The current research on credit risk is primarily focused on modeling default probabilities. Recovery rates are often treated as an afterthought; they are modeled independently, in many cases they are even assumed constant. This is despite of their pronounced effect on the tail of the loss distribution. Here, we take a step back, historically, and start again from the Merton model, where defaults and recoveries are both determined by an underlying process. Hence, they are intrinsically connected. For the diffusion process, we can derive the functional relation between expected recovery rate and default probability. This relation depends on a single parameter only. In Monte Carlo simulations we find that the same functional dependence also holds for jump-diffusion and GARCH processes. We discuss how to incorporate this structural recovery rate into reduced form models, in order to restore essential structural information which is usually neglected in the reduced-form approach.
We propose a novel credit default model that takes into account the impact of macroeconomic information and contagion effect on the defaults of obligors. We use a set-valued Markov chain to model the default process, which is the set of all defaulted obligors in the group. We obtain analytic characterizations for the default process, and use them to derive pricing formulas in explicit forms for synthetic collateralized debt obligations (CDOs). Furthermore, we use market data to calibrate the model and conduct numerical studies on the tranche spreads of CDOs. We find evidence to support that sy…
We compare the five major sources of corporate Credit Default Swap prices: GFI, Fenics, Reuters, CMA, and Markit, using the most liquid single name 5-year CDS in the iTraxx and CDX indexes from 2004 to 2010. Deviations from the common trend among prices in the different databases are not random but are explained by idiosyncratic factors, financing costs, global risk, and other trading factors. The CMA quotes lead the price discovery process. Moreover, we find that there is not a full agreement among databases in the results of the price discovery analysis between stock and CDS returns.
We study insolvency cascades in an interbank system when banks are allowed to insure their loans with credit default swaps (CDS) sold by other banks. We show that, by properly shifting financial exposures from one institution to another, a CDS market can be designed to rewire the network of interbank exposures in a way that makes it more resilient to insolvency cascades. A regulator can use information about the topology of the interbank network to devise a systemic insurance surcharge that is added to the CDS spread. CDS contracts are thus effectively penalized according to how much they cont…
We compare two models of corporate default by calculating the Jeffreys-Kullback-Leibler divergence between their predicted default probabilities when asset correlations are either high or low. Our main results show that the divergence between the two models increases in highly correlated, volatile, and large markets, but that it is closer to zero in small markets, when asset correlations are low and firms are highly leveraged. These findings suggest that during periods of financial instability the single-and multi-factor models of corporate default will generate increasingly inconsistent predi…
Banks and financial institutions all over the world manage portfolios containing tens of thousands of customers. Not all customers are high credit-worthy, and many possess varying degrees of risk to the Bank or financial institutions that lend money to these customers. Hence assessment of credit risk is paramount in the field of credit risk management. This paper discusses the use of Bayesian principles and simulation-techniques to estimate and calibrate the default probability of credit ratings. The methodology is a two-phase approach where, in the first phase, a posterior density of default …
This article presents a new model for valuing a credit default swap (CDS) contract that is affected by multiple credit risks of the buyer, seller and reference entity. We show that default dependency has a significant impact on asset pricing. In fact, correlated default risk is one of the most pervasive threats in financial markets. We also show that a fully collateralized CDS is not equivalent to a risk-free one. In other words, full collateralization cannot eliminate counterparty risk completely in the CDS market.
We study dynamic hedging of counterparty risk for a portfolio of credit derivatives. Our empirically driven credit model consists of interacting default intensities which ramp up and then decay after the occurrence of credit events. Using the Galtchouk-Kunita-Watanabe decomposition of the counterparty risk price payment stream, we recover a closed-form representation for the risk minimizing strategy in terms of classical solutions to nonlinear recursive systems of Cauchy problems. We discuss applications of our framework to the most prominent class of credit derivatives, including credit swap …
In this paper, we performs a credit risk analysis, on the data of past loan applicants of a company named Lending Club. The calculation required the use of exploratory data analysis and machine learning classification algorithms, namely, Logistic Regression and Random Forest Algorithm. We further used the calculated probability of default to design a credit derivative based on the idea of a Credit Default Swap, to hedge against an event of default. The results on the test set are presented using various performance measures.
