Corporate Bond Prices Research Articles

Structural Models of Credit Risk are Useful: Evidence from Hedge Ratios on Corporate Bonds

It is well known that structural models of credit risk provide poor predictions of bond prices. We show that they may perform much better as a predictor of debt return sensitivities to equity. This is important since it gives us an opportunity to identify much better the reasons for model failure. The main result of this paper is that even the simplest of the structural models (Merton (1974)) produces hedge ratios that are in line with those observed empirically. As well as providing insight into the determinants of corporate bond prices our results are also useful to practitioners who wish to hedge their positions in corporate debt. The paper also shows that corporate bond prices are sensitive to some variables - e.g., VIX - in a way that appears unrelated to credit risk.

Bond Games

Corporate debt indentures are complex contracts that include a variety of restrictions and options. On one side, an issuing corporation can engineer game-based transactions to escape covenant restrictions or capture option value for its stockholders. On the other side, bondholders can form coalitions to resist a corporation's endeavors and capture option value for the coalition. This article analyzes several types of such strategic debt transactions. The examples show that corporate debt games can strongly influence corporate bond prices.

An Empirical Study of Structural Credit Risk Models Using Stock and Bond Prices

Reduced-form credit risk models are often thought to be better suited than structural models for pricing corporate bonds. The authors challenge this view. Conditioned not only on equity but on bond and dividend information also, a structural model performs well compared to previously tested reduced-form models. In the pricing of bond portfolios, model errors are to a large extent diversifiable.

Structural Models of Corporate Bond Pricing: An Empirical Analysis

This article empirically tests five structural models of corporate bond pricing: those of Merton (1974), Geske (1977), Longstaff and Schwartz (1995), Leland and Toft (1996), and Collin-Dufresne and Goldstein (2001). We implement the models using a sample of 182 bond prices from firms with simple capital structures during the period 1986–1997. The conventional wisdom is that structural models do not generate spreads as high as those seen in the bond market, and true to expectations, we find that the predicted spreads in our implementation of the Merton model are too low. However, most of the other structural models predict spreads that are too high on average. Nevertheless, accuracy is a problem, as the newer models tend to severely overstate the credit risk of firms with high leverage or volatility and yet suffer from a spread underprediction problem with safer bonds. The Leland and Toft model is an exception in that it overpredicts spreads on most bonds, particularly those with high coupons. More accurate structural models must avoid features that increase the credit risk on the riskier bonds while scarcely affecting the spreads of the safest bonds. The seminal work of Black and Scholes (1973) and Merton (1974) in the area of corporate bond pricing has spawned an enormous theoretical literature on risky debt pricing. One motivating factor for this burgeoning literature is the perception that the Merton model cannot generate sufficiently high-yield spreads to match those observed in the market. Thus the recent theoretical literature includes a variety of extensions and

Estimating the Interest Rate Term Structure of Corporate Debt With a Semiparametric Penalized Spline Model

This article provides a new methodology for estimating the term structure of corporate debt using a semiparametric penalized spline model. The method is applied to a case study of AT&T bonds. Typically, very few data are available on individual corporate bond prices, too little to find a nonparametric estimate of term structure from these bonds alone. This problem is solved by “borrowing strength” from Treasury bond data. More specifically, we combine a nonparametric model for the term structure of Treasury bonds with a parametric component for the credit spread. Our methodology generalizes the work of Fisher, Nychka, and Zervos in several ways. First, their model was developed for Treasury bonds only and cannot be applied directly to corporate bonds. Second, we more fully investigate the problem of choosing the smoothing parameter, a problem that is complicated because the forward rate is the derivative-log{D(t)}, where the discount function D is the function fit to the data. In our case study, estimation of the derivative requires substantially more smoothing than selected by generalized cross-validation (GCV). Another problem for smoothing parameter selection is possible correlation of the errors. We compare three methods of choosing the penalty parameter: generalized cross-validation (GCV), the residual spatial autocorrelation (RSA) method of Ellner and Seifu, and an extension of Ruppert's empirical bias bandwidth selection (EBBS) to splines. Third, we provide approximate sampling distributions based on asymptotics for the Treasury forward rate and the bootstrap for corporate bonds. Confidence bands and tests of interesting hypotheses, for example, about the functional form of the credit spreads, are also discussed.

Modeling the business risk of financially weakened firms: A new approach for corporate bond pricing

Most structural models of default risk assume that the firm's asset return is normally distributed, with a constant volatility. By contrast, this article details the properties that the process of assets should have in the case of financially weakened firms. It points out that jump-diffusion processes with time-varying volatility provide a refined and accurate perspective on the business risk dimension of default risk. Representative Arrow–Debreu state price densities (SPD) and term structures of credit spreads are then explored. The credit curves show that the business uncertainties play a major in the pricing of corporate liabilities.

