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.     

Default Risk, Asset Pricing, and Debt Control

The pricing and control of firms’ debt has become a majorissue since Merton’s (1974) seminal article. Yet Mertonas well as other recent theories presume that the asset valueof the firm is independent of the debt of the firm. However,when using debt finance, firms may have to pay a premium foran idiosyncratic default risk and may face debt constraints.We demonstrate that firm-specific debt constraints and endogenousrisk premia, based on collateralized borrowing, affect the assetvalue of the firm and, in turn, the collateral value of thefirm. In order to explore the interdependence of debt financeand asset pricing of firms, we endogenize default premia andborrowing constraints in a production-based asset pricing model.In this context then the dynamic decision problem of maximizingthe present value of the firm faces an additional constraintgiving rise to the debt-dependent firm value. We solve for theasset value of the firm with debt finance by the use of numericaldynamic programming. This allows us to solve the debt controlproblem and to compute sustainable debt as well as the firm’sdebt value.     

Distressed Debt Restructuring in the Presence of Credit Default Swaps

The availability of credit insurance via credit default swaps has been closely associated with the emergence of empty creditors. We empirically investigate this issue by looking at the debt restructurings (distressed exchanges and bankruptcy filings) of rated, nonfinancial U.S. companies over the period January 2007–June 2011. Using different proxies for the existence of insured creditors, we do not find evidence that the access to credit insurance favors bankruptcy over a debt workout. However, we document higher recovery prices following a distressed exchange in firms where empty creditors are more likely to emerge.     

Mandated accounting changes and debt covenants: The case of oil and gas accounting

The relationships among mandated accounting changes, bond covenants and security prices has been the focus of several studies. These studies have provided mixed evidence on the existence of a bond covenant effect on security prices. This paper suggests that inconclusive prior results are a consequence of inappropriately measuring the default risk of debt. Using an option pricing framework, it is shown that the debt to equity alone is not an adequate measure of default risk. In particular, both the debt to equity ratio and the total risk of the firm are necessary to adequately model the bond covenant effects of an accounting change. These theoretical propositions are supported by the empirical analysis of the security market reaction to changes in oil and gas accounting.     

Modeling Sovereign Yield Spreads: A Case Study of Russian Debt

We construct a model for pricing sovereign debt that accounts for the risks of both default and restructuring, and allows for compensation for illiquidity. Using a new and relatively efficient method, we estimate the model using Russian dollar-denominated bonds. We consider the determinants of the Russian yield spread, the yield differential across different Russian bonds, and the implications for market integration, relative liquidity, relative expected recovery rates, and implied expectations of different default scenarios.     

The Jarrow/Turnbull default risk model—Evidence from the German market

Abstract

This article estimates default intensities within the continuous-time Jarrow and Turnbull model for German bank and corporate bond prices. It is shown that a joint implicit estimation of the default intensity and the recovery rate is numerically unstable. In addition to cross-sectional estimations, separate estimations (for each bond individually) are performed. Results strongly support separate estimation over the building of any cross-sections. In contrast to preceeding literature, the optimum volume of data required to provide reasonable estimates of the default intensity is also investigated. It is shown that calibration based on daily data as a rule does not minimize the ex ante mean squared pricing errors. Finally, it is shown that the constant default intensity assumption is not sound with the underlying data and the determinants of the default intensity are investigated. Regressions show that the lagged default intensity estimate, the level of the default-free term structure and liquidity proxies affect the estimated default intensity via joint parameters.     

Credit derivatives with multiple debt issues

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

Pricing the risk of recovery in default with absolute priority rule violation

This paper proposes a simple approach to infer the risk-neutral density of recovery rates implied by the prices of the debt securities of a firm. The proposed approach is independent of modeling default arrival rates and allows for the violation of absolute priority rule. The paper demonstrates that a new statistic, the adjusted relative spread, captures risk-neutral recovery information in debt prices. Interest rates and firm tangible assets are shown to be significant determinants of the price of recovery. An application illustrates the pricing of credit derivatives written on the realized recovery rate.     

