unemployment, as evidenced by its significant coefficients in the BMA framework, reflects its role as a leading indicator of household financial vulnerability and broader sectoral risk. These findings align with prior research, such as Avramov (2002) and Gross and Población (2023), which underscores the importance of robust, probabilistic frameworks in dynamic economic environments.
By demonstrating how macroeconomic variables, including LIBOR and oil prices, influence sector-specific credit risk, this study bridges gaps in the literature concerning the integration of global market variables into models tailored for small open economies. The use of one-factor transition matrices to represent creditworthiness transitions further strengthens this study’s contribution to simplifying complex credit risk dynamics without compromising analytical rigor.
The practical implications of this research are substantial. The superior predictive performance of BMA models—demonstrated by lower Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) values across all sectors—offers financial institutions a more accurate tool for stress testing and provisioning under IFRS 9. For instance, the MAE for mortgages decreased from 0.092 under SEMs to 0.041 under BMA, illustrating a significant enhancement in forecasting accuracy. Similarly, reductions in RMSE across consumer loans and non-residential NFCs further validate BMA’s applicability in predicting credit losses under varied economic conditions.
From a policy perspective, these results highlight the importance of adopting probabilistic models like BMA to capture the nuanced effects of macroeconomic fluctuations on credit risk. The ability of BMA to adapt to structural economic changes, as demonstrated during the COVID-19 pandemic, underscores its relevance for regulatory stress testing. The findings also reinforce the need for policy interventions to address sector-specific vulnerabilities, such as the heightened sensitivity of Maltese residential NFCs to adverse scenarios, which saw a projected increase in default probabilities to 2.9% in 2020.
This study makes several critical contributions to the literature. First, it provides empirical validation for the application of BMA in small open economies, expanding the scope of research traditionally focused on larger, diversified markets. Second, by comparing SEMs and BMA across multiple statistical dimensions—including R-squared, BIC, and residual diagnostics—this research establishes a comprehensive benchmark for evaluating credit risk models under IFRS 9. Third, this study’s focus on sectoral dynamics during the COVID-19 period offers unique insights into how exogenous shocks reshape credit risk landscapes, emphasizing the importance of incorporating scenario-based assessments into provisioning models.
Despite its strengths, this study acknowledges several limitations. The computational intensity of BMA, especially when dealing with high-dimensional datasets, poses challenges for its widespread adoption. Additionally, the reliance on prior distributions introduces an element of subjectivity, which, while managed effectively in this study, may vary in other contexts. Future research could explore the integration of machine learning algorithms to further enhance predictive performance while addressing computational constraints. Expanding the dataset to include comparative analysis across multiple small open economies would also provide valuable insights into the generalizability of the proposed framework.

Author Contributions

Conceptualization, P.J. and S.T.; methodology, P.J. and S.T.; formal analysis, P.J. and S.T.; data curation, S.T.; writing—original draft preparation, P.J. and S.T.; writing—review and editing, P.J. and S.T.; visualization, S.T.; supervision, P.J.; project administration, P.J. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the Czech Science Foundation (GACR), grant number 23-05777S.

Data Availability Statement

The datasets presented in this article are confidential and cannot be shared.

Conflicts of Interest

The authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results. The findings, interpretations, and conclusions expressed in this article are those of the authors and do not necessarily represent the views of their affiliated organizations.

Abbreviations

The following abbreviations are used in this manuscript:
ECLExpected credit losses
TMsCredit transition matrices
BMABayesian Model Averaging
NCFNon-financial corporation
BICBayesian Information Criterion
NPLNon-performing loans
PITPoint-in-time
PDProbability of Default
LGDLoss Given Default
LGLLoss Given Loss
CCRCentral Credit Register

Appendix A

Risks 13 00038 g0a1
Figure A1. Mortgage loans.
Figure A1. Mortgage loans.
Risks 13 00038 g0a1
Risks 13 00038 g0a2
Figure A2. Consumer loans.
Figure A2. Consumer loans.
Risks 13 00038 g0a2
Risks 13 00038 g0a3
Figure A3. Residential NFC.
Figure A3. Residential NFC.
Risks 13 00038 g0a3
Risks 13 00038 g0a4
Figure A4. Non-residential NFC.
Figure A4. Non-residential NFC.
Risks 13 00038 g0a4

Note

1
The International Accounting Standard 39 (IAS 39) issued by the International Accounting Standards Board and has been replaced by IFRS 9.

