Default Correlation Research Articles

Multiperiod Corporate Default Prediction with the Partially-Conditioned Forward Intensity

The forward-intensity model of Duan, {et al} (2012) is a parsimonious and practical way for predicting corporate defaults over multiple horizons. However, it has a noticeable shortcoming because default correlations through intensities are conspicuously absent when the prediction horizon is more than one data period. We propose a new forward-intensity approach that builds in correlations among intensities of individual obligors by conditioning all forward intensities on the future values of some common variables, such as the observed interest rate and/or a latent frailty factor. The new model is implemented on a large sample of US industrial and financial firms spanning the period 1991-2011 on the monthly frequency. Our findings suggest that the new model is able to correct the structural biases at longer prediction horizons reported in Duan et al (2012). Not surprisingly, default correlations are also found to be important in describing the joint default behavior.

A Structural Approach for Predicting Default Correlation

Default correlation is a critical concept in risk management for fixed income investment, bank management, and insurance industry, working capital management, among many. We extend the Leland-Toft term structure model into a two-firm environment and predict the default correlation between two firms by directly simulating the calibrate model based on the observed equity data (1990-2010) for various ratings. Using our empirical default correlation estimation as the benchmark, our investigation sheds more light on the structural approach in predicting default correlation. The results show that our approach outperforms the previous Zhou’s model, thereby our approach is not only theoretical improvement, but also has an empirical advantage.

Temporal correlation of defaults in subprime securitization

Temporal correlation of defaults in subprime securitization

Inferring Asset Correlations from CDS Spreads: A Structural Model Approach

Default correlation is a concern especially after witnessing the financial crisis. To find default correlations, we would like to know asset correlations which are unobservable. In this paper we derive a model to infer asset correlations from Credit Default Swaps (CDSs). We use a structural model approach with the first passage time as default. The resulting model is closed-form and extremely easy to compute. Using the data from 2004 to 2008, we find the average implied asset correlation from CDS to be over 0.4. The average equity correlation, which is usually used as a proxy for asset correlation, over the same period is 0.155. The result complies with the literature that there is another unobservable factor driving defaults among firms.

A Note on the Vasicek’s Model with the Logistic Distribution

The paper argues that it would be natural to replace the standard normal distribution function by the logistic function in the regulatory Basel II (Vasicek’s) formula. Such a model would be in fact consistent with the standard logistic regression PD modeling approach. An empirical study based on US commercial bank’s loan historical delinquency rates re-estimates the default correlations and unexpected losses for the normal and logistic distribution models. The results indicate that the capital requirements could be up to 90-100% higher if the normal Vasicek’s model was replaced by the logistic one.

A simple indicator of systemic risk

We examine the relevance and effectiveness of stock return correlations among financial institutions as an indicator of systemic risk. By analyzing the trends and fluctuations of daily stock return correlations and default correlations among the 22 largest bank holding companies and investment banks from 1988 to 2008, we find that daily stock return correlation is a simple, robust, forward-looking, and timely systemic risk indicator. There is an increasing trend in stock return correlation among banks, whereas there is no obvious correlation trend among non-banks. We also disaggregate the stock returns into systematic and idiosyncratic components and find that the correlation increases are largely driven by the increases in correlations between banks’ idiosyncratic risks, which give rise to increasing systemic risk. Correlation spikes tend to predict or coincide with significant economic or market events, especially during the 2007–2008 financial crisis. Furthermore, we show that stock return correlations offer a perspective on the level of systemic risk in the financial sector that is not already captured by default correlations. Stock return correlations are not subject to data limitations or model specification errors that other potential systemic risk measures may face. Therefore, we recommend that regulators and businesses monitor daily stock return correlations among those large and highly leveraged financial institutions to track the level of systemic risk.

