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A Joint Analysis of the Term Structure of Credit Default Swap Spreads and the Implied Volatility Surface
Abstract
This study analyzes the co-movements of the term structure of credit default swap (CDS) spreads and the implied volatility surface by performing a factor decomposition for both dynamics. In our joint analysis we compute the information flow between the credit and volatility factors, examine their contemporaneous interactions, and assess the effectiveness of cross-hedges. Using options and CDS data for U.S. and European indices, the credit market is found to be the main contributor to overall market innovations. Our methodology is parsimonious and captures the intrinsic relationships between both markets. The empirical study highlights cross-market linkages during the Global Financial Crisis. Factors with small associated eigenvalues can be of tremendous importance for effective cross-hedging. © 2013 Wiley Periodicals, Inc. Jrl Fut Mark
... These remarks have led to the development of a joint analysis using factor decompositions of the entire implied volatility surface and the entire term structure of CDS spreads in Da Fonseca and Gottschalk (2013). 2 The interaction between the implied volatility and CDS factors is developed for the index pairs S&P500/CDX.NA.IG and EuroStoxx/iTraxx-Europe using a daily sample from January 2007 to December 2011. ...
... As both of them are multidimensional, we need to perform a factor decomposition in order to reduce the dimension. We follow the methodology developed in Da Fonseca and Gottschalk (2013) and refer to that paper for implementation details. ...
... Similarly, as time passes the options get closer to their maturities, so the available times to maturity will change over time. Following the methodology used in Da Fonseca and Gottschalk (2013), we build a time series of implied volatility surfaces denoted {I t (m j ,τ j ); j = 1 . . . N } on a fixed grid of points {(m j ,τ j ); j = 1 . . . ...
... Zhou (2014) indicates that the US VIX and MOVE share volatility connectedness under specific regimes. Furthermore, there is evidence that implied volatilities and credit default spreads in European and US markets are interconnected, especially during the GFC (Da Fonseca & Gottschalk, 2013). The nature of relationship between these economic variables and international volatility spillovers can change depending upon prevailing market conditions. ...
Understanding the transmission of volatility across markets is essential for managing risk and financial stability, especially under crisis periods during which an extreme event occurring in one market is easily transmitted to another market. To gain such an understanding and enrich the related literature, we examine in this article the system of volatility spillovers across various equity markets and asset classes using a quantile‐based approach, allowing us to capture spillovers under normal and high volatility states. The sample period is 16 March 2011–10 November 2020 and the employed dataset comprises 12 implied volatility indices representing a forward‐looking measure of uncertainty of global equities, strategic commodities and the US Treasury bond market. The results show that the identity of transmitters and receivers of volatility shocks differ between normal and high volatility states. The US stock market is at the centre of volatility spillovers in the normal volatility state. European and Chinese stock markets and strategic commodities (e.g. crude oil and gold) become major volatility transmitters in the high volatility state, after acting as volatility receivers during normal periods. Furthermore, we study the drivers of implied volatility spillovers using regression models and find that US Default spread contributes to the total volatility spillover index in both volatility states, whereas TED spread plays a significant role in the normal volatility state. As for the role of short rate and risk aversion, it is significant in the high volatility state. These findings matter to the decision‐making process of risk managers and policymakers.
... Alexander and Kaeck (2008), using a Markov regime-switching model, discover that the CDS spread is susceptible to stock market volatility during unstable periods, whereas it is more sensitive to the interest rate during stable periods.Zang et al. (2009) estimate the volatility and jump risk of individual stock pricesto analyze the connectivity among these variables and the CDS spread, whilePires et al. (2009) find that the CDS spread could be described by the implied volatility of individual stock option, and analyze the impact of default risk and liquidity on the difference between the CDS spread and the corporate bond spread. There are ongoing efforts to find various factors of the CDS spread, includingFonseca and Gottschalk (2013). ...
