Modeling Default Dependence with Threshold Models

Since June 2007, the creditworthiness of structured finance products has deteriorated rapidly. The number of downgrades in November 2007 alone exceeded 2,000 and many downgrades were severe, with 500 tranches downgraded more than 10 notches. Massive downgrades continued in 2008. More than 11,000 of the downgrades affected securities that were rated AAA. This paper studies the credit rating crisis of 2007-2008 and in particular describes the collapse of the credit ratings of ABS CDOs. Using data on ABS CDOs we provide suggestive evidence that ratings shopping may have played a role in the current crisis. We find that tranches rated solely by one agency, and by S&P in particular, were more likely to be downgraded by January 2008. Further, tranches rated solely by one agency are more likely to suffer more severe downgrades.(This abstract was borrowed from another version of this item.)

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.

Credit risk modeling is about modeling losses. These losses are typically coming unexpectedly and triggered by shocks. So any process modeling the stochastic nature of losses should reasonable include jumps. In this paper we review a few jump driven models for the valuation of Credit Default Swaps (CDSs) and show how under these dynamic models also pricing of (exotic) derivatives on single name CDSs is possible. More precisely, we set up fundamental firm-value models that allow for fast pricing of the ‘vanillas’ of the CDS derivative markets: payer and receiver swaptions. It turns out that the proposed model is able to produce realistic implied volatility smiles. Moreover, we detail how a CDS spread simulator can be set up under this framework and illustrate its use for the pricing of exotic derivatives with single name CDSs as underliers.

Collateralized debt obligations (CDOs) were issued in 1987 by bankers at Drexel Burnham Lambert Inc. A decade later, CDOs became the leading power on the credit derivative markets, on which the value of derivative assets was derived from the value of other assets. However, unlike options and credit swamps, CDOs are not real, which means that they are constructed, and sometimes even the construction of their construction. CDOs were made to satisfy different types of investors, at one end, there is low-risk with low-income, and at the other, high-risk with high-income. By 2007, following the bubble burst on the US real estate market, losses on the CDO market started to expand. By 2008, the crisis on the CDO market turned into what we call today 'the global financial crisis.' CDOs are 'in the heart' of the crisis, and even wider. Our attempt is to reveal the mechanism of collateralized debt obligations (CDOs) and the way in which CDOs expanded the negative effects of the present global financial crisis.

In this paper, we study the problem of hedging a basket credit derivatives, in particular, we are interested in basket default swaps. For the pricing of credit derivatives, we consider a factor Copula approach. Single-name credit default swaps will be chosen as the hedging instruments. The hedging mechanism is tested using simulated data with a given measure. Numerical results reveal the efficiency of our proposed hedging method.

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.

Chapter 21 - The Basics of Portfolio Credit Risk

The objective of this paper is to help a bank originator of a collateralized debt obligation (CDO) to build a maximally profitable CDO. We consider an optimization framework for structuring CDOs. The objective is to select attachment/ detachment points and underlying instruments in the CDO pool. In addition to “standard” CDOs we study so-called “step-up” CDOs. In a standard CDO contract the attachment/detachment points are constant over the life of a CDO. In a step-up CDO the attachment/detachment points may change over time. We show that step-up CDOs can save about 25–35% of tranche spread payments (ie, profitability of CDOs can be boosted by about 25–35%). Several optimization models are developed from the bank originator perspective. We consider a synthetic CDO where the goal is to minimize payments for the credit risk protection (premium leg), while maintaining a specific credit rating (assuring the credit spread) of each tranche and maintaining the total incoming credit default swap spread payments. The case study is based on the time-to-default scenarios for obligors (instruments) generated by the Standard & Poor’s CDO Evaluator. The Portfolio Safeguard package by AORDA was used to optimize the performance of several CDOs based on example data.

