Unobserved systematic risk factor and default prediction

We conduct a thorough analysis on the role played by the unobserved systematic risk factor in default prediction. We find that this latent factor outweighs the observed systematic risk factors and can substantially improve the in-sample predictive accuracy at the firm, rating group, and aggregate levels. Thus it might be helpful to include the unobserved systematic risk factor when simulating portfolio credit losses. However, we also find that this factor only marginally improves out-of-sample model performance. Therefore, although the models we investigated all show reasonably good ability to rank order firms by default risk, accurate prediction of default rate remains challenging even when the unobserved systematic risk factor is considered.     

Discrete versus continuous state switching models for portfolio credit risk

Dynamic models for credit rating transitions are important ingredients for dynamic credit risk analyses. We compare the properties of two such models that have recently been put forward. The models mainly differ in their treatment of systematic risk, which can be modeled either using discrete states (e.g., expansion versus recession) or continuous states. It turns out that the implied asset correlations and default rate volatilities for discrete state switching models are implausibly low compared to empirical estimates from the literature. We conclude that care has to be taken when discrete state regime switching models are employed for dynamic credit risk management. As a side result of our analysis, we obtain indirect evidence that asset correlations may change over the business cycle.     

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.     

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.     

A Multifactor Model of Credit Spreads

We represent credit spreads across ratings as a function of common unobservable factors of the Vasicek form. Using a state-space approach we estimate the factors, their process parameters, and the exposure of each observed credit spread series to each factor. We find that most of the systematic variation across credit spreads is captured by three factors. The factors are closely related to the implied volatility index (VIX), the long bond rate, and S&P500 returns, supporting the predictions of structural models of default at an aggregate level. By making no prior assumption about the determinants of yield spread dynamics, our study provides an original and independent test of theory. The results also contribute to the current debate about the role of liquidity in corporate yield spreads. While recent empirical literature shows that the level and time-variation in corporate yield spreads is driven primarily by a systematic liquidity risk factor, we find that the three most important drivers of yield spread levels relate to macroeconomic variables. This suggests that if credit spread levels do contain a large liquidity premium, the time variation of this premium is likely driven by the same factors as default 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.     

An Empirical Analysis of Personal Bankruptcy and Delinquency

This article uses a new dataset of credit card accounts to analyzecredit card delinquency, personal bankruptcy, and the stabilityof credit risk models. We estimate duration models for defaultand assess the relative importance of different variables inpredicting default. We investigate how the propensity to defaulthas changed over time, disentangling the two leading explanationsfor the recent increase in default rates—a deteriorationin the risk composition of borrowers versus an increase in borrowers'willingness to default due to declines in default costs. Evenafter controlling for risk composition and economic fundamentals,the propensity to default significantly increased between 1995and 1997. Standard default models missed an important time-varyingdefault factor, consistent with a decline in default costs.     

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.     

The credit rating process and estimation of transition probabilities: A Bayesian approach

The Basel II Accord requires banks to establish rigorous statistical procedures for the estimation and validation of default and ratings transition probabilities. This raises great technical challenges when sufficient default data are not available, as is the case for low default portfolios. We develop a new model that describes the typical internal credit rating process used by banks. The model captures patterns of obligor heterogeneity and ratings migration dependence through unobserved systematic macroeconomic shocks. We describe a Bayesian hierarchical framework for model calibration from historical rating transition data, and show how the predictive performance of the model can be assessed, even with sparse event data. Finally, we analyze a rating transition data set from Standard and Poor's during 1981–2007. Our results have implications for the current Basel II policy debate on the magnitude of default probabilities assigned to low risk assets.     

Differential default risk among traditional and non-traditional mortgage products and capital adequacy standards

We develop a framework to quantify credit risks of non-traditional mortgage products (NMPs). Ex ante probabilities of default are caused by willingness-to-pay and ability-to-pay problems and the high default rates for NMPs confirm that payment shock is a critical default risk indicator. Monte Carlo simulations are conducted using three correlated stochastic variables (mortgage interest rate, home price, and household income) under normal and stressed economies. Results confirm that the default risk of 2/28 and option ARM contracts requiring a minimum monthly interest payment have a greater probability of default than other mortgage products in all economic scenarios. Additionally, the credit risk of NMPs is primarily systematic risk, suggesting that these products should require higher risk-based capital. Due to the non-linear distribution of credit risk, even the advanced internal-based rating approach of the Basle II framework can understate the risk involved in these NMPs.     

Sovereign default risk premia: Evidence from the default swap market

This study explores the risk premia embedded in sovereign default swaps using a term structure model. The risk premia remunerate investors for unexpected changes in the default intensity. A number of interesting results emerge from the analysis. First, the risk premia contribution to spreads decreases over the sample, 2003–07, and rebounds at the start of the ‘credit crunch.’ Second, daily risk premia co-move with US macro variables and corporate default risk. Third, global factors explain most of Latin American countries' premia, and local factors best explain European and Asian premia. The importance of global factors grows over time. Finally, conditioning on lagged local and global variables at a weekly frequency, sovereign risk premia are highly predictable.     