We investigate interconnectedness and the contagion effect of default risk in Asian sovereign CDS markets since the global financial crisis. Using dynamic conditional correlation analysis, we find that there are significant co-movements in Asian sovereign CDS markets; that such co-movements tend to be larger between developing countries than between developed and developing countries; and that in the co- movements intra-regional nature is stronger than inter-regional nature. With the Spillover Index model, we measure contagion probabilities of sovereign default risk in CDS markets of seven Asian countries and find evidence of contagion effects among six of them; Japan is the exception. In addition, we find that these six countries are affected more by cross-market spillovers than by their own-market spillovers. Furthermore, a rolling-sample analysis reveals that contagion in the Asian sovereign CDS markets expands during episodes of extreme economic and financial distress, such as the Lehman Brothers bankruptcy, the European financial crisis, and the US-credit downgrade.
... In practice, some arbitrage trades are based on CDS and options. Fonseca and Gottschalk [2013] discuss crosshedging strategies between CDS spreads and option volatility during crises. ...
Credit default swaps (CDS) have been growing in importance in the global financial markets. However, their role has been hotly debated, in industry and academia, particularly since the credit crisis of 2007–2009. We review the extant literature on CDS that has accumulated over the past two decades. We divide our survey into seven topics after providing a broad overview in the introduction. The second section traces the historical development of CDS markets and provides an introduction to CDS contract definitions and conventions. The third section discusses the pricing of CDS, from the perspective of no-arbitrage principles, structural, and reduced-form credit risk models. It also summarizes the literature on the determinants of CDS spreads, with a focus on the role of fundamental credit risk factors, liquidity and counterparty risk. The fourth section discusses how the development of the CDS market has affected the characteristics of the bond and equity markets, with an emphasis on market efficiency, price discovery, information flow, and liquidity. Attention is also paid to the CDS-bond basis, the wedge between the pricing of the CDS and its reference bond, and the mispricing between the CDS and the equity market. The fifth section examines the effect of CDS trading on firms' credit and bankruptcy risk, and how it affects corporate financial policy, including bond issuance, capital structure, liquidity management, and corporate governance. The sixth section analyzes how CDS impact the economic incentives of financial intermediaries. The seventh section reviews the growing literature on sovereign CDS and highlights the major differences between the sovereign and corporate CDS markets. In the eight section, we discuss CDS indices, especially the role of synthetic CDS index products backed by residential mortgage-backed securities during the financial crisis. We close with our suggestions for promising future research directions on CDS contracts and markets.
This study investigates how initiating a credit default swap (CDS) affects firm risk. Using the firm value volatility as a measure of firm risk, we document that firm risk decreases following the commencement of CDS trading. Further analysis indicates that the empty creditor channel, which arises when a debt holder with CDS protection has no interest in preserving the company it provides funds, is the primary way of influence. Our findings reveal a significant impact of financial innovation on a firm's behavior. We also document that market frictions affect the degree of such effect.
A classic approach to financial risk management is the use of scenario analysis to stress test portfolios. In the case of an S&P 500 options portfolio, for example, a scenario analysis might report a P&L of −$1m in the event the S&P 500 falls 5% and its implied volatility surface increases by 3 percentage points. But how accurate is this reported value of −$1m? Such a number is typically computed under the (implicit) assumption that all other risk factors are set to zero. But this assumption is generally not justified as it ignores the often substantial statistical dependence among the risk factors. In particular, the expected values of the non-stressed factors conditional on the values of the stressed factors are generally non-zero. Moreover, even if the non-stressed factors were set to their conditional expected values rather than zero, the reported P&L might still be inaccurate due to convexity effects, particularly in the case of derivatives portfolios. A further weakness of this standard approach to scenario analysis is that the reported P&L numbers are generally not back-tested so their accuracy is not subjected to any statistical tests. There are many reasons for this but perhaps the main one is that scenario analysis for derivatives portfolios is typically conducted without having a probabilistic model for the underlying dynamics of the risk factors under the physical measure P. In this paper we address these weaknesses by embedding the scenario analysis within a dynamic factor model for the underlying risk factors. Such an approach typically requires multivariate state-space models that can model the real-world behavior of financial markets where risk factors are often latent, and that are sufficiently tractable so that we can compute (or simulate from) the conditional distribution of unstressed risk factors. We demonstrate how this can be done for observable as well as latent risk factors in examples drawn from options and fixed income markets. We show how the two forms of scenario analysis can lead to dramatically different results particularly in the case of portfolios that have been designed to be neutral to a subset of the risk factors.
