Credit Portfolio Models Research Articles

Fast approximation methods for credit portfolio risk calculations

Credit risk is one of the main risks financial institutions are exposed to. Within the last two decades, simulation-based credit portfolio models became extremely popular and replaced closed-form analytical ones as computers became more powerful. However, especially for non-homogenous and non-granular portfolios, a full simulation of a credit portfolio model is still time consuming, which can be disadvantageous within some use cases like credit pricing or within stress testing situations where results must be available very quickly. For this purpose, we investigate if methods based on artificial intelligence (AI) can be helpful to approximate a credit portfolio model. We compare the performance of AI-based methods within three different use cases with suitable non AI-based regression methods. As a result, we see that AI-based methods can generally capture portfolio characteristics and speed-up calculations but - depending on the specific use case and the availability of training data - they are not necessarily always the best choice. Particularly, considering the time and costs for collecting data and training of the complex algorithms, non-AI-based methods can be as good as or even better than AI-based ones, while requiring less computational effort.

Estimating correlation parameters in credit portfolio models under time-varying and nonhomogeneous default probabilities

Estimating correlation parameters in credit portfolio models under time-varying and nonhomogeneous default probabilities

Scenario Weights for Importance Measurement (SWIM) – an R package for sensitivity analysis

AbstractThe Scenario Weights for Importance Measurement (SWIM) package implements a flexible sensitivity analysis framework, based primarily on results and tools developed by Pesenti et al. (2019). SWIM provides a stressed version of a stochastic model, subject to model components (random variables) fulfilling given probabilistic constraints (stresses). Possible stresses can be applied on moments, probabilities of given events, and risk measures such as Value-At-Risk and Expected Shortfall. SWIM operates upon a single set of simulated scenarios from a stochastic model, returning scenario weights, which encode the required stress and allow monitoring the impact of the stress on all model components. The scenario weights are calculated to minimise the relative entropy with respect to the baseline model, subject to the stress applied. As well as calculating scenario weights, the package provides tools for the analysis of stressed models, including plotting facilities and evaluation of sensitivity measures. SWIM does not require additional evaluations of the simulation model or explicit knowledge of its underlying statistical and functional relations; hence, it is suitable for the analysis of black box models. The capabilities of SWIM are demonstrated through a case study of a credit portfolio model.

Pro Rata Credit Risk Pooling Between Regional Banks: Economic Capital and Portfolio Granularity

German savings and cooperative banks use credit risk pooling transactions as a specific type of synthetic credit risk transfer. This paper describes the effect of pro rata credit risk pooling transactions on the granularity of these banks’ credit portfolios. The change in granularity is described analytically using general properties of concentration measures. This allows to prove independent of specific concentration measures or credit portfolio models that the granularity of a credit portfolio will increase if a bank participates in pro rata credit risk pooling with homogeneous credit risks. But simulations show that Value-at-Risk will not always decrease if a portfolio’s granularity increases, ceteris paribus. As a consequence, banks using Value-at-Risk instead of a coherent risk measure like Expected Shortfall might choose to limit their participation in credit risk pooling transactions.

A Study on Operational Risk and Credit Portfolio Risk Estimation Using Data Analytics*

ABSTRACTIn this article we consider operational risk and use data analytics to estimate the credit portfolio risk. Specifically, we consider situations in which managers need to make the optimal operational decision on total provision for risk to hedge against the potential risk in the entire supply chain. We build a new structural credit model integrated with data analytics to analyze the joint default risk of credit portfolio. Our model enables the decision maker to better assess the risk of a supply chain, so that they could determine the optimal operational decisions with total provision for risk, and react in a timely manner to economic and environmental changes. We propose an efficient simulation method to estimate the default probability of the credit portfolio with the risk factors having the multivariate t‐copula. Moreover, we develop a three‐step importance sampling (IS) method for the t‐copula credit portfolio risk measurement model to achieve an accurate estimation of the tail probability of the credit portfolio loss distribution. We apply the Levenberg–Marquardt algorithm to estimate the mean‐shift vector of the systematic risk factors after the probability measure change. Besides, we empirically examine the changes in the credit portfolio risks of 60 listed Chinese firms in different industries using our proposed method. The results show that our model can help the decision maker make the optimal operational decisions with total provision for risk, which hedges against the potential risk in the entire supply chain.

