Exploring the components of credit risk in credit default swaps

In this paper, we test the influence of various fundamental variables on the pricing of credit default swaps. The theoretical determinants that are important for pricing credit default swaps include the risk-free rate, industry sector, credit rating, and liquidity factors. We suggest a linear regression model containing these different variables, especially focusing on liquidity factors. Unlike bond spreads which have been shown to be inversely related to liquidity (i.e., the greater the liquidity, the lower the spread), there is no a priori reason that the credit default swap spread should exhibit the same relationship. This is due to the economic characteristics of a credit default swap compared to a bond. Our empirical result shows that all the fundamental variables investigated have a significant effect on the credit default swap spread. Moreover, our findings suggest that credit default swaps that trade with greater liquidity have a wider credit default swap spread.     

A mathematical model for multi-name credit based on community flocking

We present a new mathematical model for multi-name credit that employs stochastic flocking. Flocking mechanisms have been used in a variety of models of biological, sociological and physical aggregation phenomena. As a direct application of a flocking mechanism, we introduce a credit risk model based on community flocking for a credit worthiness index. Correlations between different credit worthiness indices are explained in terms of communication rates and coupling strengths from the flocking system. Based on the flocking model, we compute credit curves for individual names and default time distributions. We also apply the proposed model to the pricing of credit derivatives such as credit default swaps and collateralized debt obligations.     

Counterparty Risk for Credit Default Swaps: Markov Chain Interacting Intensities Model with Stochastic Intensity

We analyze the counterparty risk for credit default swaps using the Markov chain model of portfolio credit risk of multiple obligors with interacting default intensity processes. The default correlation between the protection seller and underlying entity is modeled by an increment in default intensity upon the occurrence of an external shock event. The arrival of the shock event is a Cox process whose stochastic intensity is assumed to follow an affine diffusion process with jumps. We examine how the correlated default risks between the protection seller and the underlying entity may affect the credit default premium in a credit default swap.     

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.     

Analysis of Credit Risks in Asset-Backed Securitization Transactions in Singapore

Asset-backed securitization (ABS) is a relatively new financial instrument in Singapore's capital market, which has been accepted by developers (originators) as an alternative source of financing. Credit assessment and rating requirements have not been imposed on the ABS bond issues. Default-risk evaluation has also been understated, if not omitted, in the process of structuring ABS deals. This is the first study that applies a theoretical default-risky swaps valuation model to evaluate credit risks in ABS bonds in Singapore. The Monte-Carlo simulation results, based on the Century Square shopping mall ABS case, show significant effects of the changes in rental volatility and default-free interest rate volatility on the default-risk premium of swap. More specifically, an increase in the rental volatility reduces the default-risky swap values significantly. However, an increase in the instantaneous default-free interest rate volatility increases the default-risk premium of swaps, and this effect is only observed in the high default-free interest rate volatility regime (above 20 percent). The results suggest that the rental dynamics of the securitized real estate are critical in determining the default risks of ABS deals. The fixed-rate (coupon yield) and floating-rate (rental cash flows) should therefore be adequately determined to reflect the default risks, which may be caused by the rental dynamics of the securitized real estate.     

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.     

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.     

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.     

The Default Risk of Swaps

We characterize the exchange of financial claims from risky swaps. These transfers are among three groups: shareholders, debtholders, and the swap counterparty. From this analysis we derive equilibrium swap rates and relate them to debt market spreads. We then show that equilibrium swaps in perfect markets transfer wealth from shareholders to debtholders. In a simplified case, we obtain closed-form solutions for the value of the default risk in the swap. For interest-rate swaps, we obtain numerical solutions for the equilibrium swap rate, including default risk. We compare these with equilibrium debt market default risk spreads.     

How well do classical credit risk pricing models fit swap transaction data?

Currency and interest rate swaps are subject to a complex, two-sided default risk. Several theoretical papers have recently addressed the problem of pricing this swap credit risk. We implement a recent credit risk pricing model in an attempt to evaluate one of the main lines of research in theoretical credit risk analysis. We compare the model's analytical results to actual transaction data thanks to a unique academic database on swap transaction data.     

Hedging of a credit default swaption in the CIR default intensity model

An important issue arising in the context of credit default swap (CDS) rates is the construction of an appropriate model in which a family of options written on credit default swaps, referred to hereafter as credit default swaptions, can be valued and hedged. The goal of this work is to exemplify the usefulness of some abstract hedging results, which were obtained previously by the authors, for the valuation and hedging of the credit default swaption in a particular hazard process setup, namely, the CIR default intensity model.     