We provide a comprehensive analysis of the co‐movement of credit default swap (CDS), equity, and volatility markets in four Asia‐Pacific countries at firm and index level during the period 2007–2010. First, we examine lead–lag relationships between CDS spread changes, equity returns, and changes in volatility using a vector autoregressive model. At the firm level equity returns lead changes in CDS spreads and realized volatility. However, at the index level the intertemporal linkages between the three markets are less clear‐cut. Second, we apply the measures proposed by Diebold and Yilmaz (2014) to an analysis of volatility spillovers among the CDS, equities, and volatility asset classes. The results suggest that realized volatility (at firm level) and implied volatility (at index level) are the main transmitters of cross‐market volatility spillovers. Third, we analyze the impact of various structural factors and confirm the importance of realized volatility of equity returns as a determinant of CDS spreads.
We review the empirical academic literature on the informational content of credit default swap (“CDS”) spreads. Most of this literature posits and empirically documents that CDS spreads generally: (i) contain valuable information about the probability and severity of adverse credit events that the underlying reference entities may experience during the life of the CDS; (ii) reflect a risk premium that protection sellers demand to compensate them for reference entity-specific and systematic risks (both credit-related and non-credit-related); and (iii) are anticipatory and contain information regarding future announcements about the credit risk and financial condition of the underlying reference entity.
Investigating linkages between credit and equity markets, we consider daily aggregate U.S. CDS spreads as well as well-chosen equity market and implied volatility indexes over ten years. We describe such robust (to spurious
correlation) relationship with the quantile (cointegrating) regression approach. Such approach handles extreme
quantiles/CDS values and their behavior with respect to the equity market’s influence. Heteroskedastic patterns such as time-varying variance, but also autocorrelation, skewness and leptokurtosis are captured. Thus, the sensitivity of aggregate CDS spreads to equity market price and volatility channels is accurately measured across quantiles and spreads. Such quantile-dependent sensitivity exhibits asymmetric responses to equity market shocks. A sub-period analysis investigates potential regime shifts in estimated quantile cointegrating regressions. Quantile cointegrating coefficients vary over time and quantiles, and exhibit different magnitudes across sub-periods and spreads. Therefore, the relationship is unstable over time. We also propose a scenario analysis and risk signaling application for credit risk management prospects. Under specific risk levels, credit risky situations are described conditional on the equity market’s information over time, and related expected aggregate CDS spreads are computed. Estimated conditional quantiles/CDS spreads act as credit alert triggers.
We present a joint analysis of the term structure of credit default swap (CDS) spreads and the implied volatility surface for the United States and five European countries from 2007– 2012, a sample period covering both the Global Financial Crisis (GFC) and the European debt crisis. We analyze to which extent effective cross-hedges can be performed between the CDS and equity derivatives markets during these two crises. We find that during a global crisis a breakdown of the relationship between credit risk and equity volatility may occur, jeopardizing any cross-hedging strategy, which happened during the GFC. This stands in sharp contrast to the more localized European debt crisis, during which this fundamental relationship was preserved despite turbulent market conditions for both the CDS and volatility markets.
This paper studies the predictive power of the time-varying shape of the credit default swap (CDS) term structure to explain changes in future implied and excess implied volatility (implied volatility of the company over and above the market volatility) and therefore provide a leading sign of potential financial distress in a company. The shape of the CDS curve is captured by fitting the Nelson-Siegel model to the term structure and creating a new binary indicator (shape indicator) to distinguish between "good" and "bad" CDS curves. Applying the methodology to twenty US-traded companies from the financial and nonfinancial sectors, we find that the credit market is generally a leading indicator for movements in the volatility market during the subprime crisis. After confirming the strong link between CDSs and implied volatility markets (the average R-2 per sector between 36% and 63% is obtained using the Nelson-Siegel parameter and shape indicator), a partial F-test is executed to see if additional information is contained within the CDS markets over and above the volatility markets. For the period studied, this is the case for the majority of names, and it is particularly significant for Lehman Brothers.
