Implied asset value distributions

We consider the problem of calculating tail loss probability and conditional excess for the Bernoulli mixture model of credit risk. This is an important problem as all credit risk models proposed in literature can be represented as Bernoulli mixture models. Thus, we deviate from the efficient simulation of credit risk literature in that we propose an efficient simulation algorithm for this general Bernoulli mixture model in contrast to previous works that focus on specific credit risk models like CreditRisk\(^+\) or Credit Metrics. The algorithm we propose is a combination of stratification, importance sampling based on cross-entropy, and inner replications using the geometric shortcut method. We evaluate the efficiency of our general method considering three different examples: CreditRisk\(^+\) and two of the latent variable models, the Gaussian and the t-copula model. Numerical results suggest that the proposed general algorithm is more efficient than the benchmark methods for these specific models.

Parameterizing Credit Risk Models

The Gaussian copula model, with all of its flaws, has become the most common approach for estimating the loss distribution of a portfolio of risky credits. In general, extensive calculations are still required, although simplification is often obtained by using an asymptotic single factor model. The model assumes idiosyncratic risks are fully diversified and dependence across names comes entirely from their joint dependence on a single common factor. However, credit risk exposure in a portfolio, such as one held by a bank, does not depend only on the probability of default, but also on uncertainty over loss given default (LGD) and even uncertainty over face amounts, or the exposure at default (EAD), in the case of revolving credits. This article extends the asymptotic model by formally introducing creditors’ draw rates and recoveries in case of default, both of which are tied to the same common factor. A closed-form asymptotic solution incorporating all three components of risk is obtained when distributions are continuous. The author also derives an approximate solution for the discrete distribution case and uses it to show how the overall loss distribution is affected by the properties of the LGD, in particular, its skewness.

Risk factor contributions in portfolio credit risk models

The measurement of portfolio credit risk focuses on rare but significant large‐loss events. This paper investigates rare event asymptotics for the loss distribution in the widely used Gaussian copula model of portfolio credit risk. We establish logarithmic limits for the tail of the loss distribution in two limiting regimes. The first limit examines the tail of the loss distribution at increasingly high loss thresholds; the second limiting regime is based on letting the individual loss probabilities decrease toward zero. Both limits are also based on letting the size of the portfolio increase. Our analysis reveals a qualitative distinction between the two cases: in the rare‐default regime, the tail of the loss distribution decreases exponentially, but in the large‐threshold regime the decay is consistent with a power law. This indicates that the dependence between defaults imposed by the Gaussian copula is qualitatively different for portfolios of high‐quality and lower‐quality credits.

This paper develops rare-event simulation methods for the estimation of portfolio credit risk—the risk of losses to a portfolio resulting from defaults of assets in the portfolio. Portfolio credit risk is measured through probabilities of large losses, which are typically due to defaults of many obligors (sources of credit risk) to which a portfolio is exposed. An essential element of a portfolio view of credit risk is a model of dependence between these sources of credit risk: large losses occur rarely and are most likely to result from systematic risk factors that affect multiple obligors. As a consequence, estimating portfolio credit risk poses a challenge both because of the rare-event property of large losses and the dependence between defaults. To address this problem, we develop an importance sampling technique within the widely used Gaussian copula model of dependence. We focus on difficulties arising in multifactor models—that is, models in which multiple factors may be common to multiple obligors, resulting in complex dependence between defaults. Our importance sampling procedure shifts the mean of the common factor to increase the frequency of large losses. In multifactor models, different combinations of factor outcomes and defaults can produce large losses, so our method combines multiple importance sampling distributions, each associated with a shift in the mean of common factors. We characterize “optimal” mean shifts. Finding these points is both a combinatorial problem and a convex optimization problem, so we address computational aspects of this step as well. We establish asymptotic optimality results for our method, showing that—unlike standard simulation—it remains efficient as the event of interest becomes rarer.

Internal ratings systems, implied credit risk and the consistency of banks’ risk classification policies

Standard market risk optimization tools, based on assumptions of normality, are ineffective for evaluating credit risk. In this article, the authors develop three scenario optimization models for portfolio credit risk. They first create the trading risk profile and find the best hedge position for a single asset or obligor. The second model adjusts all positions simultaneously to minimize the regret of the portfolio subject to general linear restrictions. Finally, a credit risk‐return efficient frontier is constructed using parametric programming. While scenario optimization of quantile‐based credit risk measures leads to problems that are not generally tractable, regret is a relevant and tractable measure that can be optimized using linear programming. The three models are applied to optimizing the risk‐return profile of a portfolio of emerging market bonds.