A comparative study of the probability of default for global financial firms

This article presents a modification of Merton’s (1976) ruin option pricing model to estimate the implied probability of default from stock and option market prices. To test the model, we analyze all global financial firms with traded options in the US and focus on the subprime mortgage crisis period. We compare the performance of the implied probability of default from our model to the expected default frequencies based on the Moody’s KMV model and agency credit ratings by constructing cumulative accuracy profiles (CAP) and the receiver operating characteristic (ROC). We find that the probability of default estimates from our model are equal or superior to other credit risk measures studied based on CAP and ROC. In particular, during the subprime crisis our model surpassed credit ratings and matched or exceeded KMV in anticipating the magnitude of the crisis. We have also found some initial evidence that adding off-balance-sheet derivatives exposure improves the performance of the KMV model.     

What is the risk of European sovereign debt defaults? Fiscal space,CDS spreads and market pricing of risk

We estimate the pricing of sovereign risk for fifty countries based on fiscal space (debt/tax; deficits/tax) and other economic fundamentals over 2005–10. We focus in particular on five countries in the South-West Eurozone Periphery, Greece, Ireland, Italy, Portugal and Spain. Dynamic panel estimates show that fiscal space and other macroeconomic factors are statistically and economically important determinants of sovereign risk. However, risk-pricing of the Eurozone Periphery countries is not predicted accurately either in-sample or out-of-sample: unpredicted high spreads are evident during global crisis period, especially in 2010 when the sovereign debt crisis swept over the periphery area. We match the periphery group with five middle income countries outside Europe that were closest in terms of fiscal space during the European fiscal crisis. Eurozone Periphery default risk is priced much higher than the matched countries in 2010, even allowing for differences in fundamentals. One interpretation is that these economies switched to a “pessimistic” self-fulfilling expectational equilibrium. An alternative interpretation is that the market prices not on current but future fundamentals, expecting adjustment challenges in the Eurozone periphery to be more difficult for than the matched group of middle-income countries because of exchange rate and monetary constraints.     

Valuation of collateralized debt obligations with hierarchical Archimedean copulae

Modelling portfolio credit risk is one of the crucial challenges faced by financial services industry in the last few years. We propose the valuation model of collateralized debt obligations (CDO) based on hierarchical Archimedean copulae (HAC) with up to three parameters, with default intensities calibrated to market data and with random loss given defaults that are correlated with default times. The methods presented are used to reproduce the spreads of the iTraxx Europe tranches. Our approach describes the market prices better than the standard pricing procedure based on the Gaussian distribution. We also obtain a flat correlation smile across tranches thereby solving the implied correlation puzzle.     

Valuation of defaultable bonds and debt restructuring

In this paper we develop a contingent valuation model for zero-coupon bonds with default. In order to emphasize the role of maturity time and place of the lender's claim in a firm's debt hierarchy, we consider a firm that issues two bonds with different maturities and different seniorage. The model allows us to analyze the implications of both debt renegotiation and capital structure of a firm on the prices of bonds. We obtain that renegotiation brings about a significant change in the bond prices and that the effect is dispersed through various channels: increasing the value of the firm, reallocating payments, and avoiding costly liquidation. Moreover, the presence of two creditors leads to qualitatively different implications for pricing, while emphasizing the importance of bond covenants and renegotiation of the entire debt.     

Omitted debt risk, financial distress and the cross-section of expected equity returns

The study of Ferguson and Shockley (2003) shows that, if the Merton (1974) model can reflect reality, the omission of debt claims from the market portfolio proxy may explain the poor pricing ability of the CAPM in empirical tests. We critically re-assess this argument by first reviewing existing, but also new avenues through which the Merton (1974) model can point to a systematic bias in market beta estimates. However, we also show that some avenues are diversifiable, and that they all rely on excessive economy-wide default risk to create a non-negligible bias. We then use the Merton (1974) model to proxy for the total debt portfolio, but find that its application in empirical tests cannot improve pricing performance. We conclude that there are (so far) no valid theoretical reasons to believe that omitted debt claims undermine CAPM tests.     

