Portfolio Credit Risk Research Articles

Basel II, Probability of Bank Run and Portfolio Credit Risk

This paper discusses the Basel II bank capital regulation in the presence of liquidity risk. Under Basel II, the credit risk taken by banks is evaluated and capital is set to limit, over a one-year horizon, the risk of bank default to a desired confidence level. However, in addition to screening and monitoring borrowers, banks also provide liquidity insurance with the supply of short-term deposits withdrawable on demand. This maturity mismatch creates a second type of risk, the risk of a bank run when new information leads depositors to worry about the value of banks' assets. It is shown, in a stylized Basel II framework, that capital regulation should incorporate a liquidity risk component. In addition, we show that credit risk diversification or a reduced probability of loan default which lead to a reduction of Basel II regulatory capital will increase the probability of a bank run. A leverage ratio which puts a floor on the capital-to-asset ratio is a way to limit such a risk.

Stress Testing Banks' Credit Risk Using Mixture Vector Autoregressive Models

This paper estimates macroeconomic credit risk of banks' loan portfolio based on a class of mixture vector autoregressive models. Such class of models can differentiate distributions of default rates and macroeconomic conditions for different market situations and can capture their dynamics evolving over time, including the feedback effect from an increase in fragility back to the macroeconomy. These extensions can facilitate the evaluation of credit risks of loan portfolio based on different credit loss distributions.

The Empirical Relation between Credit Quality, Recovery, and Correlation

The majority of industry credit portfolio risk models, as well as recent scientific results, are based on isolated modules for default probabilities and recoveries in the event of default. This paper shows that these common methods lead to various econometric drawbacks when the parameters are interpreted and aggregated for risk capital allocation and pricing purposes. This paper provides a top down approach in which individual credit risk parameters are derived analytically from a single model. This model allows for a i) dynamic, ii) consistent, and iii) unbiased modeling of credit portfolio risks. An empirical analysis provides evidence for the inferred relationship between credit quality, recovery and correlation.

Improved Modeling of Double Default Effects in Basel II - An Endogenous Asset Drop Model Without Additional Correlation

In 2005 the Internal Ratings Based (IRB) approach of `Basel II' was enhanced by a `treatment of double default effects' to account for credit risk mitigation techniques such as ordinary guarantees or credit derivatives. This paper reveals several severe problems of this approach and presents a new method to account for double default effects. This new it asset drop technique can be applied within any structural model of portfolio credit risk. When formulated within the IRB approach of Basel II, it is very well suited for practical application as it does not pose extensive data requirements and economic capital can still be computed

Modelling the credit risk for portfolios of consumer loans: Analogies with corporate loan models

The New Basel accord has highlighted the need for models of the credit risk in portfolios of consumer loans. There are really no such models of the risks in consumer loan portfolios even though there is a well established industry – credit scoring – in modelling the risk of individual loans. Yet there are a number of models of the credit risk of portfolios of corporate loans. This paper discusses if and how one could use equivalent approaches to building such models in consumer lending even if the models themselves cannot translate across because of the assumptions underlying them.

Frailty Correlated Default

We analyze portfolio credit risk in light of dynamic frailty, by which the credit qualities of different firms depend on common unobservable time-varying default covariates. Frailty is estimated to have a large impact on estimated conditional mean default rates, above and beyond those predicted by observable factors, and to cause a large increase in the likelihood of large default losses for portfolios of U.S. corporate bonds during 1980-2004.

An extended CreditRisk+ framework for portfolio credit risk management

Independent sector assumption in the CreditRisk+ has been a major obstacle to implementing the model. Attempts to overcome this limitation have not gained much success. This paper proposes an extension of the original model which accommodates a wide range of sector covariance structures. Existing numerical algorithms designed for the original model can be reused with little modification. Case studies show that our model outperforms other CreditRisk+ variants which allow sector dependency.A simulation version of our model is also introduced, which in turn used to find an optimal portfolio allocation based on the work of Andersson et al. (2001). Simulation error is very small compared to the analytic counterpart and the optimization significantly reduces portfolio credit risk.

Breaking correlation breakdowns: non-parametric estimation of downturn correlations and their application in credit risk models

In this paper we provide an approach to integrating downturn correlations into the modeling of portfolio credit risk. The model is set in the wellknown asymptotic single-risk factor framework and is extended by random factor loadings. We show how the downturn correlation can be nonparametrically estimated by bootstrap, and then assess the impact of model misspecification and calibration errors on portfolio risk.

Background filtrations and canonical loss processes for top-down models of portfolio credit risk

In single-obligor default risk modeling, using a background filtration in conjunction with a suitable embedding hypothesis (generally known as ℍ-hypothesis or immersion property) has proven a very successful tool to separate the actual default event from the model for the default arrival intensity. In this paper we analyze the conditions under which this approach can be extended to the situation of a portfolio of several obligors, with a particular focus on the so-called top-down approach. We introduce the natural ℍ-hypothesis of this setup (the successive ℍ-hypothesis) and show that it is equivalent to a seemingly weaker one-step ℍ-hypothesis. Furthermore, we provide a canonical construction of a loss process in this setup and provide closed-form solutions for some generic pricing problems.