<p>Credit risk refers to the probability of financial loss resulting from a borrower’s failure to repay a loan. Essentially, it encompasses the risk that a lender may not receive the owed principal and interest, leading to disrupted cash flows and increased collection costs. Lenders can mitigate credit risk by analyzing factors related to a borrower’s creditworthiness, such as their current debt load and income. In the last decade, many banks have started to make use of models to assess the risks of lending credit. The credit risk models are very complex and include algorithm-based methods of assessing credit risk. Such a model aims to help banks quantify, aggregate, and manage credit risk. Despite the method, the focus of credit risk assessment stays on credit quality and risk exposure. Strategies to reduce losses and manage risks are pertinent in credit risk management. However, banks have to organize and manage the lending function professionally and proactively and use advanced techniques to measure and manage risks. Credit risk management has become a hot topic due to the ongoing global economic crises, the rapid digital transformation, the recent technological innovations, and the growing use of artificial intelligence in banking. Regulators expect banks to have a clear and comprehensive understanding of their customers and their credit risk and to be transparent and capable in this area. As the Basel regulations change, banks will face more regulatory pressure. To meet the changing regulatory demands and to manage risk better, many banks are changing their credit risk practices. However, banks that see this as only a compliance issue are missing the point. The research findings indicate that the bank’s credit management practices have strongly influenced its profitability. In brief, manoeuvring through the complex risk terrain poses a significant hurdle for financial organizations. This requires ongoing adjustments and strategic choices to ensure both stability and profitability. Consequently, persistent academic research is essential to guide management, governments, and regulators.</p><p><strong> </strong></p><p><strong>JEL</strong>: G21, G32, G33, C53, E58, D81</p><p> </p><p><strong> Article visualizations:</strong></p><p><img src="/-counters-/soc/0771/a.php" alt="Hit counter" /></p>

Transition matrices are an important determinant in risk management and VAR calculations for credit portfolios. It is well known that rating migration behavior is not constant through time in that it shows cyclicality and significant change over the years. We investigate the effect of changes in migration matrices on credit portfolio risk in terms of expected loss and value-at-risk figures for illustrative loan portfolios. The estimates are based on historical transition matrices for different time horizons and a continuous-time simulation procedure. We further determine confidence sets for the probability of default (PD) in different rating classes by a bootstrapping methodology. Our findings are that there are substantial changes in VAR as well as in the width of estimated PD confidence intervals.

Chapter 11 - Estimating Parameters Required for Credit Risk Modeling

Demand for sustainable fixed-income investment solutions is surging but there is hardly research on the impact of sustainability on the risk characteristics of fixed-income portfolios. This study examines the impact of sustainability on the credit risk exposure of corporate bond portfolios between 2013 and 2020 by analyzing the returns of sustainable and non-sustainable portfolios using two different asset pricing models and environmental, social, and governance (ESG) ratings from different providers. Controlling for a set of portfolio characteristics, our results show that sustainable portfolios are significantly less exposed to credit risk than their non-sustainable peer portfolios. This finding implies that considering ESG criteria in portfolio management is a suitable means to systematically manage credit risk. Being the first study to investigate the relationship between sustainability and credit risk on a portfolio level, this study contributes to the understanding of the effects of ESG criteria in portfolio management and provides academics and investment professionals with valuable insights.

Credit risk modeling using Bayesian network with a latent variable

Continuous Monitoring: Look Before You Leap

The essential issue of this book is the term credit, either in the context of credit markets, credit risk or credit rating. Credit markets’ existence is associated with credit risk, which refers to the risk of an economic loss from the failure of a counterparty to meet its contractual obligations. Due to credit risk, suppliers of credit need to assess the creditworthiness of prospective borrowers. Although modern approaches to credit risk analysis have been developed in recent decades, examining borrowers’ ability to repay their funds is one of the oldest lending activities. The main goal of this monograph is to apply and verify certain methods of credit risk modelling to real data from selected CEE countries. For the main purpose of this work, a micro approach is used to measure credit risk based on monitoring basic indicators and allowing creditors to take the necessary actions in time. The book aims at two partial financial and methodological objectives related to credit risk modelling in this context. Both of them are interconnected, and they complement each other throughout the book. In terms of financial application, this book’s principal objective is to analyse credit risk based on real data, assess its main factors, explore mutual relations, and draw conclusions related to risk assessment and market behaviour. The application is focused on two approaches of individual credit risk assessment within the areas of credit rating and corporate survival. The methodological purpose is the application and verification of rating and bankruptcy models. Rating models estimated using conventional approaches such as discriminant analysis or logistic regression are supplemented by an alternative survival analysis approach to determine the probability of rating downgrade over time. Survival analysis is subsequently used in the following empirical studies on corporate bankruptcy. We will investigate the relationship between the rating and corporate bankruptcy rates and estimate the rating assessment depending on the used model, input variables and the company's age. This book is intended for everyone interested in credit risk, particularly rating and corporate survival modelling, mainly for academia and students at all levels of study. This monograph aims to provide complex information on credit risk fundamentals, current trends and rating systems’ principles. However, the primary purpose is the practical application and estimating models using real corporate data. Thus, we can determine the main factors of rating assessment and corporate survival and demonstrate how these models can be developed through different statistical methods. The text is structured into three central parts: The theoretical background on credit risk and the credit rating industry, a description of econometric approaches used in the applications, and empirical studies on credit rating and corporate bankruptcy modelling. If the reader is particularly interested in estimating models and their comparison and interpretation, then it is suggested that they go directly to the practical application. However, reading the book step by step is recommended to understand the essence and main principles and use them in the application.