Stock indexes are passive ‘value-weighted’ portfolios and should not have alphas which are significantly different from zero. If an index produces an insignificant alpha, then significant alphas for equity funds using this index can be attributed solely to manager performance. However, recent literature suggests that US stock indexes can demonstrate significant alphas, which ultimately raise questions regarding equity fund manager performance in both the US and abroad. In this paper, we employ the Carhart four-factor model and newly available Asian-Pacific risk factors to generate alphas and risk factor loadings for eight Australian stock indexes from January 2004 to December 2012. We find that the initial full sample period analysis does not provide indication of significant alphas in the indexes examined. However, by carrying out 36-month rolling regressions, we discover at least four significant alphas in seven of the eight indexes and factor loading variability. As previously reported in the US, this paper confirms similar issues with the four-factor model using Australian stock indexes and performance benchmarking. In effectively measuring Australian equity fund manager performance, it is therefore essential to evaluate a fund’s alpha and risk factors relative to the alpha and risk factors of the appropriate benchmark index.
This paper presents a joint analysis of the term structure of credit default swap (CDS) spreads and the implied volatility surface for five European countries from 2007–2012, a sample period covering both the Global Financial Crisis (GFC) and the European debt crisis. We analyze to which extent effective cross-hedges can be performed between the credit and equity derivatives markets during these two crises. We find that during a global crisis a breakdown of the relationship between credit risk and equity volatility may occur, jeopardizing any cross-hedging strategy, which happened during the GFC. This stands in sharp contrast to the more localized European debt crisis, during which this fundamental relationship was preserved despite turbulent market conditions for both the CDS and volatility markets.
We propose a methodology to calibrate the local volatility function under a continuous time setting. For this purpose, we used the Markov chain approximation method built on the well-established idea of local consistency. The chain was designed to approximate jump-diffusions coupled with a local volatility function. We found that this method outperforms traditional numerical algorithms that require time discretization. Furthermore, we showed that a local volatility jump-diffusion model outperformed the in- and out-of-sample pricing that the market practitioners benchmark, namely the Practitioners Black-Scholes, in turbulent periods during which at-the-money implied volatilities have risen substantially. As in previous literature concerning local volatility estimation, we represent the local volatility function using a space-time cubic spline.
We develop a simple robust link between equity out-of-the-money American put options and a pure credit insurance contract on the same reference company. Assuming that the stock price stays above a barrier B > 0 before default but drops and remains below a lower barrier A < B after default, we show that the spread between two co-terminal American put options struck within the default corridor (A, B) scaled by their strike difference replicates a standardized credit insurance con tract that pays one dollar at default whenever the company defaults prior to the option expiry and zero otherwise. Given the presence of the default corridor, this simple replicating strategy is robust to the details of pre- and post-default stock price dynamics, interest rate movements, and default risk fluctuations. We use quotes on American puts to infer the value of the credit insurance contract and compare it to that estimated from the credit default swap spreads. Collecting data on several companies, we identify strong co-movements between the credit insurance values inferred from the two markets. We also find that deviations between the two estimates cannot be fully explained by common variables used for explaining American put values, such as the underlying stock price and stock return volatility, but the cross-market deviations can pre dict future movements in American puts.
The prices of index options at a given date are usually represented via the corresponding implied volatility surface, presenting skew/smile features and term structure which several models have attempted to reproduce. However, the implied volatility surface also changes dynamically over time in a way that is not taken into account by current modelling approaches, giving rise to 'Vega' risk in option portfolios. Using time series of option prices on the SP500 and FTSE indices, we study the deformation of this surface and show that it may be represented as a randomly fluctuating surface driven by a small number of orthogonal random factors. We identify and interpret the shape of each of these factors, study their dynamics and their correlation with the underlying index. Our approach is based on a Karhunen-Loeve decomposition of the daily variations of implied volatilities obtained from market data. A simple factor model compatible with the empirical observations is proposed. We illustrate how this approach models and improves the well known 'sticky moneyness' rule used by option traders for updating implied volatilities. Our approach gives a justification for use of 'Vega's for measuring volatility risk and provides a decomposition of volatility risk as a sum of contributions from empirically identifiable factors.
We develop a simple robust link between deep out-of-the-money American put options on a company's stock and a credit insurance contract on the company's bond. We assume that the stock price stays above a barrier B before default but drops below a lower barrier A after default, thus generating a default corridor [A,B] that the stock price can never enter. Given the presence of this default corridor, a spread between two co-terminal American put options struck within the corridor replicates a pure credit contract, paying off when and only when default occurs prior to the option expiry. The Author 2010. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com., Oxford University Press.