Modeling the Dynamics of Credit Spreads with Stochastic Volatility

This paper investigates a two-factor affine model for the credit spreads on corporate bonds. The first factor can be interpreted as the level of the spread and the second factor is the volatility of the spread. The riskless interest rate is modeled using a standard two-factor affine model, thus leading to a four-factor model for corporate yields. This approach allows us to model the volatility of corporate credit spreads as stochastic, and also allows us to capture higher moments of credit spreads. We use an extended Kalman filter approach to estimate our model on corporate bond prices for 108 firms. The model is found to be successful at fitting actual corporate bond credit spreads, resulting in a significantly lower root mean square error than a standard alternative model both in sample and out of sample. In addition, key properties of actual credit spreads such as the stochastic volatility of the credit spreads and the positive skewness of the credit spread distribution are better captured by the model.

The Pricing of Options on Credit-Sensitive Bonds

We build a three-factor term-structure of interest rates model and use it to price corporate bonds. The first two factors allow the risk-free term structure to shift and tilt. The third factor generates a stochastic credit-risk premium. To implement the model, we apply the Peterson and Stapleton (2002) diffusion approximation methodology. The method approx imates a correlated and lagged-dependent lognormal diffusion processes. We then price options on credit-sensitive bonds. The recombining log-binomial tree methodology allows the rapid computation of bond and option prices for binomial trees with up to forty periods.

Pricing corporate bonds with dynamic default barriers

Merton-type models of pricing corporate bonds based on relatively simple default processes cannot generate credit spreads which replicate empirically observed spreads. This paper presents an analytical valuation model of corporate discount bond prices to address this problem. The main feature of the model is a dynamic default barrier. Different default scenarios can be incorporated into the valuation model through adjusting the default barrier's dynamics. We derive a closed-form solution of the corporate bond price based on the model as a function of the firm value and short-term interest rate, with time-dependent model parameters. The numerical results calculated from the solution show that the model is capable of producing term structures of credit spreads that are consistent with some empirical findings. This model could provide new insight for future research on corporate bond analysis and credit risk modelling.

Pricing Corporate Bonds with Rating-Based Covenants

A corporate bond indenture often includes covenants that allow bondholders to take specific actions (e.g., force prepayment or reorganization) if certain specific conditions are violated. A typical covenant is triggered by a downgrade in credit rating. This article provides a simple framework for the valuation of a corporate bond with a rating-based covenant. Basic assumptions that are consistent with empirical evidence are that a downgrade in credit rating is accompanied by more volatility in assets, and that corporate reorganization after a rating change results in a change in payments to equityholders and other securityholders. The model may be used to compare risky bonds with covenants and bonds without convenants.

Modeling the Dynamics of Credit Spreads with Stochastic Volatility

This paper investigates a two-factor affine model for the credit spreads on corporate bonds. The first factor can be interpreted as the level of the spread, and the second factor is the volatility of the spread. The riskless interest rate is modeled using a standard two-factor affine model, thus leading to a four-factor model for corporate yields. This approach allows us to model the volatility of corporate credit spreads as stochastic, and also allows us to capture higher moments of credit spreads. We use an extended Kalman filter approach to estimate our model on corporate bond prices for 108 firms. The model is found to be successful at fitting actual corporate bond credit spreads, resulting in a significantly lower root mean square error (RMSE) than a standard alternative model in both in-sample and out-of-sample analyses. In addition, key properties of actual credit spreads are better captured by the model.

The Informational Efficiency of the Corporate Bond Market: An Intraday Analysis

Using a unique dataset based on daily and hourly high-yield bond transaction prices, we find the informational efficiency of corporate bond prices is similar to that of the underlying stocks. We find that stocks do not lead bonds in reflecting firm-specific information. We further examine price behavior around earnings news and find that information is quickly incorporated into both bond and stock prices, even at short return horizons. Finally, we find that measures of market quality are no poorer for the bonds in our sample than for the underlying stocks.

Which Factors Affect Corporate Bond Pricing? Evidence from Eurobonds Primary Market Spreads

The question of which factors are relevant in determining corporate bonds pricing is empirically investigated by analyzing the issuance spreads of eurobonds completed by Canadian, European, Japanese and U.S. companies during the 1991-2001 eleven year period. A unique dataset of spreads, ratings and other relevant bond variables is used for a sample of 3,403 eurobonds issues. Four main results emerge from the empirical analysis. First, the ratings of corporate bonds are the most important determinant of spreads between the yield to maturity of bonds and that of equivalent Treasury securities. Second, bond investors' reliance on rating agencies judgements has increased over time during the sample period. Third, while a bond's expected tax treatment represents a relevant factor explaining spreads cross-sectional variability, the primary market efficiency and the expected secondary market liquidity appear as poor explanatory variables. Finally, empirical evidence shows that rating agencies adopt a different, through the cycle evaluation criteria of obligors' creditworthiness with respect to the forward looking one adopted by bond investors.

Factors Affecting the Valuation of Corporate Bonds

The valuation of corporate debt is an important issue in asset pricing. While there has been an enormous amount of theoretical modeling of corporate bond prices, there has been relatively little empirical testing of these models. Recently there has been extensive development of rating based models as a type of reduced form model. These models take as a premise that groups of bonds can be identified which are homogeneous with respect to risk. For each risk group the models require estimates of several characteristics such as the spot yield curve, the default probabilities and the recovery rate. These estimates are then used to compute the theoretical price for each bond in the group. The purpose of this article is to clarify some of the differences among these models, to examine how well they explain prices, and to examine how to group bonds to most effectively estimate prices.

