Theory and evidence on the dynamic interactions between sovereign credit default swaps and currency options

Using sovereign CDS spreads and currency option data for Mexico and Brazil, we document that CDS spreads covary with both the currency option implied volatility and the slope of the implied volatility curve in moneyness. We propose a joint valuation framework, in which currency return variance and sovereign default intensity follow a bivariate diffusion with contemporaneous correlation. Estimation shows that default intensity is much more persistent than currency return variance. The market price estimates on the two risk factors also explain the well-documented evidence that historical average default probabilities are lower than those implied from credit spreads.     

Dynamic credit default swap curves in a network topology

Systemically important banks are connected and their default probabilities have dynamic dependencies. An extraction of default factors from cross-sectional credit default swap (CDS) curves allows us to analyze the shape and the dynamics of default probabilities. In extending the Dynamic Nelson Siegel (DNS) model to an across firm multivariate setting, and employing the generalized variance decomposition of Diebold and Yilmaz [On the network topology of variance decompositions: Measuring the connectedness of financial firms. J. Econom., 2014, 182(1), 119–134], we are able to establish a DNS network topology. Its geometry yields a platform to analyze the interconnectedness of long-, middle- and short-term default factors in a dynamic fashion and to forecast the CDS curves. Our analysis concentrates on 10 financial institutions with CDS curves comprising of a wide range of time-to-maturities. The extracted level factor representing long-term default risk shows a higher level of total connectedness than those derived for short-term and middle-term default risk, respectively. US banks contributed more to the long-term default spillover before 2012, whereas European banks were major default transmitters during and after the European debt crisis, both in the long-term and short-term. The comparison of the network DNS model with alternatives proposed in the literature indicates that our approach yields superior forecast properties of CDS curves.     

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.     

An Empirical Investigation of CDS Spreads Using a Regime-Switching Default Risk Model

Default risk in equity returns can be measured by structural models of default. In this article we propose a credit warning signal (CWS) based on the Merton Default Risk (MDR) model and a Regime-Switching Default Risk (RSDR) model. The RSDR model is a generalization of the MDR model, comprises regime-switching asset distribution dynamics, and thus produces more realistic default probability estimates in cases of deteriorating credit quality. Alternatively, it reduces to the MDR model. Using a dataset of U.S. credit default swap (CDS) contracts around the 2007-8 crisis we construct rating-based indices to investigate the MDR and RSDR implied probabilities of default in relation to the market-observed CDS spreads. The proposed CWS measure indicates an increase in implied default probabilities several months ahead of notable increases in CDS spreads.     

Credit default swap calibration and derivatives pricing with the SSRD stochastic intensity model

We introduce the two-dimensional shifted square-root diffusion (SSRD) model for interest-rate and credit derivatives with (positive) stochastic intensity. The SSRD is the unique explicit diffusion model allowing an automatic and separated calibration of the term structure of interest rates and of credit default swaps (CDSs), and retaining free dynamics parameters that can be used to calibrate option data. We propose a new positivity preserving implicit Euler scheme for Monte Carlo simulation. We discuss the impact of interest-rate and default-intensity correlation and develop an analytical approximation to price some basic credit derivatives terms involving correlated CIR processes. We hint at a formula for CDS options under CIR + + CDS-calibrated stochastic intensity.Received: March 2004, Mathematics Subject Classification (2000): 60H10, 60J60, 60J75, 91B70JEL Classification: G13     

Modelling default contagion using multivariate phase-type distributions

We model dynamic credit portfolio dependence by using default contagion in an intensity-based framework. Two different portfolios (with ten obligors), one in the European auto sector, the other in the European financial sector, are calibrated against their market CDS spreads and the corresponding CDS-correlations. After the calibration, which are perfect for the banking portfolio, and good for the auto case, we study several quantities of importance in active credit portfolio management. For example, implied multivariate default and survival distributions, multivariate conditional survival distributions, implied default correlations, expected default times and expected ordered default times. The default contagion is modelled by letting individual intensities jump when other defaults occur, but be constant between defaults. This model is translated into a Markov jump process, a so called multivariate phase-type distribution, which represents the default status in the credit portfolio. Matrix-analytic methods are then used to derive expressions for the quantities studied in the calibrated portfolios.     