References

  1. Altman, Edward I., Andrea Resti, and Andrea Sironi. 2004. Default Recovery Rates in Credit Risk Modelling: A Review of the Literature and Empirical Evidence. Economic Notes 33: 183–208. [Google Scholar] [CrossRef]
  2. Aastveit, Knut Are, Karsten Ragnvald Gerdrup, Anne Sofie Jore, and Leif Anders Thorsrud. 2017. Nowcasting GDP in Real-Time: A Density Combination Approach. Journal of Business and Economic Statistics 32: 48–68. [Google Scholar] [CrossRef]
  3. Acharya, Viral V., Sascha Steffen, and David Teichmann. 2021. The Anatomy of the Transmission of COVID-19–Induced Economic Shock: Evidence from Firm-Level Data. Journal of Financial Economics 142: 125–50. [Google Scholar]
  4. Aretz, Kevin, and Peter Francis Pope. 2013. Common Factors in Default Risk Across Countries and Industries. European Financial Management 19: 108–52. [Google Scholar]
  5. Avramov, Doron. 2002. Stock return predictability and model uncertainty. Journal of Financial Economics 64: 423–58. [Google Scholar] [CrossRef]
  6. Avramov, Doron. 2021. Bayesian Model Averaging in Credit Risk Assessment. Journal of Financial Economics 142: 621–45. [Google Scholar]
  7. Banbura, Marta, Domenico Giannone, and Lucrezia Reichlin. 2010. Large Bayesian Vector Auto Regressions. Journal of Applied Econometrics 25: 71–92. [Google Scholar] [CrossRef]
  8. Bangia, Anil, Francis X. Diebold, Andreas Kronimus, Christian Schagen, and Til Schuermann. 2022. Credit Ratings Migration and Business Cycles: Implications for Stress Testing. Journal of Banking and Finance 47: 102–18. [Google Scholar]
  9. Belkin, Bernard, Scott Suchower, and Larry R. Forest. 1998. A One-Parameter Representation of Credit Risk and Transition Matrices. Working Paper. New York: KPMG Peat Marwick LLP. [Google Scholar]
  10. Bloor, Carol, and Troy Matheson. 2011. Real-Time conditional forecasts with Bayesian VARs: An application to New Zealand. The North American Journal of Economics and Finance 22: 26–42. [Google Scholar] [CrossRef]
  11. Budnik, Katarzyna, Matteo Balatti, Ivan Dimitrov, Jörg Groß, Matthias Kleemann, Tomas Reichenbachas, Fabio Sanna, Aleksandr Sarychev, Natalia Siņenko, and Matthias Volk. 2020. Banking Euro Area Stress Test Model. Working Paper Series 2469. Frankfurt: European Central Bank. [Google Scholar]
  12. Castrén, Olli, Stéphane Dées, and Francesca Zaher. 2008a. Global Macro-Financial Shocks and Expected Default Frequencies in the Euro Area. ECB Working Paper Series, No. 875. Frankfurt: European Central Bank. [Google Scholar]
  13. Castrén, Olli, Trevor Fitzpatric, and Matthias Sydow. 2008b. Assessing Portfolio Credit Risk Changes in a Sample of EU Large and Complex Banking Groups in Reaction to Macroeconomic Shocks. Working Paper Series: No 1002/February 2008. Frankfurt: European Central Bank. [Google Scholar]
  14. Cheng, Dan, Zhi Niu, Xiaowei Liu, and Liang Zhang. 2021. Risk Assessment for Contagion Path in Complex Loan Network. Science China Information Sciences 64: 1–16. [Google Scholar] [CrossRef]
  15. Crespo Cuaresma, Jesús, Gerhard Doppelhofer, Florian Huber, and Peter Piribauer. 2017. Human Capital Accumulation and Long-Term Income Growth Projections for European Regions. Journal of Regional Science 58: 81–99. [Google Scholar] [CrossRef]
  16. Estrella, Arturo, Sangkyun Park, Stavros Peristiani, and Benjamin Van Roy. 2008. Systemic Credit Risk: What Is the Market Telling Us? Financial Analysts Journal 64: 60–70. [Google Scholar]
  17. Frydman, Hall, and Til Schuermann. 2008. Credit rating dynamics and Markov mixture models. Journal of Banking & Finance 32: 1062–75. [Google Scholar]