It is common practice to identify the number and sources of shocks that move, e.g., ATM implied volatilities by principal components analysis. This approach, however, is likely to result in a loss of information, since the surface structure of implied volatilities is neglected. In this paper we analyze the implied volatility surface along maturity slices with a common principal components analysis (CPC), known from morphometrics. In CPC analysis, the space spanned by the eigenvectors is identical across groups, whereas variances associated with the common principal components vary. Our analysis shows that implied volatility surface dynamics can be traced back to a common eigenstructure in maturity slices. This empirical result is used to set up a factor model for implied volatility surface dynamics. Copyright Kluwer Academic Publishers 2003
This paper explores the time variation in the bond risk, as measured by the covariation of bond returns with stock returns and consumption growth, and in the volatility of bond returns. A robust stylized fact in empirical finance is that the spread between the yields on long- and short-term bonds forecasts future excess returns on bonds at varying horizons positively; in addition, the short-term nominal interest rate forecasts both the stock return volatility and the exchange rate volatility positively. This paper presents evidence that movements in both the short-term nominal interest rate and the yield spread are positively related to changes in the subsequent realized bond risk and bond return volatility. The yield spread appears to proxy for business conditions, while the short rate appears to proxy for inflation and economic uncertainty. A decomposition of bond betas into a real cash flow risk component and a discount rate risk component shows that yield spreads have offsetting effects in each component. A widening yield spread is correlated with a reduced cash-flow (or inflationary) risk for bonds, but it is also correlated with a larger discount rate risk for bonds. The short rate only forecasts the discount rate component of the bond beta.
We study expectations of credit market and default risk premium implicit in credit default swap prices in the case of Argentine default. We find that the default risk premium is substantial and its relation with default probability is not monotone. Default risk premium increases with rising default probability when default probability is low, but it declines when default probability reaches a certain level. This result suggests that default risk premium plays a primary role in the pricing of credit derivatives when default risk is moderate, but its impact declines when default risk becomes extremely high. We also find that the default risk premium in Argentine sovereign debt has an upward-sloping term structure throughout the sample period. Our results show that variation in default risk premiums in Argentine sovereign debt was affected by changes in the U.S. business cycle and credit conditions and the overall strength of the Argentine economy.
Recent empirical studies report predictable dynamics in the volatility surfaces that are implied by observed index option prices, such as those prescribed by general equilibrium models. Using an extensive data set from the over-the-counter options market, we document similar predictability in the factors that capture the daily variation of surfaces implied by options on 25 different foreign exchange rates. We proceed to demonstrate that simple vector autoregressive specifications for the factors can help produce accurate out-of-sample forecasts of the systematic component of the surface at short horizons. Profitable delta-hedged positions can be set up based on these forecasts; however, profits disappear when typical transaction costs are taken into account and when trading rules on wide segments of the surface are sought.
Volatility implied from observed option contracts systematically varies with the contracts' strike price and time to expiration, giving rise to an instantaneously non-flat implied volatility surface (IVS) that exhibits substantial time variation. We identify a number of latent factors that drive the dynamics of the IVSs from options on 11 Asian-Pacific exchange rates and show that these have a natural interpretation in the law of motion of each surface. We present evidence that these latent factors are related due to their common dependence on exogenous economy-wide variables. Findings suggest that the factors capturing the volatility level of the Japanese yen and the Chinese yuan, the volatility term structure of the Japanese yen, Taiwanese and Australian dollars and the risk aversion towards the Australian dollar, Japanese yen and Chinese yuan seem to incorporate first the investors' expectations regarding the volatility in the region.
This article proposes a simple approach for explaining credit default swap premia. Specifically, it investigates the effects of historical and option-implied equity volatility on credit default swap premia, thus extending an idea proposed by Campbell and Taksler (in press) in the context of corporate bond yields. Using panel data of credit default swaps on 120 international firms from 1999 to mid-2002, it becomes evident that option-implied volatility is a more important factor in explaining variation in credit default swap premia than historical volatility.