Market Pricing of Deposit Insurance

We provide an approach to the market valuation of deposit insurance that is based on reduced-form methods for the pricing of fixed-income securities under default risk. By reference to bank debt prices as well as qualitative-response models of the probability of bank failure, we suggest how a risk-neutral valuation model for deposit insurance can be applied both to the calculation of fair-market deposit insurance premia and to the valuation of long-term claims against the insurer.     

A comparison of Merton's option pricing model of corporate debt valuation to the use of book values

Many studies use the book value of debt as a proxy for its market value because most corporate debt does not trade. I call this practice the book value of debt (BVD) approximation, and it appears to be justified by the observation that the average market value of debt is close to its book value. Many corporate bonds, however, trade at values significantly different from their book values, and consequently the BVD approximation can create important biases. I compare the accuracy of the BVD approximation to Merton's option pricing (OPT) model of corporate debt valuation, and find consistent evidence that the Merton model provides more accurate estimates. I also show that this model is an easily estimated alternative to the BVD approximation. In short, the BVD approximation not only creates significant biases, but it is also an unnecessary simplification.     

Pricing distressed CDOs with stochastic recovery

In this article, a framework for the joint modelling of default and recovery risk in a portfolio of credit risky assets is presented. The model especially accounts for the correlation of defaults on the one hand and correlation of default rates and recovery rates on the other hand. Nested Archimedean copulas are used to model different dependence structures. For the recovery rates a very flexible continuous distribution with bounded support is applied, which allows for an efficient sampling of the loss process. Due to the relaxation of the constant 40% recovery assumption and the negative correlation of default rates and recovery rates, the model is especially suited for distressed market situations and the pricing of super senior tranches. A calibration to CDO tranche spreads of the European iTraxx portfolio is performed to demonstrate the fitting capability of the model. Applications to delta hedging as well as base correlations are presented.     

Financial Distress and the Cross‐section of Equity Returns

We explicitly consider financial leverage in a simple equity valuation model and study the cross‐sectional implications of potential shareholder recovery upon resolution of financial distress. Our model is capable of simultaneously explaining lower returns for financially distressed stocks, stronger book‐to‐market effects for firms with high default likelihood, and the concentration of momentum profits among low credit quality firms. The model further predicts (i) a hump‐shaped relationship between value premium and default probability, and (ii) stronger momentum profits for nearly distressed firms with significant prospects for shareholder recovery. Our empirical analysis strongly confirms these novel predictions.     

Endogenizing exogenous default barrier models: The MM algorithm

In this paper, we propose a Maximization–Maximization (MM) algorithm for the assessment of hidden parameters in structural credit risk models. Step M1 updates the value, volatility, and expected return on the firm’s assets by maximizing the log-likelihood function for the time series of equity prices; Step M2 updates the default barrier by maximizing the equity holders’ participation in the firm’s asset value. The main contribution of the method lies in the M2 step, which allows for ‘endogenizing’ the default barrier in light of actual data on equity prices. Using a large international sample of companies, we demonstrate that theoretical credit spreads based on the MM algorithm offer the lowest CDS pricing errors when compared to other, traditional default barrier specifications: smooth-pasting condition value, maximum likelihood estimate, KMV’s default point, and nominal debt.     

Liquidity and Credit Risk

We develop a structural bond valuation model to simultaneously capture liquidity and credit risk. Our model implies that renegotiation in financial distress is influenced by the illiquidity of the market for distressed debt. As default becomes more likely, the components of bond yield spreads attributable to illiquidity increase. When we consider finite maturity debt, we find decreasing and convex term structures of liquidity spreads. Using bond price data spanning 15 years, we find evidence of a positive correlation between the illiquidity and default components of yield spreads as well as support for downward‐sloping term structures of liquidity spreads.     

Termination of distressed residential mortgages: An empirical analysis

A sample of 209 distressed mortgages is used to analyze the terminations of distressed mortgages. An option-based model is compared to a traditional default model. Results show that the traditional model is statistically superior. However, the model's ability to identify a default is similar to that of the simpler option-based model. Alternative measures of borrower's equity are compared. Measuring borrower's equity using total debt more accurately explains default than using either the mortgage balance or the mortgage value.