Are credit default swaps still a sideshow? How information flow between equity and CDS markets has changed since the financial crisis

We examine the information flow between equity and credit default swap (CDS) markets using firm-level returns data before and after the global financial crisis. Before the crisis, the information flow was unidirectional, with equity returns leading CDS returns. While equity returns continue to lead CDS returns after the crisis, we find that the speed of adjustment of the CDS market to equity markets has increased during this period. We also find evidence of a bidirectional flow of information between these markets, with equity returns responding to credit protection returns in the postcrisis period. The quicker response of CDS spreads to equity returns during the postcrisis period primarily occurs among entities with lower credit ratings. In contrast, the response of equity returns to lagged CDS returns during the postcrisis period is observed among firms across different credit rating categories; however, the magnitude of the response is higher among those with lower credit ratings.     

The effects of credit default swaps on corporate investment

ABSTRACT

This paper examines how credit default swaps (CDS) affect the corporate investment of the referenced entities. We document a significant reduction in corporate investment after CDS trading, a result that is robust to alternative model specifications and a set of endogeneity tests. Our findings of the increased firm risk and cost of capital support the costly external capital channel. The cross-sectional variations in CDS effects demonstrate that both reduced monitoring and the empty creditor problem might be the underlying forces driving the costly external capital channel. Our additional analysis implies that CDS trading is associated with an enhancement in investment efficiency for firms that are prone to overinvestment.     

Structural default model with mutual obligations

In this paper we consider mutual obligations in an interconnected bank system and analyze their impact on the joint and marginal survival probabilities for individual banks. We also calculate prices of the corresponding credit default swaps and first-to-default swaps. To make the role of mutual obligations more transparent, we develop a simple structural default model with banks’ assets driven by correlated multidimensional Brownian motion with drift. We calculate closed form expressions for many quantities of interest and use them for the efficient model calibration. We demonstrate that mutual obligations have noticeable impact on the system behavior.     

The Cross‐Section of Credit Risk Premia and Equity Returns

We explore the link between a firm's stock returns and credit risk using a simple insight from structural models following Merton ( 1974 ): risk premia on equity and credit instruments are related because all claims on assets must earn the same compensation per unit of risk. Consistent with theory, we find that firms' stock returns increase with credit risk premia estimated from CDS spreads. Credit risk premia contain information not captured by physical or risk‐neutral default probabilities alone. This sheds new light on the “distress puzzle”—the lack of a positive relation between equity returns and default probabilities—reported in previous studies.     

An intensity model for credit risk with switching Lévy processes

We develop a switching regime version of the intensity model for credit risk pricing. The default event is specified by a Poisson process whose intensity is modeled by a switching Lévy process. This model presents several interesting features. First, as Lévy processes encompass numerous jump processes, our model can duplicate the sudden jumps observed in credit spreads. Also, due to the presence of jumps, probabilities do not vanish at very short maturities, contrary to models based on Brownian dynamics. Furthermore, as the parameters of the Lévy process are modulated by a hidden Markov chain, our approach is well suited to model changes of volatility trends in credit spreads, related to modifications of unobservable economic factors.     

A jump to default extended CEV model: an application of Bessel processes

We develop a flexible and analytically tractable framework which unifies the valuation of corporate liabilities, credit derivatives, and equity derivatives. We assume that the stock price follows a diffusion, punctuated by a possible jump to zero (default). To capture the positive link between default and equity volatility, we assume that the hazard rate of default is an increasing affine function of the instantaneous variance of returns on the underlying stock. To capture the negative link between volatility and stock price, we assume a constant elasticity of variance (CEV) specification for the instantaneous stock volatility prior to default. We show that deterministic changes of time and scale reduce our stock price process to a standard Bessel process with killing. This reduction permits the development of completely explicit closed form solutions for risk-neutral survival probabilities, CDS spreads, corporate bond values, and European-style equity options. Furthermore, our valuation model is sufficiently flexible so that it can be calibrated to exactly match arbitrarily given term structures of CDS spreads, interest rates, dividend yields, and at-the-money implied volatilities.     

Measuring changes in credit risk: The case of CDS event studies

This paper examines the size and power of test statistics designed to detect abnormal changes in credit risk as measured by credit default swap (CDS) spreads. We follow a simulation approach to examine the statistical properties of normal and abnormal CDS spread changes and assess the performance of normal return models and test statistics. Using daily CDS data, we find parametric test statistics to be generally inferior to non-parametric tests, with the rank test performing best. A CDS factor model based on factors identified in the empirical literature is generally well specified and more powerful in detecting abnormal performance than some of the classical normal return models. Finally, we examine abnormal CDS announcement spread changes around issuer's rating downgrades to demonstrate the effect of different CDS spread change measures and normal return models on event study results.     