The Link Between Default and Recovery Rates: Implications for Credit Risk Models and Procyclicality

This paper analyzes the impact of various assumptions about the association between aggregate default probabilities and the loss given default on bank loans and corporate bonds, and seeks to empirically explain this critical relationship. Moreover, it simulates the effects on mandatory capital requirements like those proposed in 2001 by the Basel Committee on Banking Supervision. We present the analysis and results in four distinct sections. The first section examines the literature of the last three decades of the various structural-form, closed-form and other credit risk and portfolio credit value-at-risk (VaR) models and the way they explicitly or implicitly treat the recovery rate variable. Section 2 presents simulation results under three different recovery rate scenarios and examines the impact of these scenarios on the resulting risk measures: our results show a significant increase in both expected and unexpected losses when recovery rates are stochastic and negatively correlated with default probabilities. In Section 3, we empirically examine the recovery rates on corporate bond defaults, over the period 1982-2000. We attempt to explain recovery rates by specifying a rather straightforward statistical least squares regression model. The central thesis is that aggregate recovery rates are basically a function of supply and demand for the securities. Our econometric univariate and multivariate time series models explain a significant portion of the variance in bond recovery rates aggregated across all seniority and collateral levels. Finally, in Section 4 we analyze how the link between default probability and recovery risk would affect the procyclicality effects of the New Basel Capital Accord, due to be released in 2002. We see that, if banks use their own estimates of LGD (as in the advanced IRB approach), an increase in the sensitivity of banks' LGD due to the variation in PD over economic cycles is likely to follow. Our results have important implications for just about all portfolio credit risk models, for markets which depend on recovery rates as a key variable (e.g., securitizations, credit derivatives, etc.), for the current debate on the revised BIS guidelines for capital requirements on bank credit assets, and for investors in corporate bonds of all credit qualities.

Forecasting industry sector default rates through dynamic factor models

In this paper we use a reduced-form model for the analysis of portfolio credit risk. For this purpose, we fit a dynamic factor model to a large data set of default rate proxies and macro-variables for Italy. Multiple step ahead density and probability forecasts are obtained by employing both the direct and indirect methods of prediction together with stochastic simulation of the dynamic factor model. We first find that the direct method is the best performer regarding the out-of-sample projection of financial distressful events. In a second stage of the analysis, we find that reducedform portfolio credit risk measures obtained through the dynamic factor model are lower than those corresponding to the internal-ratings-based analytic formula suggested by Basel II. Moreover, the direct method of forecasting gives the smallest portfolio credit risk measures. Finally, when using the indirect method of forecasting, the simulation results suggest that an increase in the number of dynamic factors (for a given number of principal components) increases portfolio credit risk.

Modeling Credit Risk of Portfolio of Consumer Loans

One of the issues that the Basel Accord highlighted was that though techniques for estimating the probability of default and hence the credit risk of loans to individual consumers are well established, there were no models for the credit risk of portfolios of such loans. Motivated by the reduced form models for credit risk in corporate lending, we will seek to exploit the obvious parallels between behavioural scores and the ratings ascribed to corporate bonds to build consumer lending equivalents. We incorporate both consumer specific ratings and macroeconomic factors in the framework of Cox Proportional Hazard models. Our results show that default intensities of consumers are significantly influenced by macro factors. Such models then can be used as the basis for simulation approaches to estimate the credit risk of portfolios of consumer loans.

Credit rating impact on CDO evaluation

One of the most significant developments in international credit markets in recent years has been the trade in Collateralized Debt Obligations (CDO), which has enabled financial institutions to repackage the credit risk of an asset portfolio into tranches to be transferred to investors. The present paper evaluates the credit risk of such a portfolio and the related tranches by applying two prominent prototypes for credit ratings, namely the point-in-time and through-the-cycle approach. The central parameters default probability and correlation are forecast for multiple years and related forecasting errors are included. The article's main findings are that banks which transfer debt tranches but retain an equity part and apply a through-the-cycle rating approach may be exposed to higher insolvency risk. Firstly, the credit risk retained may be underestimated resulting in an inadequate capital allocation. Secondly, the credit risk transferred may be overestimated resulting in additional risk-based transfer costs.