American step-up and step-down default swaps under Lévy models

This paper studies the valuation of a class of default swaps with the embedded option to switch to a different premium and notional principal anytime prior to a credit event. These are early exercisable contracts that give the protection buyer or seller the right to step-up, step-down, or cancel the swap position. The pricing problem is formulated under a structural credit risk model based on Lévy processes. This leads to the analytic and numerical studies of several optimal stopping problems subject to early termination due to default. In a general spectrally negative Lévy model, we rigorously derive the optimal exercise strategy. This allows for instant computation of the credit spread under various specifications. Numerical examples are provided to examine the impacts of default risk and contractual features on the credit spread and exercise strategy.     

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.     

Empirical credit cycles and capital buffer formation

We model 1927–1997 US business failure rates using an unobserved components time series model. Clear evidence is found of cyclical behavior in default rates. We also detect significant longer term movements in default rates and default correlations. In a multi-year backtest experiment we show that accommodation of default rate dynamics has important consequences for credit risk capitalization requirements. Static or myopic variants of credit portfolio models miss significant periods of credit risk accumulation. Empirically congruent dynamic models by contrast provide more timely warning signals of credit risk build-up. In this way they may mitigate some of the pro-cyclicality concerns.     

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.     

Credit Derivatives and the Default Risk of Large Complex Financial Institutions

This paper proposes and implements a multivariate model of the coevolution of the first and second moments of two broad credit default swap indices and the equity prices of sixteen large complex financial institutions. We use this empirical model to build a bank default risk model, in the vein of the classic Merton-type, which utilises a multi-equation framework to model forward-looking measures of market and credit risk using the credit default swap (CDS) index market as a measure of the conditions of the global credit environment. In the first step, we estimate the dynamic correlations and volatilities describing the evolution of the CDS indices and the banks’ equity prices and then impute the implied assets and their volatilities conditional on the evolution and volatility of equity. In the second step, we show that there is a substantial ‘asset shortfall’ and that substantial capital injections and/or asset insurance are required to restore the stability of our sample institutions to an acceptable level following large shocks to the aggregate level of credit risk in financial markets.     

The sensitivity of the credit default swap market to financial analysts’ forecast revisions

We examine the impact of analysts’ earnings per share (EPS) and cash flow per share (CPS) forecast revisions on the market for credit default swaps. We find that while the issuance of both EPS and CPS forecast revisions are inversely associated with changes in credit default swap (CDS) spreads, cash flow forecast revisions have a larger effect. We demonstrate that the relationship between CPS forecast revisions and CDS spreads tends to be stronger in cases of financial distress. We provide evidence that cash flow forecasts dominate earnings forecasts in some situations and that participants in the CDS market discriminate between analysts' forecast revisions and recommendation changes.     

Computing the survival probability in the Madan–Unal credit risk model: application to the CDS market

We obtain a quasi-analytical approximation of the survival probability in the credit risk model proposed in [Madan, D.B. and Unal, H., Pricing the risk of default. Rev. Deriv. Res., 1998, 2(2), 121–160]. Such a formula, which extensive numerical simulations reveal to be accurate and computationally fast, can also be employed for pricing credit default swaps (CDSs). Specifically, we derive a quasi-analytical approximate expression for CDS par spreads, and we use it to estimate the parameters of the model. The results obtained show a rather satisfactory agreement between theoretical and real market data.     

Covered interest parity with default risk

In this paper we derive a simple model of covered interest parity (CIP) with the assumption that interbank money market rates are risky. The model assumes that the default risk of uncollateralised loans can be hedged perfectly by credit default swap contracts. We show that the no-arbitrage condition is satisfied by a band. The location of this no-arbitrage band depends on the relative riskiness of the two counterparties in the CIP trade. We present evidence on the performance of the model for developed currency pairs in 2008–2011. We find that FX swap spreads (CIP deviations calculated from interbank interest rates of two countries) either fluctuated within the no-arbitrage bands or were close to the edges of the no-arbitrage bands.     

Credit derivatives with multiple debt issues

We evaluate the most actively traded types of credit derivatives within a unified pricing framework that allows for multiple debt issues. Since firms default on all of their obligations, total debt is instrumental in the likelihood of default and therefore in credit derivatives valuation. We use a single factor interest rate model where the exponential default frontier is based on total debt and is made coherent with observed bond prices. Analytical formulae are derived for credit default swaps, total return swaps (both fixed-for-fixed and fixed-for-floating), and credit risk options (CROs). Price behaviors and hedging properties of all these credit derivatives are investigated. Simulations document that credit derivatives prices may be significantly affected by terms of debt other than those of the reference obligation. The analysis of CROs indicates their superior ability to fine-tune the hedging of magnitude and arrival risks of default.