Correlation Smile, Volatility Skew, and Systematic Risk Sensitivity of Tranches

In collateralized debt obligations and other securitized credit derivatives, the expected tranche payoffs depend heavily on the default correlations among the securities in the pool. Like volatility, correlation is not directly observable, but it is possible to infer it from the market price of a tranche. But unfortunately, also like volatility, these implied correlations don’t behave well. They should be equal across all of the tranches created from a given pool, but they never are. Instead, implied correlations exhibit the pattern known as correlation skew. In this article, Hamerle, Igl, and Plank consider two ways in which the real world departs from the assumptions of the Gaussian copula model. Different correlations extracted from different tranches is one, but the other departure is that investors require expected risk premia for bearing a security’s downside exposure. This is not the same as a (symmetrical) distaste for “volatility,” say, and it is reflected in an asymmetrical implied volatility skew exhibited by options on a bond issuer”s equity. The standard Gaussian copula model allows for the first effect, but not the second. In this article, the authors look at both. Their most successful model estimates downside risk premia from the risk-neutral probability densities extracted from the issuers’ equity options and then imposes a fixed and moderate degree of correlation. This combination captures market pricing very well for all of the tranches above the equity tranche.

Pricing Synthetic CDOs Using a Three Regime Random-Factor-Loading Model

Synthetic Collateralized Debt Obligations (CDOs) were among the driving forces of the rapid growth of the market for credit derivatives in recent years. Possibly the most popular model beside the Gaussian copula for pricing CDO tranches is the Random-Factor-Loading-Model of Andersen and Sidenius (2005). We extend this model by allowing more than two regimes of default correlations. The model is calibrated to market spreads at times of financial distress and during calm periods. For both points in time the model correlation skews are similar to the steep skews observed in the market and lead to an improvement to the standard Random-Factor-Loading-Model.

Bayesian dynamic linear modeling for exploring the impact of recent financial crisis on Japan Credit Default Swap market

This paper investigates the effects of recent subprime financial crisis on Japan Credit Default Swap (CDS) market. We first analyze the relationship between the log return series of the reference rates of a CDS contract and the hazard rate. This provides a theoretical foundation for the use of correlation of the log CDS returns as a representation of credit risk correlation. In the dynamic Bayesian linear modeling framework, we consider an algorithm that allow us to obtain dynamic Bayesian updates for the correlation among the reference rates of an underlying CDS contract. Data from the Japan CDS market is analyzed using the proposed methodology. An empirical analyses on the data segmented by different economic environments are carried out. Results indicate that the estimated implied default correlation captures market structure very well and provides useful information for credit risk management.

An Empirical Study of US Corporate Credit Spreads

This paper presents an analysis of the factors that affect US corporate credit spreads. Using data from Bloomberg we investigate the various determinants that cause changes in credit spreads of US corporate firms. As previous research has shown, the variables that should be based on theory determine credit spread changes have limited explanatory power. Our study breaks apart a range of variables into three different sections and analyzes them individual in the groups and together using multiple regressions. We investigate the spot rate, interest rate volatility and slope for the interest rate effects and find strong relationships between spot rate and slope with credit spreads. For the effects of volatility and market uncertainty we find strong relationships between credit spreads and market volatility proxied by VIX and firm volatility proxied by an average of Call and Put implied volatility. TED spreads, SPX and RTY returns show strong relationships between macro-economic variables and credit spreads. Implied default correlations in the Investment Grade and High Yield market also show a strong positive relationship with credit spreads. Our research investigates certain macro-economic variables that have not been researched before and re-establishes previous findings for other variables post-2007 crisis.

COUNTERPARTY RISK FOR CREDIT DEFAULT SWAP WITH STATES RELATED DEFAULT INTENSITY PROCESSES

In this paper, the counterparty risk is considered in pricing a Credit Default Swap (abbr. CDS). We adopt an intensity-based reduced form model, in which the default intensity processes of the counterpart and the reference credit are modulated by the credit states of the firms. Two Markov chains are used to describe the credit state processes. We set up a model where the default correlation between the counterpart and the reference is described through the Markov chains. A semi-explicit formula for the pricing of CDS with counterparty risk is obtained. We analyze the impacts of default correlations and the state changes on the CDS price through some numerical experiments.

