IRB法下公司敞口组合的风险驱动因子计量研究

巴塞尔银行监管委员会针对防范信贷组合信用风险所需要的资本制定的内部评级法,通过风险驱动因子的变化来反映组合回报的变化,并根据风险权重函数,通过风险加权资产转化为与每一项信用风险敞口更准确匹配的资本要求.本文对违约概率、违约损失率、违约敞口、期限因素以及违约相关性等信贷组合信用风险的风险驱动因子的度量进行了综合研究.     

A simulation study of Basel II expected loss distributions for a portfolio of credit cards

Credit scoring models have been used traditionally as the basis of decisions to reject or accept credit applications. They are also used to categorize applicants or existing accounts into risk groups. Based on estimates of probability of default (PD), the risk groups may seem well separated. However, by considering distributions on risk elements such as model estimation uncertainty, exposure at default and loss given default, a simulation approach is used to compute Basel II expected loss distributions for a portfolio of credit cards. These show that discrimination between risk groups is not as clear as is immediately suggested simply by PD estimates. Based on these distributions, we also show that measuring extreme credit risk with Value at Risk can lead to considerable underestimation if distributions on these risk elements are not entered into the computation.     

Bayesian inference for issuer heterogeneity in credit ratings migration

Rating transition matrices for corporate bond issuers are often based on fitting a discrete time Markov chain model to homogeneous cohorts. Literature has documented that rating migration matrices can differ considerably depending on the characteristics of the issuers in the pool used for estimation. However, it is also well known in the literature that a continuous time Markov chain gives statistically superior estimates of the rating migration process. It remains to verify and quantify the issuer heterogeneity in rating migration behavior using a continuous time Markov chain. We fill this gap in the literature. We provide Bayesian estimates to mitigate the problem of data sparsity. Default data, especially when narrowing down to issuers with specific characteristics, can be highly sparse. Using classical estimation tools in such a situation can result in large estimation errors. Hence we adopt Bayesian estimation techniques. We apply them to the Moodys corporate bond default database. Our results indicate strong country and industry effects on the determination of rating migration behavior. Using the CreditRisk+ framework, and a sample credit portfolio, we show that ignoring issuer heterogeneity can give erroneous estimates of Value-at-Risk and a misleading picture of the risk capital. This insight is consistent with some recent findings in the literature. Therefore, given the upcoming Basel II implementation, understanding issuer heterogeneity has important policy implications.     

Asset correlations and bank capital adequacy

This paper addresses the estimation of confidence sets for asset correlations used in credit risk portfolio models. Research on the estimation of asset correlations using endogenous probabilities of default estimations has focused on the impact of concentration risk factors, such as firm size and industry. The empirical evidence from Italian small- and medium-size companies show that the assumptions underlying the Basel Committee regulatory capital risk weight function are not substantiated. The regulatory impact is that the capital adequacy is significantly compromised, driving an adverse selection, which favors the worst companies, and transferring the procyclical effects from firms to banks.     

Modeling the evolution of implied CDO correlations

CDO tranche spreads (and prices of related portfolio-credit derivatives) depend on the market’s perception of the future loss distribution of the underlying credit portfolio. Applying Sklar’s seminal decomposition to the distribution of the vector of default times, the portfolio-loss distribution derived thereof is specified through individual default probabilities and the dependence among obligors’ default times. Moreover, the loss severity, specified via obligors’ recovery rates, is an additional determinant. Several (specifically univariate) credit derivatives are primarily driven by individual default probabilities, allowing investments in (or hedging against) default risk. However, there is no derivative that allows separately trading (or hedging) default correlations; all products exposed to correlation risk are contemporaneously also exposed to default risk. Moreover, the abstract notion of dependence among the names in a credit portfolio is not directly observable from traded assets. Inverting the classical Vasicek/Gauss copula model for the correlation parameter allows constructing time series of implied (compound and base) correlations. Based on such time series, it is possible to identify observable variables that describe implied correlations in terms of a regression model. This provides an economic model of the time evolution of the market’s view of the dependence structure. Different regression models are developed and investigated for the European CDO market. Applications and extensions to other markets are discussed.     

Modeling severity risk under PD–LGD correlation

In this article, a generic severity risk framework in which loss given default (LGD) is dependent upon probability of default (PD) in an intuitive manner is developed. By modeling the conditional mean of LGD as a function of PD, which also varies with systemic risk factors, this model allows an arbitrary functional relationship between PD and LGD. Based on this framework, several specifications of stochastic LGD are proposed with detailed calibration methods. By combining these models with an extension of CreditRisk+, a versatile mixed Poisson credit risk model that is capable of handling both risk factor correlation and PD–LGD dependency is developed. An efficient simulation algorithm based on importance sampling is also introduced for risk calculation. Empirical studies suggest that ignoring or incorrectly specifying severity risk can significantly underestimate credit risk and a properly defined severity risk model is critical for credit risk measurement as well as downturn LGD estimation.     

