Measuring Credit Risk of Individual Corporate Bonds in US Energy Sector

In this paper, using the measures of the credit risk price spread (CRiPS) and the standardized credit risk price spread (S-CRiPS) proposed in Kariya’s (A CB (corporate bond) pricing model for deriving default probabilities and recovery rates. Eaton, IMS Collection Series: Festschrift for Professor Morris L., 2013) corporate bond model, we make a comprehensive empirical credit risk analysis on individual corporate bonds (CBs) in the US energy sector, where cross-sectional CB and government bond price data is used with bond attributes. Applying the principal component analysis method to the S-CRiPSs, we also categorize individual CBs into three different groups and study on their characteristics of S-CRiPS fluctuations of each group in association with bond attributes. Secondly, using the market credit rating scheme proposed by Kariya et al. (2014), we make credit-homogeneous groups of CBs and show that our rating scheme is empirically very timely and useful. Thirdly, we derive term structures of default probabilities for each homogeneous group, which reflect the investors’ views and perspectives on the future default probabilities or likelihoods implicitly implied by the CB prices for each credit-homogeneous group. Throughout this paper it is observed that our credit risk models and the associated measures for individual CBs work effectively and can timely provide the market credit information evaluated by investors.     

On the Term Structure of Default Premia in the Swap and LIBOR Markets

Existing theories of the term structure of swap rates provide an analysis of the Treasury–swap spread based on either a liquidity convenience yield in the Treasury market, or default risk in the swap market. Although these models do not focus on the relation between corporate yields and swap rates (the LIBOR–swap spread), they imply that the term structure of corporate yields and swap rates should be identical. As documented previously (e.g., in Sun, Sundaresan, and Wang (1993)) this is counterfactual. Here, we propose a model of the default risk imbedded in the swap term structure that is able to explain the LIBOR–swap spread. Whereas corporate bonds carry default risk, we argue that swap contracts are free of default risk. Because swaps are indexed on "refreshed"-credit-quality LIBOR rates, the spread between corporate yields and swap rates should capture the market's expectations of the probability of deterioration in credit quality of a corporate bond issuer. We model this feature and use our model to estimate the likelihood of future deterioration in credit quality from the LIBOR–swap spread. The analysis is important because it shows that the term structure of swap rates does not reflect the borrowing cost of a standard LIBOR credit quality issuer. It also has implications for modeling the dynamics of the swap term structure.     

CREDIT SPREADS AND THE ZERO‐COUPON TREASURY SPOT CURVE

We examine the relation between credit spreads on industrial bonds and the underlying Treasury term structure. We use zero‐coupon spot rates to eliminate the coupon bias and to allow for a consistent study both within and across the different credit ratings. Our results indicate that the level and slope of the Treasury term structure are negatively correlated with changes in the credit spread on investment‐grade corporate bonds. We also find that the relation between credit spreads and the Treasury term structure is relatively stable through time. This is good news for value‐at‐risk calculations, as this suggests that the correlations among assets of different credit classes are stable; therefore use of historic correlations to model spread relations can be valid.     

THE SLOPE OF THE TERM STRUCTURE OF CREDIT SPREADS: AN EMPIRICAL INVESTIGATION

In this article we analyze the slope of the term structure of credit spreads. We investigate the explanatory role of interest rate, market, and idiosyncratic equity variables that the recent empirical literature highlights as important determinants of credit spread levels. This study extends the analysis and assesses its effect on credit slopes for a sample of corporate bonds. We find that these factors affect credit spreads at short and long maturities in a significantly different way. A closer inspection of the credit spread slope also reveals that it is a useful indicator of the direction of changes in future short‐term credit spreads. This evidence has important implications for the trading and risk management of portfolios of bonds with different maturities.     

Tempered stable structural model in pricing credit spread and credit default swap

In this paper, we explore the features of a structural credit risk model wherein the firm value is driven by normal tempered stable (NTS) process belonging to the larger class of Lévy processes. For the purpose of comparability, the calibration to the term structure of a corporate bond credit spread is conducted under both NTS structural model and Merton structural model. We find that NTS structural model provides better fit for all credit ratings than Merton structural model. However, it is noticed that probabilities of default derived from the calibration of the term structure of a bond credit spread might be overestimated since the bond credit spread could contain non-default components such as illiquidity risk or asymmetric tax treatment. Hence, considering CDS spread as a reflection of the pure credit risk for the reference entity, we calibrate it in order to obtain more reasonable probability of default and obtain valid results in calibration of the market CDS spread with NTS structural model.     