We study fiscal behaviour and the sovereign yield curve in the U.S. and Germany in the period 1981:I-2009:IV. The latent factors, level, slope and curvature, obtained with the Kalman filter, are used in a VAR with macro and fiscal variables, controlling for financial stress conditions. In the U.S., fiscal shocks have generated (i) an immediate response of the short-end of the yield curve, associated with the monetary policy reaction, lasting between 6 and 8 quarters, and (ii) an immediate response of the long-end of the yield curve, lasting 3 years, with an implied elasticity of about 80% for the government debt ratio shock and about 48% for the budget balance shock. In Germany, fiscal shocks entail no significant reactions of the latent factors and no response of the monetary policy interest rate. In particular, while (i) budget balance shocks created no response from the yield curve shape, (ii) surprise increases in the debt ratio caused some increase in the short-end and the long-end of the yield curve in the following 2nd and 3rd quarters.
This paper studies the pricing in the CDX tranche market, and whether these instruments have been reasonably priced and integrated within the financial market generally, over the period of the financial crisis of 2008. We first design a procedure to value CDO tranches using an intensity-based model which falls into the affine model class. The CDX tranche spreads are efficiently explained by a three-factor version of this model, before and during the crisis period. We then construct tradable CDX tranche portfolios, representing the three default intensity factors. These portfolios capture the same exposure as the S&P 500 index option market, to a market crash. We regress these CDX factors against the underlying index, the volatility factor, and the smirk factor, extracted from the index option returns, and against the Fama-French market, size and book-to-market factors. We finally argue that the CDX spreads are integrated in the financial market, and their issuers have not made excess returns.
This article explores expectations of credit market and default risk premium implicit in credit default swap prices in the case of Argentine default. We find that default risk premium is substantial and its relation with default probability is not monotone. Default risk premium increases with a rising default probability when default probability is low, but it declines when default probability reaches a certain level and continues to rise. This result suggests that default risk premium plays a primary role in the pricing of credit derivatives when default risk is moderate, but its impact becomes secondary when default risk becomes extremely high. We also find default risk premium has a hump-shaped term structure with the peak of the curve around five to six years. Our results show that variation in default risk premium in Argentine sovereign debt was affected by changes in the U.S. business cycle and credit conditions and the overall strength of the Argentine economy. Comparing with market expected default probabilities, we find that major rating agencies assigned overly optimistic ratings to Argentine debt and they lagged the market in downgrading the debt.
This paper explores time variation in bond risk, as measured by the covariation of bond returns with stock returns and with consumption growth, and in the volatility of bond returns. A robust stylized fact in empirical finance is that the spread between the yield on long-term bonds and short-term bonds forecasts positively future excess returns on bonds at varying horizons, and that the short-term nominal interest rate forecasts positively stock return volatility and exchange rate volatility. This paper presents evidence that movements in both the short-term nominal interest rate and the yield spread are positively related to changes in subsequent realized bond risk and bond return volatility. The yield spread appears to proxy for business conditions, while the short rate appears to proxy for inflation and economic uncertainty. A decomposition of bond betas into a real cash flow risk component, and a discount rate risk component shows that yield spreads have offsetting effects in each component. A widening yield spread is correlated with reduced cash-flow (or inflationary) risk for bonds, but it is also correlated with larger discount rate risk for bonds. The short rate forecasts only the discount rate component of bond.
The slope of a firm's term structure of credit default swap (CDS) spreads (five-year spread minus one-year spread) negatively predicts future stock returns. Stocks with low CDS slope on average outperform stocks with high CDS slope by over 1% each month for the next six months. Our result can not be explained by standard risk factors, stock characteristics, default risk measures or changes in CDS spreads. We find that CDS slope positively predicts future changes in CDS spreads, but the information content of CDS slope only slowly gets incorporated into stock price. CDS slope predicts return mainly for stocks facing high arbitrage costs.
This article proposes a simple approach for explaining credit default swap premia. Specifically, it investigates the effects of historical and option-implied equity volatility on credit default swap premia, thus extending an idea proposed by Campbell and Taksler (in press) in the context of corporate bond yields. Using panel data of credit default swaps on 120 international firms from 1999 to mid-2002, it becomes evident that option-implied volatility is a more important factor in explaining variation in credit default swap premia than historical volatility. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:71–92, 2004
Using dealer’s quotes and transactions prices on straight industrial bonds, we investigate the determinants of credit spread changes. Variables that should in theory determine credit spread changes have rather limited explanatory power. Further, the residuals from this regression are highly cross-correlated, and principal components analysis implies they are mostly driven by a single common factor. Although we consider several macroeconomic and financial variables as candidate proxies, we cannot explain this common systematic component. Our results suggest that monthly credit spread changes are principally driven by local supply/demand shocks that are independent of both credit-risk factors and standard proxies for liquidity.