Bayesian inference for generalized linear mixed models of portfolio credit risk

The aims of this paper are threefold. First, we highlight the usefulness of generalized linear mixed models (GLMMs) in the modelling of portfolio credit default risk. The GLMM-setting allows for a flexible specification of the systematic portfolio risk in terms of observed fixed effects and unobserved random effects, in order to explain the phenomena of default dependence and time-inhomogeneity in historical default data. Second, we show that computational Bayesian techniques such as the Gibbs sampler can be successfully applied to fit models with serially correlated random effects, which are special instances of state space models. Third, we provide an empirical study using Standard and Poor's data on U.S. firms. A model incorporating rating category and sector effects, and a macroeconomic proxy variable for state-of-the-economy suggests the presence of a residual, cyclical, latent component in the systematic risk.     

Credit contagion in the presence of non-normal shocks

We generalize existing structural credit risk models that account for contagion effects across economic sectors, to capture the impact of neglected skewness and excess kurtosis in the asset return process, on the shape of the credit loss distribution. We specify Skew-Normal and Skew-Student t densities for the underlying asset return process and estimate the derived credit loss density using sector default rates based on proprietary data from the Central Bank of Mexico for six firm sectors. We show that, out of the six sectors analyzed, there is a significant contagion effect in ‘Commerce’, ‘Services’ and ‘Transport’. Moreover, we show that the non-Gaussian modelling of the common factor provides a better characterization than its Gaussian counterpart for the ‘Services’ sector. This result has a significant impact on the shape and the corresponding Value-at-Risk levels of the ‘Services’ credit loss distribution. In this context, traditional Basel and vendor-based credit risk models are inadequate as these do not consider the individual or the joint impact of contagion and non-Gaussian asset returns.     

Estimating a covariance matrix for market risk management and the case of credit default swaps

We analyze covariance matrix estimation from the perspective of market risk management, where the goal is to obtain accurate estimates of portfolio risk across essentially all portfolios—even those with small standard deviations. We propose a simple but effective visualisation tool to assess bias across a wide range of portfolios. We employ a portfolio perspective to determine covariance matrix loss functions particularly suitable for market risk management. Proper regularisation of the covariance matrix estimate significantly improves performance. These methods are applied to credit default swaps, for which covariance matrices are used to set portfolio margin requirements for central clearing. Among the methods we test, the graphical lasso estimator performs particularly well. The graphical lasso and a hierarchical clustering estimator also yield economically meaningful representations of market structure through a graphical model and a hierarchy, respectively.     

Credit cycles and macro fundamentals

We use an intensity-based framework to study the relation between macroeconomic fundamentals and cycles in defaults and rating activity. Using Standard and Poor's U.S. corporate rating transition and default data over the period 1980–2005, we directly estimate the default and rating cycle from micro data. We relate this cycle to the business cycle, bank lending conditions, and financial market variables. In line with earlier studies, the macro variables appear to explain part of the default cycle. However, we strongly reject the correct dynamic specification of these models. The problem is solved by adding an unobserved dynamic component to the model, which can be interpreted as an omitted systematic credit risk factor. By accounting for this latent factor, many of the observed macro variables loose their significance. There are a few exceptions, but the economic impact of the observed macro variables for credit risk remains low. We also show that systematic credit risk factors differ over transition types, with risk factors for downgrades being noticeably different from those for upgrades. We conclude that portfolio credit risk models based only on observable systematic risk factors omit one of the strongest determinants of credit risk at the portfolio level. This has obvious consequences for current modeling and risk management practices.     

Granularity adjustment for mark-to-market credit risk models

The impact of undiversified idiosyncratic risk on value-at-risk and expected shortfall can be approximated analytically via a methodology known as granularity adjustment (GA). In principle, the GA methodology can be applied to any risk-factor model of portfolio risk. Thus far, however, analytical results have been derived only for simple models of actuarial loss, i.e., credit loss due to default. We demonstrate that the GA is entirely tractable for single-factor versions of a large class of models that includes all the commonly used mark-to-market approaches. Our approach covers both finite ratings-based models and models with a continuum of obligor states. We apply our methodology to CreditMetrics and KMV Portfolio Manager, as these are benchmark models for the finite and continuous classes, respectively. Comparative statics of the GA reveal striking and counterintuitive patterns. We explain these relationships with a stylized model of portfolio risk.     

Empirical credit cycles and capital buffer formation

We model 1927–1997 US business failure rates using an unobserved components time series model. Clear evidence is found of cyclical behavior in default rates. We also detect significant longer term movements in default rates and default correlations. In a multi-year backtest experiment we show that accommodation of default rate dynamics has important consequences for credit risk capitalization requirements. Static or myopic variants of credit portfolio models miss significant periods of credit risk accumulation. Empirically congruent dynamic models by contrast provide more timely warning signals of credit risk build-up. In this way they may mitigate some of the pro-cyclicality concerns.     

A guide to choosing absolute bank capital requirements

Resampling implementation of a stress-scenario approach to estimating portfolio default loss distributions is proposed as the basis for estimates of the appropriate absolute level of economic capital allocations for portfolio credit risk. Estimates are presented for stress scenarios of varying severity and implications of different time horizons are analyzed. Results for a numeraire portfolio are quite sensitive to such variations. Although the analysis is framed in terms of recent proposals to revise regulatory capital requirements for banks, the arguments and results are also relevant for bankers making capital structure decisions.     