Parameter estimation, bias correction and uncertainty quantification in the Vasicek credit portfolio model

This paper is devoted to the parameterization of correlations in the Vasicek credit portfolio model. First, we analytically approximate standard errors for value-at-risk and expected shortfall based on the standard errors of intra-cohort correlations. Second, we introduce a novel copula-based maximum likelihood estimator for inter-cohort correlations and derive an analytical expression of the standard errors. Our new approach enhances current methods in terms of both computing time and, most importantly, direct uncertainty quantification. Both contributions can be used to quantify a margin of conservatism, which is required by regulators. Third, we illustrate powerful procedures that reduce the well-known bias of current estimators, showing their favorable properties. Further, an open-source implementation of all estimators in the novel R package AssetCorr is provided and selected estimators are applied to Moody’s Default & Recovery Database.

Contagious Defaults in a Credit Portfolio: A Bayesian Network Approach

The robustness of credit portfolio models is of great interest for financial institutions and regulators, since misspecified models translate into insufficient capital buffers and a crisis-prone financial system. In this paper, the authors propose a method to enhance credit portfolio models based on the model of Merton by incorporating contagion effects. While, in most models, the risks related to financial interconnectedness are neglected, the authors use Bayesian network methods to uncover the direct and indirect relationships between credits while maintaining the convenient representation of factor models. A range of techniques to learn the structure and parameters of financial networks from real credit default swaps data are studied and evaluated. Their approach is demonstrated in detail in a stylized portfolio, and the impact on standard risk metrics is estimated.

Contagious defaults in a credit portfolio: a Bayesian network approach

The robustness of credit portfolio models is of great interest for financial institutions and regulators, since misspecified models translate into insufficient capital buffers and a crisis-prone financial system. In this paper, the authors propose a method to enhance credit portfolio models based on the model of Merton by incorporating contagion effects. While, in most models, the risks related to financial interconnectedness are neglected, the authors use Bayesian network methods to uncover the direct and indirect relationships between credits while maintaining the convenient representation of factor models. A range of techniques to learn the structure and parameters of financial networks from real credit default swaps data are studied and evaluated. Their approach is demonstrated in detail in a stylized portfolio, and the impact on standard risk metrics is estimated.

A sensitivity analysis of the alpha factor

In the credit risk weighted assets formula for derivatives, the exposure-at-default is scaled by a multiplier: the so-called internal alpha factor. This has been introduced by the Basel Committee to offset the model or estimation error arising from the usage of a constant exposure amount and should account for the uncertainty of counterparty exposure, the correlation between exposures and the correlation between exposure and default. In this paper, we investigate the alpha factor’s sensitivity to key model parameters under stylized portfolio assumptions in order to better understand its complex characteristics. Our analysis is based on the numerical simulation of alpha sensitivities as well as the derivation of analytical formulas under the assumption of infinitely granular portfolios. We show that the relative exposure volatility and parameters that specify the link between the underlying credit portfolio model and the exposure variables (wrong-way/right-way risk parameters) have a particularly significant impact on the alpha factor. For small homogeneous portfolios the alpha factor is rather unstable with respect to the number of counterparties. We investigate an alternative definition based on the coherent risk measure expected shortfall, which reduces the alpha instability quite significantly.

Scenario Weights for Importance Measurement (SWIM) – An R Package for Sensitivity Analysis

The SWIM package implements a flexible sensitivity analysis framework, based primarily on results and tools developed by Pesenti et al. (2019). SWIM provides a stressed version of a stochastic model, subject to model components (random variables) fulfilling given probabilistic constraints (stresses). Possible stresses can be applied on moments, probabilities of given events, and risk measures such as Value-at-Risk and Expected Shortfall. SWIM operates upon a single set of simulated scenarios from a stochastic model, returning scenario weights, which encode the required stress and allow monitoring the impact of the stress on all model components. The scenario weights are calculated to minimise the relative entropy with respect to the baseline model, subject to the stress applied. As well as calculating scenario weights, the package provides tools for the analysis of stressed models, including plotting facilities and evaluation of sensitivity measures. SWIM does not require additional evaluations of the simulation model or explicit knowledge of its underlying statistical and functional relations; hence it is suitable for the analysis of black box models. The capabilities of SWIM are demonstrated through a case study of a credit portfolio model.