The Risk Microstructure of Corporate Bonds: A Case Study from the German Corporate Bond Market

This article presents joint econometric analysis of interest rate risk, issuer‐specific risk (credit risk) and bond‐specific risk (liquidity risk) in a reduced‐form framework. We estimate issuer‐specific and bond‐specific risk from corporate bond data in the German market. We find that bond‐specific risk plays a crucial role in the pricing of corporate bonds. We observe substantial differences between different bonds with respect to the relative influence of issuer‐specific vs. bond‐specific spread on the level and the volatility of the total spread. Issuer‐specific risk exhibits strong autocorrelation and a strong impact of weekday effects, the level of the risk‐free term structure and the debt to value ratio. Moreover, we can observe some impact of the stock market volatility, the respective stock's return and the distance to default. For the bond‐specific risk we find strong autocorrelation, some impact of the stock market index, the stock market volatility, weekday effects and monthly effects as well as a very weak impact of the risk‐free term structure and the specific stock's return. Altogether, the determinants of the spread components vary strongly between different bonds/issuers.     

The delivery option in credit default swaps

Under standard assumptions the reduced-form credit risk model is not capable of accurately pricing the two fundamental credit risk instruments – bonds and credit default swaps (CDS) – simultaneously. Using a data set of euro-denominated corporate bonds and CDS our paper quantifies this mispricing by calibrating such a model to bond data, and subsequently using it to price CDS, resulting in model CDS spreads up to 50% lower on average than observed in the market. An extended model is presented which includes the delivery option implicit in CDS contracts emerging since a basket of bonds is deliverable in default. By using a constant recovery rate standard models assume equal recoveries for all bonds and hence zero value for the delivery option. Contradicting this common assumption, case studies of Chapter 11 filings presented in the paper show that corporate bonds do not necessarily trade at equal levels following default. Our extension models the implied expected recovery rate of the cheapest-to-deliver bond and, applied to data, largely eliminates the mispricing. Calibrated recovery values lie between 8% and 47% for different obligors, exhibiting strong variation among rating classes and industries. A cross-sectional analysis reveals that the implied recovery parameter depends on proxies for the delivery option, primarily the number of available bonds and bond pricing errors. No evidence is found for a direct influence of the bid-ask spread, notional amount, coupon, or rating used as proxies for bond market liquidity.     

The joint estimation of term structures and credit spreads

We present a new framework for the joint estimation of the default-free government term structure and corporate credit spread curves. By using a data set of liquid, German mark denominated bonds, we show that this yields more realistic spreads than traditionally obtained spread curves that result from subtracting independently estimated government and corporate term structures. The obtained spread curves are smooth functions of time to maturity, as opposed to the twisting curves one gets from the traditional method, and are less sensitive to model specifications. To determine the ‘optimal’ model specification, we use a newly developed test statistic that compares spread curves from competing models.     

An Estimation Model for the Term Structure of Yield Spread

An estimation model for term structure of yield spread has become an extremely important subject to evaluate securities with default risk. By Duffie and Singleton model, yield spread was explained by two factors, namely collection rate and default probability. An estimation of the collection rate is given from historical earnings data, but estimation of default probability is known to be a remaining problem.There are some approaches to express default probability. One of them is to describe it through hazard process, and the other is to represent it by risk neutral transition probability matrix of credit-rating class. Some models that use Gaussian type hazard process or Vasicek type hazard process have already constructed.An advantage of evaluation using a rating transition probability matrix is that it is easy to obtain an image of movement of the credit-rating class. We do not need to show the calculation basis of the threshold or an assumption for distribution of prospective yield spread. But the model that uses the risk neutral transition probability matrix has not established yet, because of the computational difficulty required to estimate large number of the parameters.At first, for the purposes of this article, we will estimate the term structure of credit spreads results from the possibility of future defaults. It is assumed that credit risk is specified as a discrete-state Markov chain. And we construct a model which can be used to estimate the baseline transition matrix of the credit-rating class, risk-adjusting factors, industrial drift factors, corporate drift factors and recovery ratio, from yield spreads for individual bond. This enables us to compute the implied term structure from market data. We are capable of computing the implied term structure from market date by this process. Next, we will provide a valuation model for the term structure of yield spread.     