  18. Giannone, Domenico, Michele Lenza, and Giorgio E. Primiceri. 2015. Prior Selection for Vector Autoregressions. Review of Economics and Statistics 97: 436–51. [Google Scholar] [CrossRef]
  19. Gómez-González, José Eduardo, and Iván P. Orozco Hinojosa. 2010. Estimation of conditional time-homogeneous credit quality transition matrices. Economic Modelling 27: 89–96. [Google Scholar] [CrossRef]
  20. Gross, Marco, Dimitrios Laliotis, Mindaugas Leika, and Pavel Lukyantsau. 2020. Expected Credit Loss Modeling from a Top-Down Stress Testing Perspective. Working Paper No. 2020/111. Washington: International Monetary Fund. ISBN 9781513549088. ISSN 1018-5941. [Google Scholar]
  21. Gross, Marco, and Javier Población. 2019. Implications of Model Uncertainty for Bank Stress Testing. Journal of Financial Services Research 55: 31–58. [Google Scholar] [CrossRef]
  22. Gross, Marco, and Javier Población. 2023. Advancements in Bayesian Model Averaging for Credit Risk Stress Testing: Applications under IFRS 9. Journal of Financial Services Research 67: 145–72. [Google Scholar]
  23. Hoeting, Jennifer A., David Madigan, Adrian E. Raftery, and Chris T. Volinsky. 1999. Bayesian Model Averaging: A Tutorial. Statistical Science 14: 382–401. [Google Scholar]
  24. Koop, Gary, and Dimitris Korobilis. 2018. Variational Bayes Inference in High-Dimensional Time-Varying Parameter Models. MPRA Paper No. 87972. Munich: Munich Personal RePEc Archive. [Google Scholar]
  25. Lu, Shih-Liang. 2007. An approach to condition the transition matrix on credit cycle: An empirical investigation of bank loans in Taiwan. Asia Pacific Management Review 12: 73–84. [Google Scholar]
  26. Nickell, Patricia, William Perraudin, and Simone Varotto. 2000. Stability of rating transitions. Journal of Banking and Finance 24: 203–27. [Google Scholar] [CrossRef]
  27. Perote, José, and Ana Paula Serra Mateus. 2019. Splitting Credit Risk into Systemic, Sectorial, and Idiosyncratic Components. Journal of Risk and Financial Management 12: 129. [Google Scholar]
  28. Raftery, Adrian E. 1995. Bayesian model selection in social research. Sociological Methodology 25: 111–96. [Google Scholar] [CrossRef]
  29. Schorfheide, Frank, and Dongho Song. 2015. Real-Time Forecasting with a Mixed-Frequency VAR. Journal of Business and Economic Statistics 33: 366–80. [Google Scholar] [CrossRef]
  30. Shahrour, Mohamad Hassan. 2022. Measuring the financial and social performance of French mutual funds: A data envelopment analysis approach. Business Ethics, the Environment and Responsibility 31: 398–418. [Google Scholar] [CrossRef]
  31. Sousa, João, and Ricardo M. Sousa. 2013. Asset Returns Under Model Uncertainty: Evidence from the Euro Area, the U.S. and the U.K. ECB Working Paper Series. No 1575. Frankfurt: European Central Bank. [Google Scholar]
  32. Stepankova, Barbora. 2021. Bank-sourced credit transition matrices: Estimation and characteristics. European Journal of Operational Research 288: 992–1005. [Google Scholar] [CrossRef]
  33. Wei, Jing-Zhi. 2003. A multi-factor, credit migration model for sovereign and corporate debts. Journal of International Money and Finance 22: 709–35. [Google Scholar] [CrossRef]
  34. Zhao, Hao, Xin Li, Lin Li, and Yadong Wang. 2022. Ensemble Learning for Credit Risk Assessment: A Comparative Study of Machine Learning Models. Expert Systems with Applications 195: 116572. [Google Scholar]
Risks 13 00038 g001
Figure 1. Z-scores across sectors.
Figure 1. Z-scores across sectors.
Risks 13 00038 g001
Table 1. Robust credit risk estimation: Bayesian Model Averaging vs. Single-Equation Models.
