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.     

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.     

Credit default swaps and the market for sovereign debt

In this paper, we analyze the determinants and effects of credit default swap (CDS) trading initiation in the sovereign bond market. CDS trading initiation is associated with a 30–150 basis point reduction in sovereign bond yields, with greater yield reductions accruing to higher default risk economies. For countries with high default risk, rated B or lower by Standard and Poor’s, CDS initiation is also associated with significant price efficiency benefits in the underlying market. CDS trading initiation is more likely following increases in local equity index volatility, index spreads for regional and global CDS markets, or depreciation of the local currency relative to the US dollar, and decreases in a country’s ability to service foreign debt. Our results are robust to selection bias controls based on these factors.     

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.     

Cross-hedging strategies between CDS spreads and option volatility during crises

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 to 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.     

Market conditions,default risk and credit spreads

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

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.     

Price discovery of subordinated credit spreads for Japanese mega-banks: Evidence from bond and credit default swap markets

This paper investigates the determinants and dynamics of subordinated credit spreads for Japanese mega-banks using the bond and credit default swap (CDS) spreads. The main findings are as follows. Subordinated bond and CDS spreads are cointegrated in most cases, and the CDS spread plays a more dominant role in price discovery than the bond spread. In addition, there are significant volatility spillovers from the CDS to bond spread. This information leadership for the CDS spread can largely be explained by stronger reactions of the CDS spread to some financial market variables and bank-specific accounting variables than the bond spread.     

Credit derivatives and loan pricing

This paper examines the relation between the new markets for credit default swaps (CDS) and banks’ pricing of syndicated loans to US corporates. We find that changes in CDS spreads have a significantly positive coefficient and explain about 25% of subsequent monthly changes in aggregate loan spreads during 2000–2005. Moreover, when compared to traditional explanatory factors, they turn out to be the dominant determinant of loan spreads. In particular, they explain loan rates much better than same rated bonds. This suggests that CDS prices contain, beyond general credit risk, to a substantial extent information relevant for bank lending. We also find that, over time, new information from CDS markets is faster incorporated into loans, but information from other markets is not. Overall, our results indicate that the markets for CDS have gained an important role for banks.     

Regime dependent determinants of credit default swap spreads

Credit default swap (CDS) spreads display pronounced regime specific behaviour. A Markov switching model of the determinants of changes in the iTraxx Europe indices demonstrates that they are extremely sensitive to stock volatility during periods of CDS market turbulence. But in ordinary market circumstances CDS spreads are more sensitive to stock returns than they are to stock volatility. Equity hedge ratios are three or four times larger during the turbulent period, which explains why previous research on single-regime models finds stock positions to be ineffective hedges for default swaps. Interest rate movements do not affect the financial sector iTraxx indices and they only have a significant effect on the other indices when the spreads are not excessively volatile. Raising interest rates may decrease the probability of credit spreads entering a volatile period.     

Credit default swaps and the UK 2008–09 short sales ban

Most studies of the short sales ban of UK financial stocks from September 2008 to January 2009 fail to control for the UK’s worst ever banking crisis and the underlying increase in risk. This paper studies the ban’s impact on the 13 large financials with credit default swaps (CDS) and 20 smaller stocks without CDS. The results reveal that returns of banned stocks Granger cause CDS returns in the pre- and post-ban periods, but causality runs from CDS to stock returns during the ban period. Underlying risk proxied by the CDS probability of default increased during the ban and the immediate pre- and post-ban periods which highlights an endogeneity problem ignored in some studies. This increased risk provides a plausible rationale for why CDS and related equity bid-ask spreads - which increased during the ban period – failed to fall significantly in the post-ban period. Panel regression results indicate that probability of default was an important economic determinant of stock bid-ask spreads during the ban period. Finally, our results suggest that the ban offered direct price support for the smaller non-CDS stocks during the ban period and indirect support for CDS stocks from their pre-ban to their post-ban levels.     

Leverage Choice and Credit Spreads when Managers Risk Shift

We model the debt and asset risk choice of a manager with performance‐insensitive pay (cash) and performance‐sensitive pay (stock) to theoretically link compensation structure, leverage, and credit spreads. The model predicts that optimal leverage trades off the tax benefit of debt against the utility cost of ex‐post asset substitution and that credit spreads are increasing in the ratio of cash‐to‐stock. Using a large cross‐section of U.S.‐based corporate credit default swaps (CDS) covering 2001 to 2006, we find a positive association between cash‐to‐stock and CDS rates, and between cash‐to‐stock and leverage ratios.     