The three drivers in modeling CDOs (collateralized debt obligations) are the probability of default, the recovery rate, and correlation of the underlying pool of credits. In general, the probability of default is by far the most relevant factor and correlation, the least. Unfortunately, an unwarranted amount of attention is currently given to correlation. Worse yet, most models are driven by (or based on) asset correlation assumptions when what is really relevant is the default correlation. There is no assurance that controlling the asset correlation can produce the desired default correlation.

<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>

Hedging of credit derivatives, especially the Collateralized Debt Obligations (CDOs), is the prerequisite of risk management in financial market. Since both spread risk and default risk exist, the models in existing literature resort to the incomplete-market theory to derive the hedging strategies. From another point of view, the construction of hedging strategies of CDO might be regarded as the process of forecasting the changes in value of CDO by the changes in value of hedging instruments. Based on this idea, this paper proposes an alternative hedging approach via the combined forecasting and regression techniques, where the two individual forecasting models are Gaussian copula model and local intensity model, used to hedge against spread risk and default risk, respectively. Finally, the dynamic hedge ratios of CDO tranches with CDS index are derived. A numerical analysis is carried out and the hedge ratios obtained by the new models are compared with those from actual market spreads. It is shown that the model derived in this paper not only provides hedging strategies which agree with the market hedge ratios but that can be effectively implemented as well.

Using a unique and comprehensive dataset of loan-level home equity lines of credit serviced by large US national banks, we confirm that default risk of home equity lines of credit increases at end of draw. More importantly, we quantify the increase in default risk with the size of positive payment shock at end of draw. Furthermore, we find the effects are more pronounced when borrowers are under greater liquidity or refinance constraints and less pronounced if banks manage the credit risk proactively by freezing the credit lines. Our findings are robust across various model specifications and risk segments, payment shock definitions, and after controlling for sample selection bias from HELOC payoffs. These results have important implications for evaluating and managing HELOC credit risk: (i) the need to capture payment shocks, liquidity and refinance constraints in credit risk models, (ii) the benefit of smoothing payment shocks in contract design as well as the workout process, and (iii) the need to consider proper timing for tightening HELOC lending standards.

Political uncertainty and a firm's credit risk: Evidence from the international CDS market

This paper uses a unique data set of more than 1000 synthetic Collateralized Debt Obligations (CDOs) deals to describe typical structures, their pricing and performance with the aim of identifying the factors behind the spectacular collapse of this important segment of structured credit market in late 2008. The data suggests that mark-to-market losses on many synthetic CDO tranches were much more significant than in case of simpler, lower-rated products despite the former experiencing little or no impairment of the notional. The losses were driven instead by the concentration of relatively limited number of defaults in a short period of time, suggesting that pre-crisis pricing must have seriously underestimated such risk of default clustering. In view of the post-crisis pick-up in synthetic CDO issuance, the paper attempts to heed this lesson and offer a simple factor model of default correlation in the spirit of Marshall–Olkin that is naturally suited to capturing the temporal dimension of default dependencies that have been crucial for synthetic CDOs investors. The model allows building a rich dependence structure capable of consistently fitting standardized iTraxx and CDX index tranches, which makes it ideal for pricing bespoke CDOs.

<p style='text-indent:20px;'>This paper studies a supply chain consisting of two unreliable suppliers and a retailer, where the two suppliers' default risks are correlated. We use a mean-variance function to characterize the retailer's risk aversion. In the case of exogenous wholesale prices, we find that the retailer's risk aversion has a non-monotonic effect on its total ordering quantity. We also show that when the suppliers' default correlation increases, the retailer's total ordering quantity is non-increasing. In the case of endogenous wholesale prices, we find that the profits of the suppliers and the retailer are non-monotonic in retailer's risk aversion level or suppliers' default correlation. As risk aversion level increases, the retailer becomes less sensitive to wholesale prices. Finally, the numerical results indicate that when the suppliers' delivery rates are different, the supplier with a low delivery rate can benefit from the retailer's risk aversion under certain conditions.</p>