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.     

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.     

An Econometric Model of the Term Structure of Interest-Rate Swap Yields

This article develops a multi-factor econometric model of the term structure of interest-rate swap yields. The model accommodates the possibility of counterparty default, and any differences in the liquidities of the Treasury and Swap markets. By parameterizing a model of swap rates directly, we are able to compute model-based estimates of the defaultable zero-coupon bond rates implicit in the swap market without having to specify a priori the dependence of these rates on default hazard or recovery rates. The time series analysis of spreads between zero-coupon swap and treasury yields reveals that both credit and liquidity factors were important sources of variation in swap spreads over the past decade.     

The market for credit default swaps: new insights into investors' use of accounting information?

The market for credit default swaps has developed into a well‐functioning, global multi‐trillion dollar market, wherein investors price and transfer corporate financial instruments on the basis of credit risk. This paper first summarizes the structure and growth of the market. Next, I introduce theory and evidence on how investors price credits risk and explain how the quality of financial statement information plays a unique role in the determination of credit spread. I then review the nascent empirical accounting literature on this topic. This review sheds light on several accounting research questions that might be understood better in the setting of the credit default swap market. The final section summarizes suggestions for future work.     

A reduced form model of default spreads with Markov-switching macroeconomic factors

We examine the ability of observed macroeconomic factors and the possibility of changes in regime to explain the proportion of yield spreads caused by the risk of default in the context of a reduced form model. For this purpose, we extend the Markov-switching risk-free term structure model of Bansal and Zhou (2002) to the corporate bond setting and develop recursive formulas for default probabilities, risk-free and risky zero-coupon bond yields as well as credit default swap premia. The model is calibrated with consumption, inflation, risk-free yields and default data for Aa, A and Baa bonds from the 1987 to 2008 period. We find that our macroeconomic factors are linked with two out of three sharp increases in the spreads during this sample period, indicating that the spread variations can be related to macroeconomic undiversifiable risk.     

The dynamics of sovereign yields over swap rates in the Eurozone market

We explore the dynamics of the adjusted swap spread (calculated as the difference between the swap rate and sovereign yields over the credit default swap premium) in the Eurozone market by studying three markets simultaneously: 1) sovereign bonds, 2) credit default swaps (CDS), and 3) swap rates. We find a strong relationship between the markets. Specifically, based on the no-arbitrage argument, we show that the difference between the Euribor and Repo rates is a key driver of the adjusted swap spread. However, illiquidity premiums and systemic risk also play an essential role in times of economic stress and for less creditworthy countries. The findings also shed light on the recent negative swap spreads puzzle in the United States.     

Modelling bonds and credit default swaps using a structural model with contagion

This paper develops a two-dimensional structural framework for valuing credit default swaps and corporate bonds in the presence of default contagion. Modelling the values of related firms as correlated geometric Brownian motions with exponential default barriers, analytical formulae are obtained for both credit default swap spreads and corporate bond yields. The credit dependence structure is influenced by both a longer-term correlation structure as well as by the possibility of default contagion. In this way, the model is able to generate a diverse range of shapes for the term structure of credit spreads using realistic values for input parameters.     

Understanding liquidity and credit risks in the financial crisis

This paper develops a structured dynamic factor model for the spreads between London Interbank Offered Rate (LIBOR) and overnight index swap (OIS) rates for a panel of banks. Our model involves latent factors which reflect liquidity and credit risk. Our empirical results show that surges in the short term LIBOR-OIS spreads during the 2007-2009 financial crisis were largely driven by liquidity risk. However, credit risk played a more significant role in the longer term (twelve-month) LIBOR-OIS spread. The liquidity risk factors are more volatile than the credit risk factor. Most of the familiar events in the financial crisis are linked more to movements in liquidity risk than credit risk.     

A comparison of the information in the LIBOR and CMT term structures of interest rates

We investigate the information contained in the London Interbank Offered Rate (LIBOR) and the U.S. Constant Maturity Treasury (CMT) term structure of interest rates and report three novel findings. First, we document that the information contained in term structures are significantly different from one another. Second, we provide evidence of a significant change in the nature of this difference as the financial crisis began. Third, we find that the significant changes in the information content of CMT and LIBOR are consistent with significant shocks to credit default swap rates and tenor swap rates.     

The increasing default risk of US Treasury securities due to the financial crisis

This paper examines the impact of the current financial crisis on long-term US Treasury yields by testing the impact of a series of events from December 2007 to March 2009 on the spread between 10-year USD LIBOR swap and 10-year US Treasury (constant maturity) rates to measure risk associated with Treasuries. Controlling for the liquidity of the two markets, the default risk of the swap, and the net foreign purchases of Treasury securities, we find that 13 of the tested 20 events have significantly negative coefficients. We conclude that the lower spread is consistent with greater default risk for US Treasury securities.     

Modeling volatility and changes in the swap spread

We investigate the determinants of changes in U.S. interest rate swap spreads using a model that explicitly allows for volatility interactions between swaps of different terms to maturity. Changes in the swap spread are found to be positively related to interest rate volatility, to changes in the default risk premium in the corporate bond market, and to changes in the liquidity premium for government securities. Swap spread changes are negatively related to changes in the level of interest rates and changes in the slope of the term structure. We also find that there is a strong and significant volatility interaction among spreads for swaps of different maturities and that the process for the conditional variance of the spread is highly persistent across all 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 Impact of Collateralization on Swap Rates

Interest rate swap pricing theory traditionally views swaps as a portfolio of forward contracts with net swap payments discounted at LIBOR rates. In practice, the use of marking‐to‐market and collateralization questions this view as they introduce intermediate cash flows and alter credit characteristics. We provide a swap valuation theory under marking‐to‐market and costly collateral and examine the theory's empirical implications. We find evidence consistent with costly collateral using two different approaches; the first uses single‐factor models and Eurodollar futures prices, and the second uses a formal term structure model and Treasury/swap data.     

A first-passage-time model under regime-switching market environment

In this paper, we suggest a first-passage-time model which can explain default probability and default correlation dynamics under stochastic market environment. We add a Markov regime-switching market condition to the first-passage-time model of Zhou [Zhou, C., 2001. An analysis of default correlations and multiple defaults. Review of Financial Studies 14, 555–576]. Using this model, we try to explain various relationship between default probability, default correlation, and market condition. We also suggest a valuation method for credit default swap (CDS) with (or without) counterparty default risk (CDR) and basket default swap under this model.Our numerical results provide us with several meaningful implications. First, default swap spread is higher in economic recession than in economic expansion across default swap maturity. Second, as the difference of asset return volatility between under bear market and under bull market increases, CDS spread increases regardless of maturity. Third, the bigger the intensity shifting from bull market to bear market, the higher the spread for both CDS without CDR and basket default swap.     

The cost of bank loans in relation to bonds swapped into a floating rate

Banks never lend at less than the interbank floating rate, LIBOR. We argue that this must be because it is insufficiently profitable for those that could lend at less than LIBOR to do so and discuss circumstances in which this would be the case. Using data from 1988–1991, we show that LIBOR varies in relation to the cost of corporate bonds swapped into a floating rate, and suggest that the relative cost of LIBOR may affect bank and bond market pricing policies. the data also indicates that changes in the compensation for credit risk demanded by the bank and bond markets are not synchronous, and that swap rates have an appreciable impact on the cost of bonds swapped into floating.     

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.     

Pricing default swaps: Empirical evidence

In this paper we compare market prices of credit default swaps with model prices. We show that a simple reduced form model outperforms directly comparing bonds' credit spreads to default swap premiums. We find that the model yields unbiased premium estimates for default swaps on investment grade issuers, but only if we use swap or repo rates as proxy for default-free interest rates. This indicates that the government curve is no longer seen as the reference default-free curve. We also show that the model is relatively insensitive to the value of the assumed recovery rate.     

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.     

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 bond default risk: A 150-year perspective

We study corporate bond default rates using an extensive new data set spanning the 1866-2008 period. We find that the corporate bond market has repeatedly suffered clustered default events much worse than those experienced during the Great Depression. For example, during the railroad crisis of 1873-1875, total defaults amounted to 36% of the par value of the entire corporate bond market. Using a regime-switching model, we examine the extent to which default rates can be forecast by financial and macroeconomic variables. We find that stock returns, stock return volatility, and changes in GDP are strong predictors of default rates. Surprisingly, however, credit spreads are not. Over the long term, credit spreads are roughly twice as large as default losses, resulting in an average credit risk premium of about 80 basis points. We also find that credit spreads do not adjust in response to realized default rates.