Modelling the distribution of credit losses with observable and latent factors

This paper proposes a dynamic model to estimate the credit loss distribution of the aggregate portfolio of loans granted in a banking system. We consider a sectoral approach distinguishing between corporates and households. The evolution of their default frequencies and the size of the loans portfolio are expressed as functions of macroeconomic conditions as well as unobservable credit risk factors, which capture contagion effects between sectors. In addition, we model the distributions of the Exposures at Default and the Losses Given Default. We apply our framework to the Spanish banking system, where we find that sectoral default frequencies are not only affected by economic cycles but also by a persistent latent factor. Finally, we identify the riskier sectors, perform stress tests and compare the relative risk of small and large institutions.     

Counterparty Risk for Credit Default Swaps: Markov Chain Interacting Intensities Model with Stochastic Intensity

We analyze the counterparty risk for credit default swaps using the Markov chain model of portfolio credit risk of multiple obligors with interacting default intensity processes. The default correlation between the protection seller and underlying entity is modeled by an increment in default intensity upon the occurrence of an external shock event. The arrival of the shock event is a Cox process whose stochastic intensity is assumed to follow an affine diffusion process with jumps. We examine how the correlated default risks between the protection seller and the underlying entity may affect the credit default premium in a credit default swap.     

Contagion models a la carte: which one to choose?

We propose a copula contagion mixture model for correlated default times. The model includes the well-known factor, copula, and contagion models as its special cases. The key advantage of such a model is that we can study the interaction of different models and their pricing impact. Specifically, we model the default times of the underlying names in a reference portfolio to follow contagion intensity processes with exponential decay coupled with a copula dependence structure. We also model the default time of the counterparty and its dependence structure with the reference portfolio. Numerical tests show that correlation and contagion have an enormous joint impact on the rates of CDO tranches and the corresponding credit value adjustments are extremely high to compensate for the wrong-way risk.     

Bank-firm relationship and credit risk: An analysis on Tunisian firms

This paper analyses the impact of the intensity and length of bank-firm lending relationship on Tunisian banks’ credit risk over the period 2001–2012. The sample includes 494 bank-firm relationships for 383 firms. By applying probit and ordered probit models, our results indicate that firms which engage in intense relationships with banks are less likely to encounter a credit default. In addition, these firms exhibit a higher loan quality. However, no evidence has been found for the impact of the relationship length on credit risk. Further, the findings show that private banks, unlike public financial institutions, take advantage of their close lending relationships with borrowers to mitigate information asymmetry and therefore improve their loans portfolio quality.     

Constant Proportion Debt Obligations (CPDOs): modeling and risk analysis

Constant Proportion Debt Obligations (CPDOs) are structured credit derivatives that generate high coupon payments by dynamically leveraging a position in an underlying portfolio of investment-grade index default swaps. CPDO coupons and principal notes received high initial credit ratings from the major rating agencies, based on complex models for the joint transition of ratings and spreads for all names in the underlying portfolio. We propose a parsimonious model for analysing the performance of CPDO strategies using a top-down approach that captures the essential risk factors of the CPDO. Our approach allows us to compute default probabilities, loss distributions and other tail risk measures for the CPDO strategy and analyse the dependence of these risk measures on various parameters describing the risk factors. We find that the probability of the CPDO defaulting on its coupon payments can be made arbitrarily small—and thus the credit rating arbitrarily high—by increasing leverage, but the ratings obtained strongly depend on assumptions on the credit environment (high spread or low spread). More importantly, CPDO loss distributions are found to exhibit a wide range of tail risk measures inside a given rating category, suggesting that credit ratings are insufficient performance indicators for such complex leveraged strategies. A worst-case scenario analysis indicates that CPDO strategies have a high exposure to persistent spread-widening scenarios and that CPDO ratings are shown to be quite unstable during the lifetime of the strategy.     

Capital allocation for credit portfolios with kernel estimators

Determining the contributions of sub-portfolios or single exposures to portfolio-wide economic capital for credit risk is an important risk measurement task. Often, economic capital is measured as the Value-at-Risk (VaR) of the portfolio loss distribution. For many of the credit portfolio risk models used in practice, the VaR contributions then have to be estimated from Monte Carlo samples. In the context of a partly continuous loss distribution (i.e. continuous except for a positive point mass on zero), we investigate how to combine kernel estimation methods with importance sampling to achieve more efficient (i.e. less volatile) estimation of VaR contributions.     

Valuation of Portfolio Credit Derivatives with Default Intensities Using the Vasicek Model

We present a methodology for valuing portfolio credit derivatives under a reduced form model for which the default intensity processes of risk assets follow the one-factor Vasicek model. A closed-form solution of joint survival time distribution is obtained. The solution is applied to value credit derivatives of a credit default swap index and collateralized debt obligation. The limitation of methods using the Vasicek model is discussed. We propose that the method is valid and efficient for a portfolio with small-scale correlated risk assets, for which the acceptable size is much greater than for the traditional method. Numerical examples and parameter analysis are also presented.