The Term Structure of Credit Spreads: Theory and Evidence on Credit Default Swaps
TL;DR: In this paper, a joint analysis of the term structure of interest rates, credit spreads, and liquidity premia is performed using a large data set on credit default swaps, where reference companies fall into two broad industry sectors and two broad credit rating classes.
Abstract: Using a large data set on credit default swaps, we perform a joint analysis of the term structure of interest rates, credit spreads, and liquidity premia. We select reference companies that fall into two broad industry sectors and two broad credit rating classes. Within each sector and credit rating class, we divide the companies into two liquidity groups based on the quote updating frequency. We then study how the term structures of credit default risk premia differ across industry sectors, credit rating classes, and liquidity groups.
We develop a class of dynamic term structure models that include two benchmark interest-rate factors, two credit risk factors for the high-liquidity groups, and an additional default risk factor and a liquidity risk factor that capture the difference between the two liquidity groups. We link these factors to the instantaneous benchmark interest rate and credit spread via both an affine function and a quadratic function, and compare their relative performance.
We estimate the models using a three-step procedure. First, we estimate the interest-rate factor dynamics and the instantaneous interest rate function using the libor and swap rates. Second, we take the interest-rate factors and estimate the default-risk dynamics and the instantaneous credit spread function using the average credit default spreads of the high-liquidity group for each industry sector and credit rating class. Third, we identify an additional credit risk factor and a liquidity risk factor using the credit default swap spreads in the low-liquidity group. At each step, we cast the models into a state-space form and estimate the model parameters using quasi-maximum likelihood method.
Estimation shows that the quadratic specifications generate better and more uniform performance across the term structure of interest rates and credit spreads. Furthermore, firms in different industry and credit rating classes have different default risk dynamics. Nevertheless, in all cases, default risks exhibit intricate dynamic interactions with the interest-rate factors. Interest-rate factors both predict the default risk and have a contemporaneous impact on it.
Within each industry and credit rating class, the average credit default swap spreads for the high-liquidity group are significantly higher than for the low-liquidity group. Estimation shows that the difference is driven by both default risk and liquidity difference. The low-liquidity group has a lower default arrival rate, and also a much heavier discounting due to low liquidity.
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01 Dec 2001
TL;DR: In this article, the authors analyze the components of corporate credit spreads and conclude that default risk may represent only a small portion of the total corporate credit spread, but is mainly attributed to taxes, jumps, liquidity, and market risk factors.
Abstract: This paper analyzes the components of corporate credit spreads. The analysis is based on a structural model that can offer a framework to understand the decomposition. The paper contends that default risk may correctly represent only a small portion of corporate credit spreads. This idea stems both from empirical evidence and from the following theoretical assumptions underlying contingent claim models of default: that markets for corporate stocks and bonds are (i) perfect, (ii) complete, and (iii) trading takes place continuously. Thus, in these models there are no transaction or bankruptcy costs, no tax effects, no liquidity effects, no jump effects reflecting market incompleteness, and no market risk factors effecting the pricing of corporate stocks or bonds. The paper starts with the use of a modified version of the Black-Scholes-Merton diffusion based option approach. We estimate corporate default spreads as simply a component of corporate credit spreads using data from November 1991 to December 1998, which includes the Asian Crisis in the Fall, 1998. First we measure the difference between the observed corporate credit spreads and option based estimates of default spreads. We define this difference as the residual spread. We show that for AAA (BBB) firms only a small percentage, 5% (22%), of the credit spread can be attributed to default risk. We show that recovery risk also cannot explain this residual spread. Next, we show that state taxes on corporate bonds also cannot explain the residual. We note that the pure diffusion assumption may lead to underestimates of the default risk. In order to include jumps to default, we next estimate what combined jump-diffusion parameters would be necessary to force default spread to eliminate the residual spread. In each rating class on average firms would be required to experience annual jumps that decrease firm value by 20% and increase stock volatility by more than 100% over their observed volatility in order to eliminate the residual spread. We consider this required increase in stock volatility to be unrealistic as the sole explanation of the residual spread. So next we consider whether the unexplained component can be partly attributable to interest rates, liquidity, and market risk factors. We find the following empirical results: i) increases in liquidity as measured by changes in each firm’s trading volume significantly reduces the residual spread, but does not alter the default spread; ii) increases in stock market volatility significantly reduces the residual spread by increasing the default spread relative to the credit spread, and iii) increases in stock market returns significantly increases the residual spread by reducing the default spread relative to the credit spread. This paper concludes that credit risk and credit spreads are not primarily explained by default and recovery risk, but are mainly attributable to taxes, jumps, liquidity, and market risk factors.
223 citations
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TL;DR: In this article, the authors investigated a family of credit risk models driven by a two-factor structure for the short-interest rate and an additional third factor for firm-specific distress, using the reduced-form framework of Duffie and Singleton (1999).
Abstract: This paper proposes and empirically investigates a family of credit risk models driven by a two-factor structure for the short-interest rate and an additional third factor for firm-specific distress, using the reduced-form framework of Duffie and Singleton (1999). The set of firm-specific distress factors analyzed in the study include leverage, book-to-market, profitability, equity-volatility, and distance-to-default. Our estimation approach and performance yardsticks show that interest rate risk is of first-order importance for explaining variations in single-name defaultable coupon bond yields and credit spreads. When applied to low-grade bonds, a credit risk model that takes leverage into consideration reduces absolute yield mispricing by as much as 30% relative to a competing model that ignores leverage. None of the distress factors improve performance for high-grade bonds. A strategy relying on traded Treasury instruments is surprisingly effective in dynamically hedging credit exposures for firms in our sample.
116 citations
TL;DR: In this paper, the authors propose and empirically investigate a family of credit risk models driven by a two-factor structure for the short interest rate and an additional factor for firm-specific distress.
Abstract: This paper proposes and empirically investigates a family of credit risk models driven by a two‐factor structure for the short interest rate and an additional factor for firm‐specific distress. The firm‐specific distress factors include leverage, book‐to‐market, profitability, equity‐volatility, and distance‐to‐default. Our estimation approach and performance yardsticks show that interest rate risk is of first‐order importance for explaining variations in single‐name defaultable bond yields. When applied to low‐grade bonds, a credit risk model that takes leverage into consideration reduces absolute yield mispricing by as much as 30%. A strategy relying on Treasury instruments is effective in dynamically hedging credit exposures.
91 citations
Posted Content•
TL;DR: This article examined the pricing of Asian and non-Asian credit default swaps that traded during the 1997 to 1999 time period, and found negative economic values for Asian CDS during the recent Asian currency crisis, which they attribute to moral hazard.
Abstract: We examine the pricing of Asian and non-Asian credit default swaps that traded during the 1997 to 1999 time period. We employ two credit risk models, Duffie and Singleton (1999) and Jarrow and Turnbull (1995). We argue that credit default swaps should have a positive economic value since credit spreads reflect differences in liquidity as well as credit risk. However, in the presence of moral hazard we expect to see negative economic values since asymmetric information would motivate sellers of credit default swaps to demand a “restructuring premium”. While we generally find positive economic values for credit default swaps, both models find negative economic values for Asian credit default swaps during the recent Asian currency crisis, which we attribute to moral hazard.
5 citations
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TL;DR: In this article, a simple method of calculating a heteroskedasticity and autocorrelation consistent covariance matrix that is positive semi-definite by construction is described.
Abstract: This paper describes a simple method of calculating a heteroskedasticity and autocorrelation consistent covariance matrix that is positive semi-definite by construction. It also establishes consistency of the estimated covariance matrix under fairly general conditions.
18,117 citations
"The Term Structure of Credit Spread..." refers methods in this paper
...The standard deviatio n calculation adjusts for serial dependence according to Newey and West (1987), with the number of lag s chosen optimally according to Andrews (1991) based on an AR(1) specification....
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...The standard deviation calculation adjusts for serial dependence according to Newey and West (1987), with the number of lags chosen optimally according to Andrews (1991) based on an AR(1) specification....
[...]
Posted Content•
TL;DR: In this article, a simple method of calculating a heteroskedasticity and autocorrelation consistent covariance matrix that is positive semi-definite by construction is described.
Abstract: This paper describes a simple method of calculating a heteroskedasticity and autocorrelation consistent covariance matrix that is positive semi-definite by construction. It also establishes consistency of the estimated covariance matrix under fairly general conditions.
5,822 citations
TL;DR: In this article, the authors propose simple and directional likelihood-ratio tests for discriminating and choosing between two competing models whether the models are nonnested, overlapping or nested and whether both, one, or neither is misspecified.