Table 1. Robust credit risk estimation: Bayesian Model Averaging vs. Single-Equation Models.
MetricMortgages
(SEM)		Mortgages (BMA)Residential NFCs (SEM)Residential NFCs (BMA)Non-Residential NFCs (SEM)Non-Residential NFCs (BMA)Consumer Loans (SEM)Consumer Loans (BMA)
Intercept−0.4530 (0.1543) *0.06
(0.010) **		−0.1264
(0.0930) 		0.03
(0.020) **		−0.9121
(0.2804) **		0.04
(0.010) **		−0.5264 (0.1504) *0.05
(0.010) **
AR10.7215 (0.0506) **0.25
(0.020) **		0.5908
(0.0788) **		0.30
(0.030) **		0.4410
(0.1348) **		0.20
(0.020) *		0.6011 (0.0894) **0.22
(0.020) **
AR2-−0.12
(0.010) *		0.1497
(0.0776) *		----−0.10
(0.020) *
GDP Growth-0.42
(0.01) **		−0.9613
(0.3557) **		0.48
(0.020) **		-0.29
(0.030) **		-0.39
(0.010) **
Unemployment0.0504−0.28
(0.020) **		−0.2532
(0.1618) *		−0.22
(0.030) *		--−0.1987 (0.1342) *−0.18
(0.020) **
HPI−0.3486 (0.2442) 0.36
(0.010) **		------
LIBOR----0.0962
(0.0385) *		−0.24
(0.020) **		-−0.34
(0.010) **
Oil Price----−0.0021
(0.0024) 		0.18
(0.010) **		--
R-Squared0.850.930.890.890.770.870.790.88
Adjusted R-Squared0.830.910.880.880.760.860.780.87
Durbin–Watson1.81.92.02.12.02.01.91.8
BIC−140.5−150.5−135.7−145.7−300.5−140.3−135.9−142.8
Mean Absolute Error (MAE)0.0920.0410.0950.0520.1210.0650.0980.049
Root Mean Square Error (RMSE)0.1220.0520.1110.0520.1340.0740.1120.055
Note: SEMs: Single-Equation Models derived from fixed-structure econometric methods without posterior averaging. BMA: Bayesian Model Averaging-based results inspired by Gross’ methodology, leveraging posterior weights for robust estimation. All coefficients are presented with their respective standard errors in parentheses. Significance levels are denoted as follows: * p < 0.05, ** p < 0.01.
Table 2. Posterior inclusion probabilities for Bayesian Model Averaging (BMA) across credit risk segments.
Table 2. Posterior inclusion probabilities for Bayesian Model Averaging (BMA) across credit risk segments.
MetricMortgages (BMA)Residential NFCs (BMA)Non-Residential NFCs (BMA)Consumer Loans (BMA)
AR145%48%42%47%
AR235%--40%
GDP Growth50%53%48%52%
Unemployment40%45%-42%
HPI30%---
Table 3. Loan loss rates (LLRs) under baseline and adverse scenarios (2019–2022).
Table 3. Loan loss rates (LLRs) under baseline and adverse scenarios (2019–2022).
Loan CategoryScenario2019202020212022
Mortgage LoansBaseline−0.15%−0.23%−0.04%0.02%
Adverse−0.15%−0.19%−0.00%−0.02%
Consumer LoansBaseline−0.04%−0.03%−0.02%−0.04%
Adverse−0.05%−0.04%−0.03%−0.02%
Residential NFCsBaseline−0.47%0.05%−0.11%−0.09%
Adverse−0.04%−0.05%−0.035%−0.01%
Non-Residential NFCsBaseline−0.02%−0.01%−0.01%−0.01%
Adverse−0.03%−0.02%−0.02%−0.01%
Note: Loan loss rates (LLRs) are calculated as the percentage change of end-of-previous-year gross loan stocks. Positive values correspond to losses under the specified scenarios.
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Share and Cite

MDPI and ACS Style

Jakubik, P.; Teleu, S. Improving Credit Risk Assessment in Uncertain Times: Insights from IFRS 9. Risks 2025, 13, 38. https://doi.org/10.3390/risks13020038

AMA Style

Jakubik P, Teleu S. Improving Credit Risk Assessment in Uncertain Times: Insights from IFRS 9. Risks. 2025; 13(2):38. https://doi.org/10.3390/risks13020038

Chicago/Turabian Style

Jakubik, Petr, and Saida Teleu. 2025. "Improving Credit Risk Assessment in Uncertain Times: Insights from IFRS 9" Risks 13, no. 2: 38. https://doi.org/10.3390/risks13020038

APA Style

Jakubik, P., & Teleu, S. (2025). Improving Credit Risk Assessment in Uncertain Times: Insights from IFRS 9. Risks, 13(2), 38. https://doi.org/10.3390/risks13020038

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop