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 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.     

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.     

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.     

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.     

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.     

Market conditions,default risk and credit spreads

This study empirically examines the impact of the interaction between market and default risk on corporate credit spreads. Using credit default swap (CDS) spreads, we find that average credit spreads decrease in GDP growth rate, but increase in GDP growth volatility and jump risk in the equity market. At the market level, investor sentiment is the most important determinant of credit spreads. At the firm level, credit spreads generally rise with cash flow volatility and beta, with the effect of cash flow beta varying with market conditions. We identify implied volatility as the most significant determinant of default risk among firm-level characteristics. Overall, a major portion of individual credit spreads is accounted for by firm-level determinants of default risk, while macroeconomic variables are directly responsible for a lesser portion.     

Factors affecting the yields of emerging market issuers: Evidence from the Asia-Pacific region

We investigate the yield spread between the sovereign bonds issued in international markets by major Asia-Pacific issuers (China, Korea, Malaysia, Philippines and Thailand) and matched with near maturity benchmark U.S. Treasury bonds (2, 5, 10 year maturities) to determine the extent that various factors affect changes in credit spreads. The results suggest that the credit spreads of these sovereign bonds tend to be negatively related to changes in interest rates on U.S. benchmark bonds and positively related to changes in the slope of the yield curve. The asset and exchange rate variables were only significant for spreads on Philippine bonds where it was negatively related to changes in the local stock market index, and positively to changes in the exchange rate. The complex dynamics of these processes highlight concerns for portfolio mangers when constructing portfolios of sovereign Asian bonds by aggregating bonds of different credit ratings.     

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.     

The analytic pricing of asymmetric defaultable swaps

Swaps where both parties are exposed to credit risk still lack convincing pricing mechanisms. This article presents a reduced-form model where the event of default is related to structural characteristics of each party. The cash flows submitted to credit risk are identified before the swap is priced. Analytical pricing formulas for interest rate and currency swaps are computed using a Gaussian model for risky bonds. Currency swaps exhibit additional correlation risk. The benefits from netting depend on the balance between exposures and market conditions in valuation. We show that sources of credit risk asymmetries are also likely to impact on credit spreads.     

Hedging in the Possible Presence of Unspanned Stochastic Volatility: Evidence from Swaption Markets

This paper examines whether higher order multifactor models, with state variables linked solely to underlying LIBOR‐swap rates, are by themselves capable of explaining and hedging interest rate derivatives, or whether models explicitly exhibiting features such as unspanned stochastic volatility are necessary. Our research shows that swaptions and even swaption straddles can be well hedged with LIBOR bonds alone. We examine the potential benefits of looking outside the LIBOR market for factors that might impact swaption prices without impacting swap rates, and find them to be minor, indicating that the swaption market is well integrated with the LIBOR‐swap market.     

THE CHALLENGE OF MANAGING CREDIT SPREADS: NEW TOOLS ON THE HORIZON

Broadly speaking, "credit spread" is the excess of a bond's yield over the appropriate Treasury rate that is necessary to compensate lenders for the perceived risk of default. In the primary market, credit spreads can significantly increase a corporation's borrowing cost. In the secondary market, the effect of fluctuating spreads is of material concern to investors and traders.
Credit spreads have exhibited considerable volatility in recent years, particularly during the fall of 1998. Although the absolute levels of spreads have ranged widely in recent years, from a few basis points to several hundred depending on rating category, their volatilities have been remarkably similar—about 25 to 39% on an annual basis. In spite of this high volatility, there are currently no cost-effective means of hedging credit spreads.
The recently announced S&P Credit Indices presage a leap forward in credit derivatives. Computed from the prices of selected liquid bonds, these indices can serve as a basis for exchange-traded futures contracts and options—tools that are in great demand for managing credit spread exposure.     

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.     

LIBOR and swap market models and measures

A self-contained theory is presented for pricing and hedging LIBOR and swap derivatives by arbitrage. Appropriate payoff homogeneity and measurability conditions are identified which guarantee that a given payoff can be attained by a self-financing trading strategy. LIBOR and swap derivatives satisfy this condition, implying they can be priced and hedged with a finite number of zero-coupon bonds, even when there is no instantaneous saving bond. Notion of locally arbitrage-free price system is introduced and equivalent criteria established. Stochastic differential equations are derived for term structures of forward libor and swap rates, and shown to have a unique positive solution when the percentage volatility function is bounded, implying existence of an arbitrage-free model with such volatility specification. The construction is explicit for the lognormal LIBOR and swap “market models”, the former following Musiela and Rutkowski (1995). Primary examples of LIBOR and swap derivatives are discussed and appropriate practical models suggested for each.     

What drives the cost of US dollar bond funding for banks?

This paper decomposes issue spreads on US dollar-denominated bonds issued by LIBOR panel banks into credit risk and liquidity premium components. We attribute the recent increase in issue spreads to the investor perception that banks are less creditworthy than in the past. Although the behaviour of the credit risk component is well-explained by a structural model of default, this mechanism is nullified by the introduction of government guarantees. The behaviour of the liquidity premium component is partially explained by the bid/ask spread in the secondary market and issue size. Government guarantees also reduce the liquidity component of the issue spread.     

Correlation in credit risk changes

The current economic climate makes understanding credit risk correlation particularly important. After allowing for a comprehensive set of observable firm-specific, industry, market, and macroeconomic factors, there is an economically significant co-movement in credit default swap spreads that remains to be explained. Including a time dummy completely accounts for the remaining co-movement, confirming the existence of a systematic component that has been previously unaccounted for. Our findings suggest that it may be important to consider unobservable risk factor(s) in credit risk models.     

The term structure of interbank risk

We infer a term structure of interbank risk from spreads between rates on interest rate swaps indexed to the London Interbank Offered Rate (LIBOR) and overnight indexed swaps. We develop a tractable model of interbank risk to decompose the term structure into default and non-default (liquidity) components. From August 2007 to January 2011, the fraction of total interbank risk due to default risk, on average, increases with maturity. At short maturities, the non-default component is important in the first half of the sample period and is correlated with measures of funding and market liquidity. The model also provides a framework for pricing, hedging, and risk management of interest rate swaps in the presence of significant basis risk.     

Generic market models

Currently, there are two market models for valuation and risk management of interest rate derivatives: the LIBOR and swap market models. We introduce arbitrage-free constant maturity swap (CMS) market models and generic market models featuring forward rates that span periods other than the classical LIBOR and swap periods. We develop generic expressions for the drift terms occurring in the stochastic differential equation driving the forward rates under a single pricing measure. The generic market model is particularly apt for pricing of, e.g., Bermudan CMS swaptions and fixed-maturity Bermudan swaptions.     

The impact of central clearing on counterparty risk,liquidity, and trading: Evidence from the credit default swap market

This paper examines the impact of central clearing on the credit default swap (CDS) market using a sample of voluntarily cleared single-name contracts. Consistent with central clearing reducing counterparty risk, CDS spreads increase around the commencement of central clearing and are lower than settlement spreads published by the central clearinghouse. Furthermore, the relation between CDS spreads and dealer credit risk weakens after central clearing begins, suggesting a lowering of systemic risk. These findings are robust to controls for frictions in both CDS and bond markets. Finally, matched sample analysis reveals that the increased post-trade transparency following central clearing is associated with an improvement in liquidity and trading activity.