The economic-political instability of a country, which is tied to its credit risk, often leads to sharp depreciation and heightened volatility in its currency. This paper shows that not only the creditworthiness of the euro-area countries with weaker fiscal positions but also that of the member countries with more sound fiscal positions are important determinants of the deep out-of-the-money euro put option prices, which embedded information on the euro crash risk during the sovereign debt crisis of 2009–2010. We also find evidence of information flow from the sovereign credit default swap market to the currency option market during the crisis.
Applied Nonparametric Regression is the first book to bring together in one place the techniques for regression curve smoothing involving more than one variable. The computer and the development of interactive graphics programs have made curve estimation possible. This volume focuses on the applications and practical problems of two central aspects of curve smoothing: the choice of smoothing parameters and the construction of confidence bounds. Härdle argues that all smoothing methods are based on a local averaging mechanism and can be seen as essentially equivalent to kernel smoothing. To simplify the exposition, kernel smoothers are introduced and discussed in great detail. Building on this exposition, various other smoothing methods (among them splines and orthogonal polynomials) are presented and their merits discussed. All the methods presented can be understood on an intuitive level; however, exercises and supplemental materials are provided for those readers desiring a deeper understanding of the techniques. The methods covered in this text have numerous applications in many areas using statistical analysis. Examples are drawn from economics as well as from other disciplines including medicine and engineering.
We propose a dynamically consistent framework that allows joint valuation and estimation of stock options and credit default swaps written on the same reference company. We model default as controlled by a Cox process with a stochastic arrival rate. When default occurs, the stock price drops to zero. Prior to default, the stock price follows a jump-diffusion process with stochastic volatility. The instantaneous default rate and variance rate follow a bivariate continuous process, with its joint dynamics specified to capture the observed behavior of stock option prices and credit default swap spreads. Under this joint specification, we propose a tractable valuation methodology for stock options and credit default swaps. We estimate the joint risk dynamics using data from both markets for eight companies that span five sectors and six major credit rating classes from B to AAA. The estimation highlights the interaction between market risk (return variance) and credit risk (default arrival) in pricing stock options and credit default swaps. Copyright The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oupjournals.org, Oxford University Press.
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.
Credit default swaps (CDS) are similar to out-of-the-money put options in that both offer a low cost and effective protection against downside risk. This study investigates whether put option-implied volatility is an important determinant of CDS spreads. Using a large sample of firms with both CDS and options data, we find that individual firms’ put option-implied volatility dominates historical volatility in explaining the time-series variation in CDS spreads. To understand this result, we show that implied volatility is a more efficient forecast for future realized volatility than historical volatility. More importantly, the volatility risk premium embedded in option prices covaries with the CDS spread. These findings complement existing empirical evidence based on market-level data.
Insider trading in the credit derivatives market has become a significant concern for regulators and participants. This paper attempts to quantify the problem. Using news reflected in the stock market as a benchmark for public information, we find significant incremental information revelation in the credit default swap market under circumstances consistent with the use of non-public information by informed banks. The information revelation occurs only for negative credit news and for entities that subsequently experience adverse shocks, and increases with the number of a firm's relationship banks. We find no evidence, however, that the degree of asymmetric information adversely affects prices or liquidity in either the equity or credit markets.
This paper introduces measures of volatility and jump risk that are based on individual stock options to explain credit spreads on corporate bonds. Implied volatilities of individual options are shown to contain useful information for credit spreads and improve on historical volatilities when explaining the cross-sectional and time-series variation in a panel of corporate bond spreads. Both the level of individual implied volatilities and (to a lesser extent) the implied-volatility skew matter for credit spreads. Detailed principal component analysis shows that a large part of the time-series variation in credit spreads can be explained in this way.
This paper explores the dynamic relationship between stock market implied credit spreads, CDS spreads, and bond spreads. A general VECM representation is proposed for changes in the three credit spread measures which accounts for zero, one, or two independent cointegration equations, depending on the evidence provided by any particular company. Empirical analysis on price discovery, based on a proprietary sample of North American and European firms, and tailored to the specific VECM at hand, indicates that stocks lead CDS and bonds more frequently than the other way round. It likewise confirms the leading role of CDS with respect to bonds.