Understanding the market reaction to shockwaves: Evidence from the failure of Lehman Brothers

The spectacular failure of the 150-year-old investment bank Lehman Brothers on September 15th, 2008 was a major turning point in the global financial crisis that broke out in the summer of 2007. Through the use of stock market data and credit default swap (CDS) spreads, this paper examines investors’ reaction to Lehman's collapse in an attempt to identify a spillover effect on the surviving financial institutions. The empirical analysis indicates that (i) the collateral damage was limited to the largest financial firms; (ii) the institutions most affected were the surviving “non-bank” financial services firms; and (iii) the negative effect was correlated with the financial conditions of the surviving institutions. We also detect significant abnormal jumps in CDS spreads that we interpret as evidence of sudden upward revisions in the market assessment of future default probabilities assigned to the surviving financial firms.     

A Macrofinance View of U.S. Sovereign CDS Premiums

Premiums on U.S. sovereign credit default swaps (CDS) have risen to persistently elevated levels since the financial crisis. We examine whether these premiums reflect the probability of a fiscal default—a state in which a balanced budget can no longer be restored by raising taxes or eroding the real value of debt by increasing inflation. We develop an equilibrium macrofinance model in which the fiscal and monetary policy stances jointly endogenously determine nominal debt, taxes, inflation, and growth. We show that the CDS premiums reflect the endogenous risk-adjusted probabilities of fiscal default. The calibrated model is consistent with elevated levels of CDS premiums but leaves dynamic implications quantitatively unresolved.     

Fast simulations in credit risk

We consider the problem of simulating tail loss probabilities and expected losses conditioned on exceeding a large threshold (expected shortfall) for credit portfolios. Our new idea, called the geometric shortcut, allows an efficient simulation for the case of independent obligors. It is even possible to show that, when the average default probability tends to zero, its asymptotic efficiency is higher than that of the naive algorithm. The geometric shortcut is also useful for models with dependent obligors and can be used for dependence structures modeled with arbitrary copulae. The paper contains the details for simulating the risk of the normal copula credit risk model by combining outer importance sampling with the geometric shortcut. Numerical results show that the new method is efficient in assessing tail loss probabilities and expected shortfall for credit risk portfolios. The new method outperforms all known methods, especially for credit portfolios consisting of weakly correlated obligors and for evaluating the tail loss probabilities at many thresholds in a single simulation run.     

Credit default swap prices as risk indicators of listed German banks

This paper explores empirically the usefulness of credit default swap (CDS) prices as market indicators. The sample of reference entities consists of large, internationally active German banks and the observation period covers 3 years. By analysing the explanatory power of three risk sources: idiosyncratic credit risk, systematic credit risk and liquidity risk, we gain important insights into modeling the dynamics of CDS spreads. The impact of systematic risk, for example, has three components; one is related to the overall state of the economy, another related to the risk of the internationally active banking sector, and the third is an unobservable systematic factor. Default probabilities, inferred from a tractable reduced form model for CDS spreads, are compared with expected default frequencies from the Moody’s KMV model. The results lend empirical support to the hypothesis that structural models can be less informative than reduced-form models of CDS spreads in the case of banks with major investment banking activities as the leverage loses explanatory power. Although the CDS market appears to have matured over the observation period, during certain periods premiums for liquidity risk can increase substantially thus limiting the value of CDS spreads as market indicators. We conclude that equity prices and CDS premia should be considered together to fully exploit the information content of both market indicators and to mitigate their respective drawbacks.

A dynamic programming approach for pricing CDS and CDS options

We propose a flexible framework for pricing single-name knock-out credit derivatives. Examples include Credit Default Swaps (CDSs) and European, American and Bermudan CDS options. The default of the underlying reference entity is modelled within a doubly stochastic framework where the default intensity follows a CIR++ process. We estimate the model parameters through a combination of a cross sectional calibration-based method and a historical estimation approach. We propose a numerical procedure based on dynamic programming and a piecewise linear approximation to price American-style knock-out credit options. Our numerical investigation shows consistency, convergence and efficiency. We find that American-style CDS options can complete the credit derivatives market by allowing the investor to focus on spread movements rather than on the default event.     

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.     

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.