Abstract: In this paper, we propose a classical approach to model selection. Using the Kullback-Leibler Information measure, we propose simple and directional likelihood-ratio tests for discriminating and choosing between two competing models whether the models are nonnested, overlapping or nested and whether both, one, or neither is misspecified. As a prerequisite, we fully characterize the asymptotic distribution of the likelihood ratio statistic under the most general conditions.
5,661 citations
"The Term Structure of Credit Spread..." refers methods in this paper
...Nevertheless, we follow Vuong (1989) in constructing a statistic based on the difference between the daily log likelihood values from the two non-nested models: lr t = l Q t − lAt (38) wherelQt andl A t denote the time-t log likelihood value of the quadratic and affine models, respectively....
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...The one-factor quadratic model also generates higher likelihood values than the corresponding affine model for each of the four industry sector and credit rating classes, but the differences are not statistically significant in terms of the Vuong (1989) statistic....
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TL;DR: Using these results, data-dependent automatic bandwidth/lag truncation parameters are introduced and asymptotically optimal kernel/weighting scheme and bandwidth/agreement parameters are obtained.
Abstract: This paper is concerned with the estimation of covariance matrices in the presence of heteroskedasticity and autocorrelation of unknown forms. Currently available estimators that are designed for this context depend upon the choice of a lag truncation parameter and a weighting scheme. Results in the literature provide a condition on the growth rate of the lag truncation parameter as T \rightarrow \infty that is sufficient for consistency. No results are available, however, regarding the choice of lag truncation parameter for a fixed sample size, regarding data-dependent automatic lag truncation parameters, or regarding the choice of weighting scheme. In consequence, available estimators are not entirely operational and the relative merits of the estimators are unknown. This paper addresses these problems. The asymptotic truncated mean squared errors of estimators in a given class are determined and compared. Asymptotically optimal kernel/weighting scheme and bandwidth/lag truncation parameters are obtained using an asymptotic truncated mean squared error criterion. Using these results, data-dependent automatic bandwidth/lag truncation parameters are introduced. The finite sample properties of the estimators are analyzed via Monte Carlo simulation.
4,219 citations
"The Term Structure of Credit Spread..." refers methods in this paper
...The standard deviation calculation adjusts for serial dependence according to Newey and West (1987), with the number of lags chosen optimally according to Andrews (1991) based on an AR(1) specification....
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TL;DR: In this paper, a reduced-form model of the valuation of contingent claims subject to default risk is presented, focusing on applications to the term structure of interest rates for corporate or sovereign bonds and the parameterization of losses at default in terms of the fractional reduction in market value that occurs at default.
Abstract: This article presents convenient reduced-form models of the valuation of contingent claims subject to default risk, focusing on applications to the term structure of interest rates for corporate or sovereign bonds. Examples include the valuation of a credit-spread option. This article presents a new approach to modeling term structures of bonds and other contingent claims that are subject to default risk. As in previous “reduced-form” models, we treat default as an unpredictable event governed by a hazard-rate process. 1 Our approach is distinguished by the parameterization of losses at default in terms of the fractional reduction in market value that occurs at default. Specifically, we fix some contingent claim that, in the event of no default, pays X at time T . We take as given an arbitrage-free setting in which all securities are priced in terms of some short-rate process r and equivalent martingale measure Q [see Harrison and Kreps (1979) and Harrison and Pliska (1981)]. Under this “risk-neutral” probability measure, we letht denote the hazard rate for default at time t and let Lt denote the expected fractional loss in market value if default were to occur at time t , conditional
2,589 citations
"The Term Structure of Credit Spread..." refers methods or result in this paper
...We value the credit default swap spread using the reduced-form framework of Duffie (1998), Lando (1998), Duffie and Singleton (1997), Duffie and Singleton (1999), and Duffie,P dersen, and Singleton (2003)....
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...Following Duffie (1998), Lando (1998), and Duffie and Singleton (1999), we can represent the value of a defaultable coupon-bond in terms of the benchmark instantaneous interest rater and the Poisson intensity λ of the default arrival: CB(c,w,τ) = E [ c ∫ τ 0 exp ( − ∫ t 0 (ru…...
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...They compare the pricing results of the Duffie and Singleton (1999) and Jarrow nd Turnbull (1995) models....
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