Corporate Credit Spreads and the Sovereign Ceiling in Latin America

We exploit a panel of 72 US dollar-denominated bonds issued by Latin American publicly listed firms between 1996 and 2004, a period of regional financial crises, to answer the following three questions: (1) Is sovereign risk a statistically and economically significant determinant of the corporate credit spread, controlling for firm- and bond-specific characteristics? (2) If yes, do market participants apply the sovereign ceiling rule adopted by rating agencies in the pricing of our bond market data? And (3) how do market views compare with the rating agencies ceiling policy for each corporate bond? We find strong evidence of an economically and statistically significant effect of sovereign risk on corporate spreads across different panel econometric specifications and bonds. Moreover, markets do not apply the ceiling rule in 77–90% of the bonds we sample and these findings are consistent with rating agencies’ policies toward the latter for about 50% of the firms. These results are robust to the inclusion of firm- and bond-specific variables derived from the structural approach to credit risk and to the business cycle in each country.     

Estimating the term structures of corporate debt

This paper investigates the corporate bond market by estimating monthly interest rate term structures for investment grade credit classes using both S&P's and Moody's ratings. Term structures are modeled by a piecewise constant forward rate curve and estimated on noncallable coupon paying bonds issued by industrial firms. The iterative estimation algorithm minimizes the sum of squared errors between market prices and model prices while identifying and removing outliers from the sample. Although the forward rate model is successful at pricing corporate debt, additional factors are found to be significant at explaining the residual price error that remains after the forward rate model is fit to market prices. Six necessary no-arbitrage conditions are derived for the term structures of risky and risk-free debt. Occasionally, some of these no-arbitrage conditions are violated and a few violations are asymptotically statistically significant. Finally, trading strategies that capture mispricing in the corporate debt market and violations of no-arbitrage bounds are discussed.This paper was adapted from my dissertation, completed at Cornell University. An earlier version of this paper was titled The Term Structures of Corporate Debt. Thanks to participants at the Cornell University finance workshop, Warren Bailey, Peter Carr, Antoine Giannetti, and especially Robert Jarrow for their helpful comments.     

Determinants of yield spread dynamics: Euro versus US dollar corporate bonds

This paper presents a systematic comparison between the determinants of euro and US dollar yield spread dynamics. The results show that US dollar yield spreads are significantly more affected by changes in the level and the slope of the default-free term structure and the stock market return and volatility. Surprisingly, euro yield spreads are strongly affected by the US (and not the euro) level and slope. This confirms the dominance of US interest rates in the corporate bond markets. Interestingly, I find that liquidity risk is higher for US dollar corporate bonds than euro corporate bonds. For both regions, the effect of changes in the bid-ask spread is mainly significant during periods of high liquidity risk. Finally, the results indicate that the credit cycle as measured by the region-specific default probability significantly increases US yield spreads. This is not the case for euro yield spreads.     

Decomposing swap spreads

We analyze a six-factor model for Treasury bonds, corporate bonds, and swap rates and decompose swap spreads into three components: a convenience yield from holding Treasuries, a credit risk element from the underlying LIBOR rate, and a factor specific to the swap market. The convenience yield is by far the largest component of spreads. There is a discernible contribution from credit risk as well as from a swap-specific factor with higher variability which in certain periods is related to hedging activity in the mortgage-backed security market. The model also sheds light on the relation between AA hazard rates and the spread between LIBOR rates and General Collateral repo rates and on the level of the riskless rate compared to swap and Treasury rates.     

Credit Spread Changes and Equity Volatility: Evidence from Daily Data

We investigate the determinants of daily changes in credit spreads in the U.S. corporate bond market. Using a sample of liquid investment grade and high‐yield bonds, we show that both systematic bond and stock market factors as well as idiosyncratic equity market factors affect changes in the yield spread at the daily frequency. In particular, we find that increase in stock market volatility has a positive effect on changes in the spread of corporate bonds over the corresponding Treasuries beyond that captured by standard term structure variables. Our results show that there is an almost contemporaneous inverse relationship between changes in the bond yield spread and the stock return of the issuing firm.     