A new approach for option pricing under stochastic volatility

We develop a new approach for pricing European-style contingent claims written on the time T spot price of an underlying asset whose volatility is stochastic. Like most of the stochastic volatility literature, we assume continuous dynamics for the price of the underlying asset. In contrast to most of the stochastic volatility literature, we do not directly model the dynamics of the instantaneous volatility. Instead, taking advantage of the recent rise of the variance swap market, we directly assume continuous dynamics for the time T variance swap rate. The initial value of this variance swap rate can either be directly observed, or inferred from option prices. We make no assumption concerning the real world drift of this process. We assume that the ratio of the volatility of the variance swap rate to the instantaneous volatility of the underlying asset just depends on the variance swap rate and on the variance swap maturity. Since this ratio is assumed to be independent of calendar time, we term this key assumption the stationary volatility ratio hypothesis (SVRH). The instantaneous volatility of the futures follows an unspecified stochastic process, so both the underlying futures price and the variance swap rate have unspecified stochastic volatility. Despite this, we show that the payoff to a path-independent contingent claim can be perfectly replicated by dynamic trading in futures contracts and variance swaps of the same maturity. As a result, the contingent claim is uniquely valued relative to its underlying’s futures price and the assumed observable variance swap rate. In contrast to standard models of stochastic volatility, our approach does not require specifying the market price of volatility risk or observing the initial level of instantaneous volatility. As a consequence of our SVRH, the partial differential equation (PDE) governing the arbitrage-free value of the contingent claim just depends on two state variables rather than the usual three. We then focus on the consistency of our SVRH with the standard assumption that the risk-neutral process for the instantaneous variance is a diffusion whose coefficients are independent of the variance swap maturity. We show that the combination of this maturity independent diffusion hypothesis (MIDH) and our SVRH implies a very special form of the risk-neutral diffusion process for the instantaneous variance. Fortunately, this process is tractable, well-behaved, and enjoys empirical support. Finally, we show that our model can also be used to robustly price and hedge volatility derivatives.     

Volatility spreads and earnings announcement returns

Prior research documents that volatility spreads predict stock returns. If the trading activity of informed investors is an important driver of volatility spreads, then the predictability of stock returns should be more pronounced during major information events. This paper investigates whether the predictability of equity returns by volatility spreads is stronger during earnings announcements. Volatility spreads are measured by the implied volatility differences between pairs of strike price and expiration date matched put and call options and capture price pressures in the option market. During a two-day earnings announcement window, the abnormal returns to the quintile that includes stocks with relatively expensive call options is more than 1.5% greater than the abnormal returns to the quintile that includes stocks with relatively expensive put options. This result is robust after measuring volatility spreads in alternative ways and controlling for firm characteristics and lagged equity returns. The degree of announcement return predictability is stronger when volatility spreads are measured using more liquid options, the information environment is more asymmetric, and stock liquidity is low.     

Hedging credit: Equity liquidity matters

We theorize and confirm a new channel by means of which liquidity costs are embedded in CDS spreads. We show that credit default swap (CDS) spreads are directly related to equity market liquidity in the Merton [Merton, R.C., 1974. On the pricing of corporate debt: The risk structure of interest rates. J. Finance 29, 449–470] model via hedging. We confirm this relationship empirically using a sample of 1452 quarterly CDS spreads over 2001–2005. In the model, this relationship is monotone increasing when credit quality worsens. These results are robust to alternative measures of equity liquidity and other possible determinants of CDS spreads.     

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.     

Surprises,sentiments, and the expectations hypothesis of the term structure of interest rates

Between 2005 and 2009, we document evident time-varying credit risk price discovery between the equity and credit default swap (CDS) markets for 174 US non-financial investment-grade firms. We test the economic significance of a simple portfolio strategy that utilizes fluctuation in CDS spreads as a trading signal to set stock positions, conditional on the CDS price discovery status of the reference entities. We show that a conditional portfolio strategy which updates the list of CDS-influenced firms over time, yields a substantively larger realized return net of transaction cost over the unconditional strategy. Furthermore, the conditional strategy’s Sharpe ratio outperforms a series of benchmark portfolios over the same trading period, including buy-and-hold, momentum and dividend yield strategies.     

Pricing and static hedging of European-style double barrier options under the jump to default extended CEV model

This paper develops two novel methodologies for pricing and hedging European-style barrier option contracts under the jump to default extended constant elasticity of variance (JDCEV) model, namely: a stopping time approach based on the first passage time densities of the underlying asset price process through the barrier levels; and a static hedging portfolio approach in which the barrier option is replicated by a portfolio of plain-vanilla and binary options. In doing so, both valuation methodologies are extended to a more general set-up accommodating endogenous bankruptcy, time-dependent barriers and the commonly observed stylized facts of a positive link between default and equity volatility and of a negative link between volatility and stock price. The two proposed numerical methods are shown to be accurate, easy to implement and efficient under both the JDCEV model and the nested constant elasticity of variance model.     

The effect of interest rate volatility and equity volatility on corporate bond yield spreads: A comparison of noncallables and callables

This research investigates the impact of interest rate volatility upon corporate bond yield spreads. We first consider the impact of interest rate volatility upon noncallable bond spreads. Because greater interest rate volatility likely increases the volatility of the firm's debt, we hypothesize that the relation will be positive. Given that we do find a positive relation, we thus investigate whether the positive effect of interest rate volatility on yield spreads is stronger or weaker for callable bonds. We find that the effect is weaker for callable bonds. This result indicates that there is a negative relation between default spreads and call spreads, which is consistent with the theory of Acharya and Carpenter (2002), but in contrast to the theory of King (2002). Furthermore, our results for the relationship between equity volatility and yield spread tend to support Acharya and Carpenter (2002) more than King (2002).     

Determinants of yield spread dynamics: Euro versus US dollar corporate bonds

This paper presents a systematic comparison between the determinants of euro and US dollar yield spread dynamics. The results show that US dollar yield spreads are significantly more affected by changes in the level and the slope of the default-free term structure and the stock market return and volatility. Surprisingly, euro yield spreads are strongly affected by the US (and not the euro) level and slope. This confirms the dominance of US interest rates in the corporate bond markets. Interestingly, I find that liquidity risk is higher for US dollar corporate bonds than euro corporate bonds. For both regions, the effect of changes in the bid-ask spread is mainly significant during periods of high liquidity risk. Finally, the results indicate that the credit cycle as measured by the region-specific default probability significantly increases US yield spreads. This is not the case for euro yield spreads.