How rating agencies achieve rating stability

Surveys on the use of agency credit ratings reveal that some investors believe that rating agencies are relatively slow in adjusting their ratings. A well-accepted explanation for this perception on the timeliness of ratings is the through-the-cycle methodology that agencies use. According to Moody’s, through-the-cycle ratings are stable because they are intended to measure default risk over long investment horizons, and because they are changed only when agencies are confident that observed changes in a company’s risk profile are likely to be permanent. To verify this explanation, we quantify the impact of the long-term default horizon and the prudent migration policy on rating stability from the perspective of an investor – with no desire for rating stability. This is done by benchmarking agency ratings with a financial ratio-based (credit-scoring) agency-rating prediction model and (credit-scoring) default-prediction models of various time horizons. We also examine rating-migration practices. The final result is a better quantitative understanding of the through-the-cycle methodology.By varying the time horizon in the estimation of default-prediction models, we search for a best match with the agency-rating prediction model. Consistent with the agencies’ stated objectives, we conclude that agency ratings are focused on the long term. In contrast to one-year default prediction models, agency ratings place less weight on short-term indicators of credit quality.We also demonstrate that the focus of agencies on long investment horizons explains only part of the relative stability of agency ratings. The other aspect of through-the-cycle methodology – agency-rating migration policy – is an even more important factor underlying the stability of agency ratings. We find that rating migrations are triggered when the difference between the actual agency rating and the model predicted rating exceeds a certain threshold level. When rating migrations are triggered, agencies adjust their ratings only partially, consistent with the known serial dependency of agency-rating migrations.     

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.     

Cyclical default and recovery in stress testing loan losses

We present a macro variable-based empirical model for corporate bank loans’ credit risk. The model captures the well-known positive relationship between probability of default (PD) and loss given default (LGD; i.e., the inverse of recovery) and their counter-cyclical movement with the business cycle. In the absence of proper micro data on LGD, we use a random-sampling method to estimate the annual average LGD. We specify a two equation model for PD and LGD which is estimated with Finnish time-series data from 1989 to 2008. We also use a system of time-series models for the exogenous macro variables to derive the main macroeconomic shocks which are then used in stress testing aggregate loan losses. We show that the endogenous LGD makes a considerable difference in stress tests compared to a constant LGD assumption.     

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.     

The systematic risk of corporate bonds: default risk,term risk,and index choice

In this paper, we empirically examine the systematic risk of corporate bonds in the Euro area. Based on a unique sample of 784 bonds from 1999 to 2010, we show that the systematic risk of constructed bond portfolios and individual bonds—measured against three different market indices—depends on credit quality, term risk, and index choice. A significant increase in systematic risk for lower-rated bonds is observed following the start of the financial crisis. In multi-factor models, bond portfolios load significantly on default and term risk, which are included as additional factors. Conducting Fama and MacBeth cross-sectional tests, we find that default and term risk are priced with economically relevant premiums that range from 0.35 to 0.62 % per month. Our results are robust to the inclusion of characteristics such as rating and time to maturity.     

Parameterizing credit risk models with rating data

Estimates of average default probabilities for borrowers assigned to each of a financial institution's internal credit risk rating grades are crucial inputs to portfolio credit risk models. Such models are increasingly used in setting financial institution capital structure, in internal control and compensation systems, in asset-backed security design, and are being considered for use in setting regulatory capital requirements for banks. This paper empirically examines properties of the major methods currently used to estimate average default probabilities by grade. Evidence of potential problems of bias, instability, and gaming is presented. With care, and perhaps judicious application of multiple methods, satisfactory estimates may be possible. In passing, evidence is presented about other properties of internal and rating-agency ratings.     

On cox processes and credit risky securities

A framework is presented for modeling defaultable securities and credit derivatives which allows for dependence between market risk factors and credit risk. The framework reduces the technical issues of modeling credit risk to the same issues faced when modeling the ordinary term structure of interest rates. It is shown how to generalize a model of Jarrow, Lando and Turnbull (1997) to allow for stochastic transition intensities between rating categories and into default. This generalization can handle contracts with payments explicitly linked to ratings. It is also shown how to obtain a term structure model for all different rating categories simultaneously and how to obtain an affine-like structure. An implementation is given in a simple one factor model in which the affine structure gives closed form solutions.     

Default correlation: An empirical investigation of a subprime lender

In recent years, subprime lending has grown substantially as an important sector of the credit markets. This paper is concerned with the risk management of subprime loan portfolios and the importance of default correlation in measuring that risk. Using a large portfolio of residential subprime loans from an anonymous subprime lender, we show that default correlation is substantial for this lender. In particular, the significance of default correlation increases as the internal credit rating declines. Our results suggest that lenders and regulators would be well served investing in the understanding of default correlation in subprime portfolios.     

Modeling Corporate Bond Returns

We propose a conditional factor model for corporate bond returns with five factors and time-varying factor loadings. We have three main empirical findings. First, our factor model excels in describing the risks and returns of corporate bonds, improving over previously proposed models in the literature by a large margin. Second, our model recommends a systematic bond investment portfolio whose high out-of-sample Sharpe ratio suggests that the credit risk premium is notably larger than previously estimated. Third, we find closer integration between debt and equity markets than found in prior literature.