Efficient simulations for a Bernoulli mixture model of portfolio credit risk

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.

<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>

Enterprise Valuation and Credit Risk Evaluation Research I DCF-Based Credit Risk Model—Application in Project/Corporate Bonds & CLO ABSTRACT There are many research models about enterprise credit risk and can be roughly categorized into structural-form and reduced-form according to their assumptions and focuses. Under these two types of credit risk models, few people use stochastic cash flow model to evaluate enterprise credit risk. It’s because people generally think it difficult to estimate cash flow, and no one had ever developed an applicable model to describe the stochastic characteristics of cash flow. Through our observations of cash flow, however, we discover that the behavior of cash flow exist some stochastic characteristics, including mean-reversion and fluctuating above or under zero. We therefore use the concept of “varying coefficient model” (also called time-varying parameter models) to construct a “Time-dependent stochastic cash flow model”. And then based on this model, we further establish a “Multi-periods DCF-Based Credit Risk Model” to estimate a firm’s value and to evaluate a firm’s credit risk. By using these two models and the concept of expected payoff ratio used to evaluate risky bonds developed by Jarrow-Turnbull Model (1995), we can now value the project bonds and corporate bonds. Furthermore, we expand the single firm’s “Multi-periods DCF-Based Credit Risk Model” to multi-firms and then construct a “Multi-assets & periods DCF-Based Credit Risk Model”. In this way, we then can valuing the securitized products including CLO(Collateralized Loan Obligation), CDO(Collateralized Debt Obligation) re-pooled from all kinds of collateral debts . In our research, we select 24 companies as our sample and then make empirical tests of valuation and credit risk by our models. The empirical results show that our models precisely value more than two-third of sample companies and successfully assess credit risks of more than three-fourth of sample companies. These results indicate that our models are preliminarily supported by the empirical evidences. However, in valuing the securitized products such as the CLO by using the “Multi-assets & periods DCF-Based Credit Risk Model” is limited because the model correctly can only deal with the portfolio that assets are cross-default. To handle with this limitation, the Fourier Transform Method (FTM) can be introduced into our models. Fortunately, it seems very promising that the limitation can be relieved by FTM. It is also the focus of our further study. Research II The Influencing Factors’ Research of Market’s Acceptance on M&A Activities—Empirical Tests on Stock Exchange Cases ABSTRACT Due to hot merges and acquisitions in the recent years in the world, we are interested in the roles and hidden meanings of market’s reaction toward M&A activities. However, market reaction is primarily influenced by expected synergy and merger premium, which individually represents expected benefit in the future and cost for mergers. For this reason, the relationship between expected synergy and merger premium becomes the focus of our research. But in historical researches, there doesn’t exist an integrated-analytical framework to describe the relationship. In this paper, we set a measure for expected synergy through stock price’s fluctuating. Additionally, we construct a new plane for firm’s value and exchange ratio based on L-G model by consideration of the expected synergy and the time-varying earning performance. Furthermore, we develop a LMA model which can integrate expected synergy and merger premium in the analytical framework. This model overcomes the difficulties that expected synergy is hard to compare with merger premium in the past. Moreover, we also create a new measure “the level of market’s acceptance” (LMA) through the analytical framework. Therefore, there are two main purposes in our research. First, to examine whether the merger case is reasonable or not. Second, to find out what are the factors which can explain market’s reaction (LMA) and discuss the meanings of these significant factors. In our research, we select 251 stock-exchange mergers (214 for positive premium, 37 for negative premium) as our sample and make judgments for the merger reasonableness by LMA model and statistical tests. As a result, we make some important conclusions: First, 148 of the 251 proposed mergers produced sufficient combined value to maintain each participant’s quadrant I status at the time of merger announcement. Alternatively, the announcement effects produced wealth losses for one or both firms in 103 of the mergers. In the merger period examined (i.e., announcement to the month following completion), at least 40% do not conform to the rationality assumption of LMA model. Second, acquiring firms of the 148 cases outperform the market since one month prior to announcement. It reveals that there may be information leakage. Third, some ratios of relative wealth status significantly influence the level of market’s acceptance in the same direction during the three periods. To sum up, the main contributions of this study is that, by constructing LMA model and making expected synergy can be efficiently compared with merger premium. We not only solve the constraint of the original L-G model but also create a new and effective measurement of market‘s reaction toward M&A activities. In addition, we explore the relationship between LMA and relative wealth’s ratio and try to discuss its economic meanings.

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.

