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.     

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.     

Loan Portfolio Swaps and Optimal Lending

Theories on loan portfolio swap hedging are based on a portfolio-choice approach. This paper presents an alternative: a firm-theoretic model for bank behavior with loan portfolio swaps. Our paper derives the optimal loan rate and rate-taking loan amount of the banks portfolio, and relates them to the market loan rate, counterparty loan rate, swap default risk, capital-to-deposits ratio, and deposit insurance. We find that in the bilateral default risk approach, the comparative static results are generated by four factors: the banks risk magnitude about the equity market value, loan composition in the swap contract, the substitution effect in the loan portfolio, and the income effect from the swap transaction. The results imply that changes in the payoff asymmetry in the event of swap default and the banks regulatory parameters have a direct effect on the banks loan portfolio for lending and swap transactions.We would like to thank two anonymous referees for helpful comments and advice.     

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.     

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.     

Large EU banks’ capital and liquidity: Relationship and impact on credit default swap spreads

This paper explores the interrelations between bank capital and liquidity and their impact on the market probability of default. We employ an unbalanced panel of large European banks with listed credit default swap (CDS) contracts during the period 2005–2015, which allow us to consider the impact of the recent financial crisis. Our evidence suggests that bank capital and funding liquidity risk as defined in Basel III have an economically meaningful bidirectional relationship. However, the effect on CDS spread is ambiguous. While capital appears to have a relatively large impact on CDS spread changes, liquidity risk is priced only when it falls below the regulatory threshold.     

Credit Derivatives in an Affine Framework

An efficient method for valuing credit derivatives based on three entities is developed in an affine framework. This includes interdependence of market and credit risk, joint credit migration and counterparty default risk of three firms. As an application we provide closed form expressions for the joint distribution of default times, default correlations, and default swap spreads in the presence of counterparty default risk. Vienna Institute of Finance is funded by WWTF (Vienna Science and Technology Fund).     

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.     

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.     

Counterparty credit risk and the credit default swap market

Counterparty credit risk has become one of the highest-profile risks facing participants in the financial markets. Despite this, relatively little is known about how counterparty credit risk is actually priced. We examine this issue using an extensive proprietary data set of contemporaneous CDS transaction prices and quotes by 14 different CDS dealers selling credit protection on the same underlying firm. This unique cross-sectional data set allows us to identify directly how dealers' credit risk affects the prices of these controversial credit derivatives. We find that counterparty credit risk is priced in the CDS market. The magnitude of the effect, however, is vanishingly small and is consistent with a market structure in which participants require collateralization of swap liabilities by counterparties.     

Demand–supply imbalances in the credit default swap market: empirical evidence

This paper empirically examines demand–supply imbalances in the credit default swap (CDS) market and provides evidence of its effect on the CDS spread dynamics. Analysis is conducted on a large and homogenous data set of the 92 non-financial European companies with the most quoted Euro-denominated CDS contracts during the 2002–2008 period. Main findings indicate that short-term CDS price movements, not related to fundamentals, are positively affected by demand–supply imbalances when protection buyers outstrip protection sellers. Results illustrate that CDS spreads reflect not only the price of credit protection, but also a liquidity premium for the anticipated cost of unwinding the position of protection sellers, especially during stress periods.     

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.     

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.     

The Information Content of Ratings: An Analysis of Australian Credit Default Swap Spreads

We examine the information content of Australian credit rating announcements by measuring the abnormal changes in credit default swap (CDS) spreads. CDS spreads provide a direct view of credit quality and thus should impound information quickly when investors receive new credit risk related information via a rating event. Using an event study methodology, we show that watch downs and rating upgrades contain valuable information even after controlling for sources of contamination. We find that watch downs elicit statistically significant market reactions, while subsequent downgrades are anticipated. Upgrades are associated with a significant but small abnormal reduction in CDS spreads, whereas watch ups appear to contain no new information.     