How much can illiquidity affect corporate debt yield spread?

We present a structural method for measuring the upper bound for the illiquidity risk of liabilities issued by a levered firm. The method calculates the upper bound of illiquidity spread of a corporate bond given its duration and the issuing firm’s asset risk and leverage ratio. Consistent with the empirical literature the illiquidity spread is positively related to the issuing firm’s asset risk and leverage ratio and the illiquidity component increases with a bond’s credit quality. The term structure of illiquidity spread has a humped shape, where its maximum level depends on the firm’s leverage ratio. Finally, we demonstrate how the method’s implied restricted trading period can be used as a measure for illiquidity in the bonds’ market.     

Tracking bond indices in an integrated market and credit risk environment

Abstract

The management of credit risky assets requires simulation models that integrate the disparate sources of credit and market risk, and suitable optimization models for scenario analysis. In this paper we integrate Monte Carlo simulation models for credit risk with scenario optimization, and develop a methodology for tracking broadly defined corporate bond indices. Testing of the models shows that the integration of the multiple risk factors improves significantly the performance of tracking models. Good tracking performance can be achieved by optimizing strategic asset allocation among broad classes of corporate bonds. However, extra value is generated with a tactical model that optimizes bond picking decisions as well. It is also shown that adding small corporate bond holdings in portfolios that track government bond indices improves the risk/return characteristics of the portfolios. The empirical results to substantiate the findings of this study are obtained by backtesting the model over a recent 30 month period.     

Asymptotic Expansion for Term Structures of Defaultable Bonds with Non-Gaussian Dependent Innovations

In the context of credit risk, the term structure models that have been studied in the literature are typically models driven by Brownian motion or standard jump diffusions. These models provide coherent modeling that is straightforward to implement. To make these models more flexible, we develop a discrete-time approximation of a continuous-time Vasicek term structure analysis with non-Gaussian and dependent innovations. Higher-order asymptotic theory enables us to evaluate the term structures of defaultable bonds. Numerical examples show that the effects of non-Gaussianity and the dependency of both risk-free rate and default process strongly influence the evaluation of defaultable bonds. As an application, we estimate the parameters of our proposed models for the Japanese corporate credit default swap market.     

Illiquidity or credit deterioration: A study of liquidity in the US corporate bond market during financial crises

We investigate whether liquidity is an important price factor in the US corporate bond market. In particular, we focus on whether liquidity effects are more pronounced in periods of financial crises, especially for bonds with high credit risk, using a unique data set covering more than 20,000 bonds, between October 2004 and December 2008. We employ a wide range of liquidity measures and find that liquidity effects account for approximately 14% of the explained market-wide corporate yield spread changes. We conclude that the economic impact of the liquidity measures is significantly larger in periods of crisis, and for speculative grade bonds.     

Modelling multiple term structures of defaultable bonds with common and idiosyncratic state variables

In this paper we develop a multi-factor “reduced-form” model that is general enough to capture simultaneously the dynamics of multiple term structures of corporate bonds, each with a different credit rating. In this way, we are able to fully incorporate a number of “stylised facts”, reported on a number of previous empirical studies. More specifically, we are able to estimate the different degrees of covariation between the term structure of each credit rating and the default-free yield curve. Furthermore, we report the differing sensitivities of the credit curves to a number of observable macro-factors that reflect changes in credit conditions, both domestic and international. Finally, the dependence of each credit curve on a number of idiosyncratic state-variables is also documented. Our results are based on two special cases of the model, estimated using US and UK corporate bond data.     

What determines the Japanese corporate credit spread? A new evidence

This paper investigates the determinants of the corporate credit spreads changes in the Japanese bond markets. We show that the business cycle risk and market skewness risk affect changes in the credit spread in Japan even after controlling for the frequently used variables. We also find that the magnitude of market skewness risk is relatively higher for low-rated bonds. Our results are robust to changes in credit ratings, different maturity groups and time periods around the recent global financial crisis.