We estimate generic statistical properties of a structural credit risk model by considering an ensemble of correlation matrices. This ensemble is set up by Random Matrix Theory. We demonstrate analytically that the presence of correlations severely limits the effect of diversification in a credit portfolio if the correlations are not identically zero. The existence of correlations alters the tails of the loss distribution considerably, even if their average is zero. Under the assumption of randomly fluctuating correlations, a lower bound for the estimation of the loss distribution is provided.
We study the problem of finding the worst-case joint distribution of a set of risk factors given prescribed multivariate marginals and a nonlinear loss function. We show that when the risk measure is CVaR, and the distributions are discretized, the problem can be conveniently solved using linear programming technique. The method has applications to any situation where marginals are provided, and bounds need to be determined on total portfolio risk. This arises in many financial contexts, including pricing and risk management of exotic options, analysis of structured finance instruments, and ag…
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 …
Nowadays small and medium-sized enterprises have become an essential part of the national economy. With the increasing number of such enterprises, how to evaluate their credit risk becomes a hot issue. Unlike big enterprises with massive data to analyze, it is hard to find enough information of small enterprises to assess their financial status. Limited by the lack of primary data, how to inference small enterprises' credit risk from secondary data, like information of their upstream, downstream, parent, and subsidiary enterprises attracts big attention from industry and academy. Targeting on …
The insufficient understanding of the credit network structure was recognized as a key factor for regulators' underestimation of the destructive systematic risk during the financial crisis that started in 2007. The existing credit network research either took a macro perspective to clarify the topological properties of financial systems at a descriptive level or analyzed the risk transmission path and characteristics of individual entities with much pre-assumptions of the network. Here, we used the theory of complex network to model China's credit system from 2000 to 2014 based on actual finan…
The use of CVA to cover credit risk is widely spread, but has its limitations. Namely, dealers face the problem of the illiquidity of instruments used for hedging it, hence forced to warehouse credit risk. As a result, dealers tend to offer a limited OTC derivatives market to highly risky counterparties. Consequently, those highly risky entities rarely have access to hedging services precisely when they need them most. In this paper we propose a method to overcome this limitation. We propose to extend the CVA risk-neutral framework to compute an initial margin (IM) specific to each counterpart…
This work presents a theoretical and empirical evaluation of Anderson-Darling test when the sample size is limited. The test can be applied in order to backtest the risk factors dynamics in the context of Counterparty Credit Risk modelling. We show the limits of such test when backtesting the distributions of an interest rate model over long time horizons and we propose a modified version of the test that is able to detect more efficiently an underestimation of the model's volatility. Finally we provide an empirical application.
The stability of the financial system is associated with systemic risk factors such as the concurrent default of numerous small obligors. Hence it is of utmost importance to study the mutual dependence of losses for different creditors in the case of large, overlapping credit portfolios. We analytically calculate the multivariate joint loss distribution of several credit portfolios on a non-stationary market. To take fluctuating asset correlations into account we use an random matrix approach which preserves, as a much appreciated side effect, analytical tractability and drastically reduces th…
The Basel II internal ratings-based (IRB) approach to capital adequacy for credit risk plays an important role in protecting the Australian banking sector against insolvency. We outline the mathematical foundations of regulatory capital for credit risk, and extend the model specification of the IRB approach to a more general setting than the usual Gaussian case. It rests on the proposition that quantiles of the distribution of conditional expectation of portfolio percentage loss may be substituted for quantiles of the portfolio loss distribution. We present a more economical proof of this prop…
We propose a unified structural credit risk model incorporating both insolvency and illiquidity risks, in order to investigate how a firm's default probability depends on the liquidity risk associated with its financing structure. We assume the firm finances its risky assets by mainly issuing short- and long-term debt. Short-term debt can have either a discrete or a more realistic staggered tenor structure. At rollover dates of short-term debt, creditors face a dynamic coordination problem. We show that a unique threshold strategy (i.e., a debt run barrier) exists for short-term creditors to d…
We introduce an additive stochastic mortality model which allows joint modelling and forecasting of underlying death causes. Parameter families for mortality trends can be chosen freely. As model settings become high dimensional, Markov chain Monte Carlo (MCMC) is used for parameter estimation. We then link our proposed model to an extended version of the credit risk model CreditRisk$^+$. This allows exact risk aggregation via an efficient numerically stable Panjer recursion algorithm and provides numerous applications in credit, life insurance and annuity portfolios to derive P\&L distributio…
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…
Credit risk may be warehoused by choice, or because of limited hedging possibilities. Credit risk warehousing increases capital requirements and leaves open risk. Open risk must be priced in the physical measure, rather than the risk neutral measure, and implies profits and losses. Furthermore the rate of return on capital that shareholders require must be paid from profits. Profits are taxable and losses provide tax credits. Here we extend the semi-replication approach of Burgard and Kjaer (2013) and the capital formalism (KVA) of Green, Kenyon, and Dennis (2014) to cover credit risk warehous…
In structural credit risk models, default events and the ensuing losses are both derived from the asset values at maturity. Hence it is of utmost importance to choose a distribution for these asset values which is in accordance with empirical data. At the same time, it is desirable to still preserve some analytical tractability. We achieve both goals by putting forward an ensemble approach for the asset correlations. Consistently with the data, we view them as fluctuating quantities, for which we may choose the average correlation as homogeneous. Thereby we can reduce the number of parameters …
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…
This paper develops the Jungle model in a credit portfolio framework. The Jungle model is able to model credit contagion, produce doubly-peaked probability distributions for the total default loss and endogenously generate quasi phase transitions, potentially leading to systemic credit events which happen unexpectedly and without an underlying single cause. We show the Jungle model provides the optimal probability distribution for credit losses, under some reasonable empirical constraints. The Dandelion model, a particular case of the Jungle model, is presented, motivated and exactly solved. T…
We develop a method to decompose the PnL of a portfolio of assets into four parts: (a) PnL due to FX rate changes, (b) PnL due to interest rate changes, (c) carry gain due to time passing, (d) PnL due to residual market risk changes (credit risk, liquidity risk, volatility risk etc.). We demonstrate the usefulness of our approach by decomposing the performance of an FX- and interest rate-hedged negative basis position in our fund XAIA Credit Basis II, and we apply the methodology to decompose the performance of our fund XAIA Credit Debt Capital in the first quarter of 2022 into PnL contributio…
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.