Pricing equity default swaps under the jump-to-default extended CEV model

Equity default swaps (EDS) are hybrid credit-equity products that provide a bridge from credit default swaps (CDS) to equity derivatives with barriers. This paper develops an analytical solution to the EDS pricing problem under the jump-to-default extended constant elasticity of variance model (JDCEV) of Carr and Linetsky. Mathematically, we obtain an analytical solution to the first passage time problem for the JDCEV diffusion process with killing. In particular, we obtain analytical results for the present values of the protection payoff at the triggering event, periodic premium payments up to the triggering event, and the interest accrued from the previous periodic premium payment up to the triggering event, and we determine arbitrage-free equity default swap rates and compare them with CDS rates. Generally, the EDS rate is strictly greater than the corresponding CDS rate. However, when the triggering barrier is set to be a low percentage of the initial stock price and the volatility of the underlying firm’s stock price is moderate, the EDS and CDS rates are quite close. Given the current movement to list CDS contracts on organized derivatives exchanges to alleviate the problems with the counterparty risk and the opacity of over-the-counter CDS trading, we argue that EDS contracts with low triggering barriers may prove to be an interesting alternative to CDS contracts, offering some advantages due to the unambiguity, and transparency of the triggering event based on the observable stock price.     

Pricing Property Index Linked Swaps with Counterparty Default Risk

This paper extends Bjork and Clapham (Journal of Housing Economics 11:418–432, 2002) model for pricing real estate index total return swaps. Our extension considers counterparty default risk within a first passage contingent claims model. We price total return swaps on property indices with different levels of default risk. We develop this model under same assumptions as Bjork and Clapham (Journal of Housing Economics 11:418–432, 2002) and find that total return swap price is no longer zero. Total return swap payer must charge a spread over the market interest rate that compensates him for the exposure to this additional risk. Based on commercial property indices in the UK, we observe that computed spreads are much lower than a sample of quotes obtained from one of the traders in the market.     

Valuation of credit default swaps and swaptions

This paper presents a conceptual and general framework for valuation of single-name credit derivatives. The general subfiltration approach of [J-R] to modelling default risk, which includes the Cox-process setting of [L], is integrated with a numeraire invariant approach. Several known results are reformulated and extended in this framework. New concepts and results are presented for change of numeraire in presence of default and valuation of credit swaptions. A new formula on fractional recovery of pre-default value is derived, generalizing that of [D-S]. A Black-Scholes formula for credit default swaptions due to [S] is shown to serve as a least-squares approximation to the general case.Received: 1 November 2003, Mathematics Subject Classification: 91B28, 60G44, 60G40JEL Classification: E43, G13I would like to thank the editor and two anonymous referees for their valuable comments and suggestions.     

Credit risk modeling strategies: the road to serfdom?

This paper aims at presenting some practical issues in modeling default risk of a single commercial credit counterparty from the perspective of a large retail bank. We define default risk as the probability that a counterparty’s intrinsic credit quality deteriorates within a given time horizon such that contractual agreements cannot be honored. This work gives an insight into using scoring/rating models in a credit environment of a large European bank. Contrary to many banks, we did not define the segments in a first step with a view to developing the rating tools in a second step. Our approach has, to some extent, followed a different path. Iteratively, we both defined the borders for a particular segment and selected an appropriate rating tool. More particularly, customer segmentation has been carried out on the basis of various rating tools’ goodness-of-fit criteria. The topics cover customer segmentation using goodness-of-fit measures, data measurement levels and optimization algorithms, rating tool calibration to the central default tendency and communication to the end user. Copyright © 1999 John Wiley & Sons, Ltd.     

Insured uncovered interest parity

The current literature suggests that uncovered interest parity (UIP) does not hold because of differences in risk in holding different currency denominated debt. We test whether this risk is related to sovereign credit risk in government bonds. We consider an insured uncovered interest parity relationship – that is, one where debt is insured with credit default swap (CDS) contracts. CDS rates help explain the UIP puzzle but have no predictive power for carry trade returns and currency movements.     

The use of credit default swaps by bond mutual funds: Liquidity provision and counterparty risk

Corporate bond mutual funds increased their selling of credit protection in the credit default swaps (CDS) market during the 2007–2008 financial crisis. This trading activity was primarily in multi-name CDS, greater among larger and established funds, and directed toward counterparty dealers in financial distress. Funds that sold credit protection during the crisis experienced greater credit market risk and superior post-crisis performance, consistent with higher expected returns from liquidity provision. Funds using Lehman Brothers as a counterparty experienced abnormal outflows and returns of –2% immediately following Lehman's bankruptcy, suggesting that funds’ opportunistic trading in CDS exposed investors to counterparty risk.