Fast Simulation of Multifactor Portfolio Credit Risk

This paper develops rare-event simulation methods for the estimation of portfolio credit risk—the risk of losses to a portfolio resulting from defaults of assets in the portfolio. Portfolio credit risk is measured through probabilities of large losses, which are typically due to defaults of many obligors (sources of credit risk) to which a portfolio is exposed. An essential element of a portfolio view of credit risk is a model of dependence between these sources of credit risk: large losses occur rarely and are most likely to result from systematic risk factors that affect multiple obligors. As a consequence, estimating portfolio credit risk poses a challenge both because of the rare-event property of large losses and the dependence between defaults. To address this problem, we develop an importance sampling technique within the widely used Gaussian copula model of dependence. We focus on difficulties arising in multifactor models—that is, models in which multiple factors may be common to multiple obligors, resulting in complex dependence between defaults. Our importance sampling procedure shifts the mean of the common factor to increase the frequency of large losses. In multifactor models, different combinations of factor outcomes and defaults can produce large losses, so our method combines multiple importance sampling distributions, each associated with a shift in the mean of common factors. We characterize “optimal” mean shifts. Finding these points is both a combinatorial problem and a convex optimization problem, so we address computational aspects of this step as well. We establish asymptotic optimality results for our method, showing that—unlike standard simulation—it remains efficient as the event of interest becomes rarer.

Dynamic Factor Analysis of Industry Sector Default Rates and Implication for Portfolio Credit Risk Modelling

In this paper we use a reduced form model for the analysis of Portfolio Credit Risk. For this purpose, we fit a Dynamic Factor model, DF, to a large dataset of default rates proxies and macro-variables for Italy. Multi step ahead density and probability forecasts are obtained by employing both the direct and indirect method of prediction together with stochastic simulation of the DF model. We, first, find that the direct method is the best performer regarding the out of sample projection of financial distressful events. In a second stage of the analysis, the direct method of forecasting through principal components is shown to provide the least sensitive measures of Portfolio Credit Risk to various multifactor model specifications. Finally, the simulation results suggest that the benefits in terms of credit risk diversification tend to diminish with an increasing number of factors, especially when using the indirect method of forecasting.

PRICING AND HEDGING OF PORTFOLIO CREDIT DERIVATIVES WITH INTERACTING DEFAULT INTENSITIES

We consider reduced-form models for portfolio credit risk with interacting default intensities. In this class of models default intensities are modeled as functions of time and of the default state of the entire portfolio, so that phenomena such as default contagion or counterparty risk can be modeled explicitly. In the present paper this class of models is analyzed by Markov process techniques. We study in detail the pricing and the hedging of portfolio-related credit derivatives such as basket default swaps and collaterized debt obligations (CDOs) and discuss the calibration to market data.

Credit cycles and macro fundamentals

Abstract 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.

Term Structure Models with Shot-Noise Effects

This work proposes term structure models consisting of two parts: a part which can be represented in exponential quadratic form and a shot noise part. These term structure models allow for explicit expressions of various derivatives. In particular, they are very well suited for credit risk models. The goal of the paper is twofold. First, a number of key building blocks useful in term structure modelling are derived in closed-form. Second, these building blocks are applied to single and portfolio credit risk. This approach generalizes Duffie & Gýrleanu (2001) and is able to produce realistic default correlation and default clustering. We conclude with a specific model where all key building blocks are computed explicitly.

The Pricing of Correlated Default Risk

Observed tranche spreads of a popular credit default swap (CDS) index reflect the pricing of portfolio credit risk, which we benchmark against “predicted” tranche spreads implied by the single-name CDS market. The overall levels and time profiles of the two sets of spreads reveal that the index and single-name markets are in agreement regarding the risk-neutral probabilities of default (PDs) associated with individual credit exposures. However, substantial tranche-specific differences between observed and predicted spreads suggest that the physical asset return correlations, which are extracted from the single-name market, are too low to account for prices of portfolio credit risk. We explain much of these differences via a correlation risk premium, which amounts on average to 66% of the physical correlations over our sample period. <b>TOPICS:</b>Credit default swaps, credit risk management, statistical methods, analysis of individual factors/risk premia

Portfolio Credit Risk with Extremal Dependence: Asymptotic Analysis and Efficient Simulation

We consider the risk of a portfolio comprising loans, bonds, and financial instruments that are subject to possible default. In particular, we are interested in performance measures such as the probability that the portfolio incurs large losses over a fixed time horizon, and the expected excess loss given that large losses are incurred during this horizon. Contrary to the normal copula that is commonly used in practice (e.g., in the CreditMetrics system), we assume a portfolio dependence structure that is semiparametric, does not hinge solely on correlation, and supports extremal dependence among obligors. A particular instance within the proposed class of models is the so-called t-copula model that is derived from the multivariate Student t distribution and hence generalizes the normal copula model. The size of the portfolio, the heterogeneous mix of obligors, and the fact that default events are rare and mutually dependent make it quite complicated to calculate portfolio credit risk either by means of exact analysis or naïve Monte Carlo simulation. The main contributions of this paper are twofold. We first derive sharp asymptotics for portfolio credit risk that illustrate the implications of extremal dependence among obligors. Using this as a stepping stone, we develop importance-sampling algorithms that are shown to be asymptotically optimal and can be used to efficiently compute portfolio credit risk via Monte Carlo simulation.