Measurement and management of credit concentration risk is critical for banks and relevant for micro-prudential requirements. While several methods exist for measuring credit concentration risk within institutions, the systemic effect of different institutions' exposures to the same counterparties has been less explored so far. In this paper, we propose a measure of the systemic credit concentration risk that arises because of common exposures between different institutions within a financial system. This approach is based on a network model that describes the effect of overlapping portfolios.…
This paper investigates calculations of robust XVA, in particular, credit valuation adjustment (CVA) and funding valuation adjustment (FVA) for over-the-counter derivatives under distributional uncertainty using Wasserstein distance as the ambiguity measure. Wrong way counterparty credit risk and funding risk can be characterized (and indeed quantified) via the robust XVA formulations. The simpler dual formulations are derived using recent infinite dimensional Lagrangian duality results. Next, some computational experiments are conducted to measure the additional XVA charges due to distributio…
We discuss a general dynamic replication approach to counterparty credit risk modeling. This leads to a fundamental jump-process backward stochastic differential equation (BSDE) for the credit risk adjusted portfolio value. We then reduce the fundamental BSDE to a continuous BSDE. Depending on the close out value convention, the reduced fundamental BSDE's solution can be represented explicitly or through an accurate approximate expression. Furthermore, we discuss practical aspects of the approach, important for the its industry applications: (i) efficient numerical methodology for solving a BS…
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.
Credibility theory provides tools to obtain better estimates by combining individual data with sample information. We apply the Credibility theory to a Uniform distribution that is used in testing the reliability of forecasting an interest rate for long term horizons. Such empirical exercise is asked by Regulators (CRR, 2013) in validating an Internal Model Method for Counterparty Credit Risk. The main results is that risk managers consider more reliable the output of a test with limited sample size when the Credibility is applied to define a confidence interval.
Machine learning plays an essential role in preventing financial losses in the banking industry. Perhaps the most pertinent prediction task that can result in billions of dollars in losses each year is the assessment of credit risk (i.e., the risk of default on debt). Today, much of the gains from machine learning to predict credit risk are driven by gradient boosted decision tree models. However, these gains begin to plateau without the addition of expensive new data sources or highly engineered features. In this paper, we present our attempts to create a novel approach to assessing credit ri…
This article presents a generic model for pricing financial derivatives subject to counterparty credit risk. Both unilateral and bilateral types of credit risks are considered. Our study shows that credit risk should be modeled as American style options in most cases, which require a backward induction valuation. To correct a common mistake in the literature, we emphasize that the market value of a defaultable derivative is actually a risky value rather than a risk-free value. Credit value adjustment (CVA) is also elaborated. A practical framework is developed for pricing defaultable derivativ…
JD Digits（京东数字科技）；City University of Hong Kong（香港城市大学）
This paper takes a deep learning approach to understand consumer credit risk when e-commerce platforms issue unsecured credit to finance customers' purchase. The "NeuCredit" model can capture both serial dependences in multi-dimensional time series data when event frequencies in each dimension differ. It also captures nonlinear cross-sectional interactions among different time-evolving features. Also, the predicted default probability is designed to be interpretable such that risks can be decomposed into three components: the subjective risk indicating the consumers' willingness to repay, the …
Aiming at quantifying and evaluating the regional commercial environment along with the level of economic development among cities in mainland China, the concept of China City Commercial Environment Credit Index(CEI) was first introduced and established in 2010. In this manuscript, a historical review and detailed introduction of CEI is included, followed by statistical studies. In particular, an independent statistical cross-check for the existing CEI-2012 is performed and significant factors that play the most in influential roles are discussed.
Conditional Generative Modeling for Enhanced Credit Risk Management in Supply Chain Finance
School of Management, Fudan University（复旦大学管理学院）；Department of Decision Analytics and Operations, College of Business, City University of Hong Kong（城市大学商学院决策分析与运作部门）；Department of Industrial and Systems Engineering, University of Minnesota（明尼苏达大学工业与系统工程系）；The Laboratory for AI-Powered Financial Technologies（人工智能金融技术实验室）
We design a system for risk-analyzing and pricing portfolios of non-performing consumer credit loans. The rapid development of credit lending business for consumers heightens the need for trading portfolios formed by overdue loans as a manner of risk transferring. However, the problem is nontrivial technically and related research is absent. We tackle the challenge by building a bottom-up architecture, in which we model the distribution of every single loan's repayment rate, followed by modeling the distribution of the portfolio's overall repayment rate. To address the technical issues encount…