The calculation of portfolio unexpected loss in credit and operational risk

In effective risk management, it is of importance to take account of risk aspects from both a credit and operational risk viewpoint. This paper attempts to address both of these areas. The essential tool is the calculation of joint default probabilities starting with an asset correlation and a bivariate normal joint distribution assumption, for log returns of asset values in the case of credit risk, and, an event correlation and a bivariate normal joint distribution assumption for performance scores in the case of operational risk. From this it is shown how to calculate default correlations between counterparties or operational risks and hence a method for assessing unexpected loss for portfolios. The method of moments may then be used to construct a portfolio loss distribution and an appropriate extremal loss measure such as 99.9 per cent value at risk (VaR) or tail VaR.

Macro stress testing of credit risk focused on the tails

This paper investigates macro stress testing of system-wide credit risk with special focus on the tails of the credit risk distributions conditional on adverse macroeconomic scenarios. These tails determine the ex-post solvency probabilities derived from the scenarios. This paper estimates the macro-credit risk link by the traditional Wilson (1997a,b) model as well as by an alternative proposed quantile regression (QR) method (Koenker and Xiao, 2002), in which the relative importance of the macro variables can vary along the credit risk distribution, conceptually incorporating uncertainty in default correlations. Stress-testing exercises on the Brazilian household sector at the one-quarter horizon indicate that unemployment rate distress produces the most harmful effect, whereas distressed inflation and distressed interest rate show higher impacts at longer periods. Determining which of the two stress-testing approaches perceives the scenarios more severely depends on the type of comparison employed. The QR approach is revealed more conservative based on a suggested comparison of vertical distances between the tails of the conditional and unconditional credit risk cumulative distributions.

Multiple Risky Securities Valuation II

In this paper we develop an approach to valuation of a multiple names security portfolio. The goal of the paper to present pricing and calculation of the risk characteristics of the corporate debt based on randomization of the historical data of portfolio assets. Our approach close but it does not coincide with the reduced form interpretation of the credit risk. Based on stochastic interpretation of the default it follows that the market price of a bond is a stochastic process. Therefore, a spot price of a corporate bond implies risk and the bond value shows how market weights the risk. We will show in details how default correlation within securities will affect the basket exposure.

The Impact of Government Interventions on CDS and Equity Markets

We question the impact of government guarantees on the pricing of default risk in credit and stock markets and, using a Merton-type credit model, provide evidence of a structural break in the valuation of U.S. bank debt in the course of the 2007-2009 financial crisis, manifesting in a lowered default boundary, or, under the pre-crisis regime, in higher stock-implied credit spreads. A possible explanation is the asymmetric treatment of debt and equity in rescue measures, which tend to favor creditors. The discrepancies are driven by several factors including firm size, default correlation, and high ratings, thus corroborating our too-big-to-fail hypothesis.

Joint Default Events and Correlated Migration Moves

In the banking industry, the common practice to correlate default and migration events of various guarantors is to use correlated asset price returns. This approach, which is basically a copula approach, is used also by KMV's GCorr model and JPMorgan's CreditMetrics model. However, these models are one-step discrete-time models that are not capable to model joint default events and correlated migration moves for various time horizons in a consistent way, i.e. the forward joint density of default events and migration moves cannot be derived. In this paper we introduce a novel approach to model joint default events and correlated migration moves. After introducing a new definition for describing the dependence structure of processes, we correlate continuous-time Markov chain processes. We show that releasing the Gaussian assumptions and modelling with jumps a new dimension of model uncertainties arises. We introduce various concepts to parameterise the concentration of default events. Furthermore, we extend our models by accounting for the stochastic behaviour of the business time. As part of our comparative analysis, we calculate IRC portfolio loss distributions for various time horizons and hypothetical portfolios and we assess the term structure of default correlations that are implied by the various modelling approaches.