Introduction Three main variables affect the credit risk of a financial asset: (i) the probability of default (PD), (ii) the ‘loss given default’ (LGD), which is equal to one minus the recovery rate in the event of default (RR), and (iii) the exposure at default (EAD). While significant attention has been devoted by the credit risk literature on the estimation of the first component (PD), much less attention has been dedicated to the estimation of RR and to the relationship between PD and RR. This is mainly the consequence of two related factors. First, credit pricing models and risk management applications tend to focus on the systematic risk components of credit risk, as these are the only ones that attract risk-premia. Second, credit risk models traditionally assumed RR to be dependent on individual features (e.g. collateral or seniority) that do not respond to systematic factors, and therefore to be independent of PD. This traditional focus only on default analysis has been partly reversed by the recent increase in the number of studies dedicated to the subject of RR estimation and the relationship between the PD and RR (Fridson et al . 2000, Gupton et al . 2000, Altman et al . 2001, Altman et al . 2003, 2005, Frye 2000a, 2000b, 2000c, Hu and Perraudin 2002, Hamilton et al . 2001, Jarrow 2001 and Jokivuolle and Peura 2003). This is partly the consequence of the parallel increase in default rates and decrease of recovery rates registered during the 1999–2002 period.

In portfolio credit risk models, correlated credit events are often modelled by means of correlated latent variables. The latent variables are interpreted as the firms’ asset values, and assumed to follow a normal distribution. A procedure is described that uses the information embodied in rating transition matrices to infer the shape of the latent variable distribution. Applying the approach to transition matrices of different origin yields consistent results. Compared to the normal distribution, the implied asset value distributions are fat-tailed, leading to a substantial increase of portfolio credit risk relative to the one under normality. The results are thus highly relevant for the design of credit risk measurement systems.

As is well known, most models of credit risk have failed to measure the credit risks in the context of the global financial crisis. In this context, financial industry representatives, regulators and academics worldwide have given new impetus to efforts to improve credit risk modeling for countries, corporations, financial institutions, and financial instruments. The paper summarizes some of the recent advances in this regard. It considers modifications of structural models, including of the classical Merton model, and efforts to reconcile the structural and the reduced-form models. It also discusses the reassessment of the default correlations using copulas, the pricing of credit index options, and the determination of the prices of distressed debt and estimation of recovery values.

In this article we present a survey of recent developments in the structural approach to modeling of credit risk. We first review some models for measuring credit risk based on the structural approach. We then discuss the empirical evidence in the literature on the performance of structural models of credit risk.

Parameterizing Credit Risk Models

One of the issues that the Basel Accord highlighted was that, though techniques for estimating the probability of default and hence the credit risk of loans to individual consumers are well established, there were no models for the credit risk of portfolios of such loans. Motivated by the reduced form models for credit risk in corporate lending, we seek to exploit the obvious parallels between behavioural scores and the ratings ascribed to corporate bonds to build consumer-lending equivalents. We incorporate both consumer-specific ratings and macroeconomic factors in the framework of Cox Proportional Hazard models. Our results show that default intensities of consumers are significantly influenced by macro factors. Such models then can be used as the basis for simulation approaches to estimate the credit risk of portfolios of consumer loans.

Credit Risk Modelling with Shot-Noise Processes

Prognostic personal credit risk model considering censored information

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.

As the development of financial market and maturity of derivatives's pricing theories, different connotations of credit risk come into being, and many classical credit risk models come up. This paper makes a comparative analysis of current credit risk models and summarizes some of the recent advances in credit risk modeling.

In 2018, corporate credit risk had notably increased in the Egyptian banking industry because its nonperforming loan (NPL) ratios had reversed the downward sloping curve shaping upward ones while the retail NPL ratio struggled the reverse, shaping a flat curve. In the present work, the paper aims to study the macroeconomic and microeconomic factors of corporate and retail credit risk to develop customized models that better predict the future value of the credit risk in the banks of Egypt to provide better insight to the credit officers and regulators to help in enhancing their credit decisions and regulations. The paper has utilized the Fixed-Random effects regression models for data analysis using panel data from 2013 to 2020. The findings showed that the macroeconomic and bank-specific variables affect the corporate and retail credit risks differently showing the importance of dividing the credit risk into categories to avoid generating misleading results and to create more robust and accurate predictive models of credit risk. The results also revealed that asset size, income diversification, loan-to-deposit ratio, interest rate, and external debt significantly affect corporate credit risk. In contrast, retail credit risk is affected only by macroeconomic variables such as external debt, GDP, interest rate, and foreign direct investment.