A Method for Off-Site Evaluation of the Insurance Sector

This work aims at offering a parsimonious off-site evaluation approach for insurance sector. In a way, it computes an index for systemic risk of the whole insurance industry. Methodology consists the adaption of two well-known credit portfolio risk models: CreditMetrics and CreditRisk+. Main frame is built on CreditRisk+ single sector model and is enhanced by simulations following the CreditMetrics simulation based approach. It is shown that implementing the methodology developed at this paper, authority is able to follow the level of risk associated with the financial status of the sector and order the firms in terms of their riskiness. Moreover, methodology also allows users to compute the individual risk contribution of each insurance company.

M‐PRESS‐CreditRisk: Microprudential and Macroprudential Capital Requirements for Credit Risk under Systemic Stress

AbstractM‐PRESS‐CreditRisk is a novel stress testing approach that can help authorities gauge banks' capital adequacy related to credit risk. For the first time, it combines the assessment of microprudential capital requirements under Pillars 1 and 2 and macroprudential buffers in a unified, coherent framework. Its core element is an advanced credit portfolio model—SystemicCreditRisk—built upon a rich, nonlinear dependence structure for correlated bank portfolios. The model is applied to a sample of 12 systemically important German banking groups and delivers measures for systemic credit risk and the banks' contributions to it in both baseline and stress scenarios.

A Discussion on Recent Risk Measures with Application to Credit Risk: Calculating Risk Contributions and Identifying Risk Concentrations

In both financial theory and practice, Value-at-risk (VaR) has become the predominant risk measure in the last two decades. Nevertheless, there is a lively and controverse on-going discussion about possible alternatives. Against this background, our first objective is to provide a current overview of related competitors with the focus on credit risk management which includes definition, references, striking properties and classification. The second part is dedicated to the measurement of risk concentrations of credit portfolios. Typically, credit portfolio models are used to calculate the overall risk (measure) of a portfolio. Subsequently, Euler’s allocation scheme is applied to break the portfolio risk down to single counterparties (or different subportfolios) in order to identify risk concentrations. We first carry together the Euler formulae for the risk measures under consideration. In two cases (Median Shortfall and Range-VaR), explicit formulae are presented for the first time. Afterwards, we present a comprehensive study for a benchmark portfolio according to Duellmann and Masschelein (2007) and nine different risk measures in conjunction with the Euler allocation. It is empirically shown that—in principle—all risk measures are capable of identifying both sectoral and single-name concentration. However, both complexity of IT implementation and sensitivity of the risk figures w.r.t. changes of portfolio quality vary across the specific risk measures.

What influences banks’ choice of credit risk management practices? Theory and evidence

Banks use different risk management practices with varying levels of sophistication. This paper examines the factors that determine the choice of risk-management practices. In a theoretical model, we identify two main determinants for the choice of risk management tools: bank competition and sector concentration in the loan market. We empirically test the predictions of our model using hand-collected data on the credit risk management of 249 German savings banks. The results are in line with our theory: Competition pushes banks to implement advanced risk management practices. Sector concentration in the loan market promotes credit portfolio modeling, but it inhibits credit risk transfer.

BEHAVIORAL VALUE ADJUSTMENTS

Assets or liabilities with embedded prepayment/extension options can be subject to behavioral risk, due to the unpredictable exercise strategy followed by the option holder who does not act purely on the strength of financial convenience. When seen from the viewpoint of the option seller, such behavior results in a lower option value and an additional source of uncertainty in future cash flows. In this paper, we propose a general framework to model behavioral risk by taking advantage of a full parallel with credit portfolio modeling and by combining the features of option-based and intensity models. Our approach is micro-structural, meaning that the aggregate prepayment rate derives from the sum of individual decisions. In principle, a detailed characterization of the behavior of a pool of investors can be performed depending on available data. A particular emphasis is placed on the precise definition of behavioral risk and on the modeling of nonmarket factors, which may contribute significantly to the variance of future cash flows. Finally, we discuss the calibration of a behavioral risk premium and the pricing of contracts with embedded options by introducing the concept of behavioral risk adjustment ([Formula: see text]VA), in line with the recent development of XVA methodology.