A new procedure is presented for the objective comparison and evaluation of default definitions. This allows the lender to find a default threshold at which the financial loss of a loan portfolio is minimised, in accordance with Basel II. Alternative delinquency measures, other than simply measuring payments in arrears, can also be evaluated using this optimisation procedure. Furthermore, a simulation study is performed in testing the procedure from `first principles' across a wide range of credit risk scenarios. Specifically, three probabilistic techniques are used to generate cash flows, whi…
The existence of asymmetric information has always been a major concern for financial institutions. Financial intermediaries such as commercial banks need to study the quality of potential borrowers in order to make their decision on corporate loans. Classical methods model the default probability by financial ratios using the logistic regression. As one of the major commercial banks in France, we have access to the the account activities of corporate clients. We show that this transactional data outperforms classical financial ratios in predicting the default event. As the new data reflects t…
The modeling of the probability of joint default or total number of defaults among the firms is one of the crucial problems to mitigate the credit risk since the default correlations significantly affect the portfolio loss distribution and hence play a significant role in allocating capital for solvency purposes. In this article, we derive a closed-form expression for the probability of default of a single firm and the probability of the total number of defaults by any time $t$ in a homogeneous portfolio of firms. We use a contagion process to model the arrival of credit events that causes the…
We introduce a novel class of credit risk models in which the drift of the survival process of a firm is a linear function of the factors. The prices of defaultable bonds and credit default swaps (CDS) are linear-rational in the factors. The price of a CDS option can be uniformly approximated by polynomials in the factors. Multi-name models can produce simultaneous defaults, generate positively as well as negatively correlated default intensities, and accommodate stochastic interest rates. A calibration study illustrates the versatility of these models by fitting CDS spread time series. A nume…
We present two methodologies on the estimation of rating transition probabilities within Markov and non-Markov frameworks. We first estimate a continuous-time Markov chain using discrete (missing) data and derive a simpler expression for the Fisher information matrix, reducing the computational time needed for the Wald confidence interval by a factor of a half. We provide an efficient procedure for transferring such uncertainties from the generator matrix of the Markov chain to the corresponding rating migration probabilities and, crucially, default probabilities. For our second contribution, …
A standard quantitative method to access credit risk employs a factor model based on joint multivariate normal distribution properties. By extending a one-factor Gaussian copula model to make a more accurate default forecast, this paper proposes to incorporate a state-dependent recovery rate into the conditional factor loading, and model them by sharing a unique common factor. The common factor governs the default rate and recovery rate simultaneously and creates their association implicitly. In accordance with Basel III, this paper shows that the tendency of default is more governed by system…
Since the 1990s, there have been significant advances in the technology space and the e-Commerce area, leading to an exponential increase in demand for cashless payment solutions. This has led to increased demand for credit cards, bringing along with it the possibility of higher credit defaults and hence higher delinquency rates, over a period of time. The purpose of this research paper is to build a contemporary credit scoring model to forecast credit defaults for unsecured lending (credit cards), by employing machine learning techniques. As much of the customer payments data available to len…
我们回顾了衡量流动性对CDS价格影响的不同方法。我们从简化形式的模型开始，将流动性作为一个额外的贴现率。我们回顾了Chen，Fabozzi and Sverdlove（2008）和Buhler and Trapp（2006，2008），对流动性利率如何进入CDS溢价率公式、流动性利率过程的动态以及信用流动性相关性采用了不同的假设。Buhler和Trapp（2008）提供了最普遍和最现实的框架，包括流动性和信用之间的相关性，债券和CDS合约之间的流动性溢出效应，以及CDS溢价率的非对称流动性效应。然后，我们讨论了Bongaerts，De Jong和Driessen（2009）的研究，该研究导出了一个包含流动性效应的均衡资产定价模型。研究结果包括，预期的非流动性和流动性风险对预期CDS回报有统计上的显着影响。最后，我们讨论了Predescu et al（2009），该研究也分析了危机中的数据。这是一个统计模型，将有序流动性得分与每个CDS参考实体相关联，并允许比较超过2400个参考实体的流动性。本研究指出，信用与流动性不足是相关的，并呈现微笑模式。所有这些研究都强调，CDS溢价率并不是信用风险的纯粹指标。需要进一步的研究来衡量CDS合约水平的流动性溢价，并有效地将流动性与信贷分离。