Long-Term Skewness and Systemic Risk

Financial risk management has generally focused on short-term risks rather than long-term risks, and arguably this was an important component of the recent financial crisis. Econometric approaches to measuring long-term risk are developed in order to estimate the term structure of value at risk and expected shortfall. Long-term negative skewness increases the downside risk and is a consequence of asymmetric volatility models. A test is developed for long-term skewness. In a Merton style structural default model, bankruptcies are accompanied by substantial drops in equity prices. Thus, skewness in a market factor implies high defaults and default correlations even far in the future corroborating the systemic importance of long-term skewness. Investors concerned about long-term risks may hedge exposure as in the Intertemporal Capital Asset Pricing Model (ICAPM). As a consequence, the aggregate wealth portfolio should have asymmetric volatility and hedge portfolios should have reversed asymmetric volatility. Using estimates from VLAB, reversed asymmetric volatility is found for many possible hedge portfolios such as volatility products, long- and shortterm treasuries, some exchange rates, and gold. ( JEL: G01)

Comparison of market models for measuring and hedging synthetic CDO tranche spread risks

The recent credit crisis has focused attention on the models used for pricing and assessing risk of structured credit transactions including synthetic CDOs. The market standard one factor Gaussian copula model has been criticized for its unrealistic constant correlation assumption. In this paper, a range of market models that allow a positive relationship between default correlation and default probability, including the correlation mapping methods and the implied copula models, are compared with the Gaussian copula model, based on their relative performance in hedging credit spread risk and pricing bespoke CDOs. The models assessed are calibrated to the traded CDO tranche spreads prior to the credit crisis and then compared based on the mean absolute pricing errors over a time period including the credit crisis. The results of the analysis highlight a number of issues including the accuracy of "mark-to-model" valuations of bespoke CDOs, the value of including past information in pricing and hedging, and the relative performance of the base correlation Gaussian copula model compared to the other market models in this study.

CDO pricing with nested Archimedean copulas

Companies in the same industry sector are usually more correlated than firms in different sectors, as they are similarly affected by macroeconomic effects, political decisions, and consumer trends. Despite the many stock return models taking this fact into account, there are only a few credit default models that take it into consideration. In this paper we present a default model based on nested Archimedean copulas that is able to capture hierarchical dependence structures among the obligors in a credit portfolio. Nested Archimedean copulas have a surprisingly simple and intuitive interpretation. The dependence among all companies in the same sector is described by an inner copula and the sectors are then coupled via an outer copula. Consequently, our model implies a larger default correlation for companies in the same industry sector than for companies in different sectors. A calibration to CDO tranche spreads of the European iTraxx portfolio is performed to demonstrate the fitting capability of the model. This portfolio consists of CDS on 125 companies from six different industry sectors and is therefore an excellent portfolio for a comparison of our generalized model with a traditional copula model of the same family that does not take different sectors into account.

Macro Stress Testing of Credit Risk Focused on the Tails

This paper investigates macro stress testing of system-wide credit risk with special focus on the tails of the credit risk distributions conditional on bad macroeconomic scenarios. These tails determine the ex-post solvency probabilities derived from the scenarios. This paper estimates the macro-credit risk link by both the traditional Wilson (1997) model as well as an alternative proposed quantile regression (QR) method (Koenker and Xiao, 2002), in which the relative importance of the macro variables can vary along the credit risk distribution, conceptually incorporating uncertainty in default correlations. Stress-testing exercises on the Brazilian household sector at the one-quarter horizon indicate that unemployment rate distress produces the most harmful effect, whereas distressed inflation and distressed interest rate show higher impacts at longer periods. Determining which of the two stress-testing approaches perceives the scenarios more severely depends on the type of comparison employed. The QR approach is concluded more conservative based on a proposed comparison of vertical distances between the tails of the conditional and unconditional credit risk cumulative distributions.