Importance Sampling for Credit Portfolio Risk with Risk Factors Having t-Copula

This paper proposes an efficient simulation method for calculating credit portfolio risk when risk factors have a heavy-tailed distributions. In modeling heavy tails, its features of return on underlying asset are captured by multivariate [Formula: see text]-Copula. Moreover, we develop a three-step importance sampling (IS) procedure in the [Formula: see text]-copula credit portfolio risk measure model for further variance reduction. Simultaneously, we apply the Levenberg–Marquardt algorithm associated with nonlinear optimization technique to solve the problem that estimates the mean-shift vector of the systematic risk factors after the probability measure change. Numerical results show that those methods developed in the [Formula: see text]-copula model can produce large variance reduction relative to the plain Monte Carlo method, to estimate more accurately tail probability of credit portfolio loss distribution.

Heterogeneous T-Copula Implementation in a Credit Portfolio Model

A flexible way to incorporate heterogeneous tail-dependency into dependency modeling based on a recently proposed modification of the t-copula is presented and applied to a realistic credit portfolio. The heterogeneous t-copula is assumed for the underlying multivariate factor model and it is shown that the capital allocation will change significantly once heterogeneity is introduced.

Behavioral Value Adjustments

Assets or liabilities with embedded prepayment/extension options can be subject to behavioral risk, due to the unpredictable exercise strategy followed by the option holder who does not act purely on the strength of financial convenience. When seen from the viewpoint of the option seller, such behavior results in a lower option value and an additional source of uncertainty in future cash flows. In this paper we propose a general framework to model behavioral risk by taking advantage of a full parallel with credit portfolio modeling and by combining the features of option-based and intensity models. Our approach is micro-structural, meaning that the aggregate prepayment rate derives from the sum of individual decisions. In principle, a detailed characterization of the behavior of a pool of investors can be performed depending on available data. A particular emphasis is placed on the precise definition of behavioral risk and on the modeling of non-market factors, which may contribute significantly to the variance of future cash flows. Finally, we discuss the calibration of a behavioral risk premium and the pricing of contracts with embedded options by introducing the concept of behavioral risk adjustment (bVA), in line with the recent development of XVA methodology.

M-Press-CreditRisk: A Holistic Micro- and Macroprudential Approach to Capital Requirements

M-PRESS-CreditRisk is a new top-down macro stress testing framework that can help supervisors gauge banks' capital adequacy related to credit risk. For the first time, it combines calibration of microprudential capital requirements and macroprudential buffers in a unified, coherent framework. Its core element is an advanced credit portfolio model - SystemicCreditRisk - built upon a rich, non-linear dependence structure for interconnected bank portfolios. Incorporating numerous sector/country-specific systematic factors, the model focuses on credit default concentration risk as a major source of large losses that may have systemic impact. A test run using a sample of 12 systemically important German banks provides measures for systemic credit risk and the banks' contributions to it in both baseline and stress scenarios. Capital requirements calibrated to the results combine elements of Pillar 1 and Pillar 2, whereas macroprudential buffers can internalize the system's tail risk. The maximum model-based combined requirements range between 6.3% and 27.2% of credit RWA depending on the bank. A comparison with the reported capital figures suggests that there appears to be enough capital in the banking system, but its distribution might be suboptimal from a systemic point of view as the capital level of a number of banks might need improvement.

Asymptotic behaviour of multivariate default probabilities and default correlations under stress

Abstract We investigate default probabilities and default correlations of Merton-type credit portfolio models in stress scenarios where a common risk factor is truncated. For elliptically distributed asset variables, the asymptotic limits of default probabilities and default correlations depend on the max-domain of attraction of the asset variables. In the regularly varying case, we derive an integral representation for multivariate default probabilities, which turn out to be strictly smaller than 1. Default correlations are in (0, 1). In the rapidly varying case, asymptotic multivariate default probabilities are 1 and asymptotic default correlations are 0.