Is Default Event Risk Priced in Corporate Bonds?

We provide an empirical decomposition of the default, liquidity, and tax factors that determine credit spreads and expected corporate bond returns. In particular, we estimate the risk premium associated with a default event. We model default as a jump process with stochastic intensity. The default intensities are a function of common and firm-specific factors. In the model, excess corporate bond returns can be due to risk premia on factors driving the intensities and due to a risk premium on the default jump risk, besides tax and liquidity effects. The model is estimated using data on corporate bond prices for 104 US firms and historical default rates. We find significant risk premia on the common factors that drive intensities, as well as important tax and liquidity effects. These components go a long way towards explaining the level of credit spreads and expected corporate bond returns. Adding a positive default event risk premium helps to explain the remaining error, although this premium cannot be estimated with high statistical precision.

Structural Models of Corporate Bond Pricing: An Empirical Analysis

This paper empirically tests five structural models of corporate bond pricing: Those of Merton (1974), Geske (1977), Leland and Toft (1996), Longstaff and Schwartz (1995), and Collin-Dufresne and Goldstein (2001). We implement the models using a sample of 182 bond prices from firms with simple capital structures during the period 1986-1997. The conventional wisdom is that structural models do not generate spreads as high as those seen in the bond market, and true to expectations we find that the predicted spreads in our implementation of the Merton model are too low. The compound option approach of Geske comes much closer to the spreads observed in the market, on average, but still underpredicts spreads. In contrast, the Leland and Toft model substantially overestimates credit risk on most bonds, and especially so for high coupon bonds. The Longstaff and Schwartz model modifies Merton to incorporate a stochastic interest rate and a correlation between interest rates and firm value. While the correlation and the level of interest rates have little effect, higher interest rate volatility leads to higher predicted spreads. However, this and other features of this model result in spreads that are often too high for risky bonds and too low for safe bonds. The target leverage ratio model of Collin-Dufresne and Goldstein helps to raise the spreads on the bonds that were considered very safe by the Longstaff and Schwartz model, but overall tends toward overestimation of credit risk. We conclude that structural models do not systematically underpredict spreads, as the previous literature implies, but accuracy is a problem. Moreover, some of the simplifications made to date lead to overestimation of credit risk on the riskier bonds while scarcely affecting the spreads of the safest bonds.

A Simple Approach to Infer Recovery Rates with APR Violation from Debt Spreads

A Simple Approach to Estimate Recovery Rates with APR Violation from Debt Spreads by Haluk Unal, Dilip Madan, and Levent Guntay This paper proposes a simple approach to estimate the implied recovery rates embedded in the prices of the debt securities of a firm that differ in priority at time of default. The approach allows for a complex capital structure setting assuming that the absolute priority rule (APR) can be violated. The paper demonstrates that a new statistic, the adjusted relative spread, captures recovery information in debt prices. Model implied recovery rates from corporate bond prices are observed to be consistent with the findings of Altman and Kishmore (1996). Interest rates and firm tangible assets are shown to be significant determinants of recovery rates.

Credit Risk: Constructing the Basic Building Blocks

This paper uses three basic results to address three problems. The first problem concerns the pricing of corporate bonds, when in the event of default the claim of the bond holders is on the principal of the bond plus accrued interest. The second concerns the pricing of revolver loans, and the third problem we address is the valuation of the collateral associated with a loan.(J.E.L.: G12, G13)

A Simple Multi-Factor Model of Corporate Bond Prices

We propose a multi-factor structural model of corporate bond prices. Bonds are valued in an arbitrage-free setting. The term structure of credit spreads is a function of a set of observable variables, including the issuer's leverage ratio, the riskfree interest rate and other stochastic factors that proxy for the issuer's likelihood of default. The set of factors may include both systematic and idiosyncratic components. We test the model using prices of Delta Airlines' bonds. Factors included in this empirical analysis are the growth rate of GDP and the volatility on Delta's stock. The root mean squared error between actual credit spreads and model-determined credit spreads decreases from 45 to 40 basis points when these factors are included in the analysis. Several extant models in the literature are special cases of the structure developed here and rejected in the empirical work.

A NOTE ON RISKY BOND VALUATION

This paper develops a corporate bond valuation model that incorporates a default barrier with dynamics depending on stochastic interest rates and variance of the corporate bond function. Since the volatility of the firm value affects the level of leverage over time through the variance of the corporate bond function, more realistic default scenarios can be put into the valuation model. When the firm value touches the barrier, bondholders receive an exogenously specified number of riskless bonds. We derive a closed-form solution of the corporate bond price as a function of firm value and a short-term interest rate, with time-dependent model parameters governing the dynamics of the firm value and interest rate. The numerical results show that the dynamics of the barrier has material impact on the term structures of credit spreads. This model provides new insight for future research on risky corporate bonds analysis and modelling credit risk.