We propose a semiparametric factor model, which approximates the implied volatility surface (IVS) in a finite dimensional function space. Unlike standard principal component approaches typically used to reduce complexity, our approach is tailored to the degenerated design of IVS data. In particular, we only fit in the local neighborhood of the design points by exploiting the expiry effect present in option data. Using DAX index option data, we estimate the nonparametric components and a low-dimensional time series of latent factors. The modeling approach is completed by studying vector autoregressive models fitted to the latent factors.
This empirical study is motivated by the literature on “smile-consistent” arbitrage pricing with stochastic volatility. We investigate the number and shape of shocks that move implied volatility smiles and surfaces by applying Principal Components Analysis. Two components are identified under a variety of criteria. Subsequently, we develop a “Procrustes” type rotation in order to interpret the retained components. The results have implications for both option pricing and hedging and for the economics of option pricing. Copyright Kluwer Academic Publishers 2000
This paper explores the nature of default arrival and recovery implicit in the term structures of sovereign "CDS" spreads. We argue that term structures of spreads reveal not only the arrival rates of credit events , but also the loss rates given credit events. Applying our framework to Mexico, Turkey, and Korea, we show that a single-factor model with following a lognormal process captures most of the variation in the term structures of spreads. The risk premiums associated with unpredictable variation in are found to be economically significant and co-vary importantly with several economic measures of global event risk, financial market volatility, and macroeconomic policy. Copyright (c) 2008 The American Finance Association.
Both credit default swap (CDS) and options markets often experience abnormal swings prior to the announcement of negative credit news. With the exclusion of negative earnings announcements, we find that options prices reveal information about such forthcoming adverse events at least as early as do credit spreads. Prior to negative credit news being publicly disclosed, we find that the equity market does not respond to abnormal movement in options prices unless that information has also manifested itself in the CDS market. A potential explanation is that options are more likely to trade on unsubstantiated rumors than are default swaps.
This paper explores the effect of equity volatility on corporate bond yields. Panel data for the late 1990s show that idiosyncratic firm-level volatility can explain as much cross-sectional variation in yields as can credit ratings. This finding, together with the upward trend in idiosyncratic equity volatility documented by Campbell, Lettau, Malkiel, and Xu (2001) , helps to explain recent increases in corporate bond yields. Copyright 2003 by the American Finance Association.
A structural model with stochastic volatility and jumps implies particular relationships between observed equity returns and credit spreads. This paper explores such effects in the credit default swap (CDS) market. We use a novel approach to identify the realized jumps of individual equity from high frequency data. Our empirical results suggest that volatility risk alone predicts 50% of CDS spread variation, while jump risk alone forecasts 19%. After controlling for credit ratings, macroeconomic conditions, and firms' balance sheet information, we can explain 77% of the total variation. Moreover, the marginal impacts of volatility and jump measures increase dramatically from investment grade to high-yield entities. The estimated nonlinear effects of volatility and jumps are in line with the model implied relationships between equity returns and credit spreads.
Pricing and integration of the CDX tranches in the financial market. Working paper The CBOE Volatility Index—VIX Predictable dynamics in implied volatility surfaces: Evidence from OTC currency options
- A P Carverhill
- D Luo
Carverhill, A. P., & Luo, D. (2011). Pricing and integration of the CDX tranches in the financial market. Working paper. CBOE (2003). The CBOE Volatility Index—VIX, http://www.cboe.com/micro/vix/ vixwhite.pdf Chalamandaris, G., & Tsekrekos, A. E. (2010). Predictable dynamics in implied volatility surfaces: Evidence from OTC currency options. Journal of Banking and Finance, 34, 1175–1188.
Do equity markets favor credit market news over options market news? Working paper Studies of stock price volatility changes
- A Berndt
- A Ostrovnaya
Berndt, A., & Ostrovnaya, A. (2008). Do equity markets favor credit market news over options market news? Working paper. Black, F. (1976). Studies of stock price volatility changes. Proceedings of the 1976 Meetings of the American Statistical Association, pp. 171–181.
Explaining credit default swap spreads with the equity volatility and jump risks of individual firms
- Zhang