• Selected
• Entire List

Abstract:
We suggest a methodology for valuing corporate securities that allows the straightforward derivation of closed form solutions for complex capital structure scenarios. The tractability of the approach stems from its modularity - we provide a number of intuitive building blocks that are sufficient for valuation in most typical situations. A further advantage of our approach is that it makes economic interpretation far easier than what is typically possible with other approaches such as solving partial differential equations. As examples we consider a corporate coupon bond with discrete payments and debt subject to strategic debt service.

Abstract:
We suggest a methodology for valuing corporate securities that allows the straightforward derivation of closed form solutions for complex capital structure scenarios. The tractability of the approach stems from its modularity - we provide a number of intuitive building blocks that are sufficient for valuation in most typical situations. A further advantage of our approach is that it makes economic interpretation far easier than what is typically possible with other approaches such as solving partial differential equations. As examples we consider a corporate coupon bond with discrete payments and debt subject to strategic debt service.

Abstract:
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.

Corporate bonds, financial distress, renegotiation, liquidity risk

Abstract:
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.

Credit risk, corporate bonds, renegotiation, illiquidity

Abstract:
A difficulty which arises when implementing structural bond pricing models is the estimation of the value and risk of the firm's assets - neither of which is directly observable. We perform a simulation experiment in order to evaluate a maximum likelihood method applicable to this problem. Contrasting the performance of the maximum likelihood estimators to that of estimators traditionally used in academia and industry, we find strong support for the maximum likelihood approach. In fact, the inefficiency of the traditional estimator may help to explain the failure of past attempts to implement structural bond pricing models.

Default risk, corporate bonds, credit spreads, maximum likelihood

Abstract:
A difficulty which arises when implementing structural bond pricing models is the estimation of the value and risk of the firm's assets - neither of which is directly observable. We perform a simulation experiment in order to evaluate a maximum likelihood method applicable to this problem. The properties of the bond price estimators are examined using four theoretical bond pricing models: the Black & Scholes (1973) / Merton (1974) model, the Leland & Toft (1996) model, the Briys & de Varenne (1997) model, as well as the Ericsson & Reneby (2001) model. We contrast the performance of the maximum likelihood estimators to that of estimators traditionally used in academia and industry. The results are strongly supportive of the maximum likelihood approach. In fact, the inefficiency of the traditional estimator may explain the failure of past attempts to implement structural bond pricing models.

Credit Risk, Maximum Likelihood, Corporate Bonds

Abstract:
I suggest a continuous time model for debt and equity valuation where leverage and maturity structure are chosen optimally by the firm's management. The capital structure decision involves trading off the tax benefits of leverage, financial distress costs and the agency costs associated with risk shifting incentives. Closed form solutions for the values of corporate securities, the levered firm and agency costs are obtained. I provide quantitative illustrations of how the capital structure decision is influenced by the potential for asset substitution. I show that in a typical scenario, a firm could afford to take on an additional 20% of leverage and use distinctly longer term debt maturity if asset substitution were ruled out. Furthermore I show that when deviations from the Absolute Priority Rule in bankruptcy are present, management is encouraged to increase risk ex post but will compensate ex ante by reducing leverage and using shorter maturity debt.

Capital Structure, Corporate Bond Pricing, Agency Problems

Abstract:
Using a new dataset of bid and offer quotes for credit default swaps, we investigate the relationship between theoretical determinants of default risk and actual market premia using linear regression. These theoretical determinants are firm leverage, volatility and the riskless interest rate. We find that estimated coefficients for these variables are consistent with theory and that the estimates are highly significant both statistically and economically. The explanatory power of the theoretical variables for levels of default swap premia is approximately 60%. The explanatory power for the differences in the premia is approximately 23%. Volatility and leverage by themselves also have substantial explanatory power for credit default swap premia. A principal component analysis of the residuals and the premia shows that there is only weak evidence for a residual common factor and also suggests that the theoretical variables explain a significant amount of the variation in the data. We therefore conclude that leverage, volatility and the riskfree rate are important determinants of credit default swap premia, as predicted by theory.

Credit risk, Credit default swaps

Abstract:
Using a set of structural models, we evaluate bond yield spreads and the price of default protection for a sample of US corporations. Theory predicts that if credit risk alone explains these two quantities, their magnitudes should be similar. Our findings concur with previous results that bond yield spreads are underestimated. However, this is not systematically the case for CDS premia, which in our dataset are much lower than bond spreads. Furthermore, our results highlight the strong relationship between bond residuals and nondefault proxies, in particular illiquidity. CDS residuals exhibit no such relations. This suggests that the bond spread underestimation by our structural models may not stem from their inability to properly account for default risk, but rather from the importance of the omitted risk factors.

Credit risk, credit derivatives, corporate bonds, structural models

Abstract:
We suggest a comprehensive model that values securities as options and consequently ordinary stock options as compound options. Extending the basic Black-Scholes model, we can incorporate common contractual features and stylized facts.

More specifically, we derive a closed form solution for the price of a call option on a down-and-out call. We then show how the obtained result can be generalized in order to price options on complex corporate securities, allowing among other things for corporate taxation, costly financial distress and deviations from the absolute priority rule. The characteristics of the model are illustrated with numerical examples.

Abstract:
We develop a structural bond pricing approach and implement it
on a large panel of US industrial bonds using an efficient maximum
likelihood methodology. We evaluate the model's ability to predict
yield spread levels and changes out-of-sample. Errors are smaller and
distinctly less variable than those found in previous implementations
of structural as well as reduced form models. Furthermore, our analysis
provide evidence that bond yield spreads incorporate a substantial
liquidity component on top of the default spread structural models are
designed to capture.

Abstract:
At any point in time, most firms are not in financial distress. This implies that they must suffer value losses unrelated to their leverage--economic shocks--before becoming financially distressed. We show that if estimates of ex-ante financial distress costs are not filtered from the effects of future economic shocks, they are significantly biased upward, as far as an order of magnitude. Filtered from economic shocks, pure ex-ante distress costs average less than 1% of current firm value. We also estimate sensitivities of ex-ante distress costs to leverage that are generally far too small to offset the expected tax benefits. Extending our analysis to the cross section and time series, we confirm that ex-ante distress costs are highest: i) when the risk premium in debt markets is high, and ii) among firms with high systematic risk. Overall, our results suggest that most firms use debt too conservatively, but we characterize conditions under which they do not.

financial distress costs, default probabilities

Abstract:
Corporate bond prices are known to be influenced by default and term structure risk in addition to non-default risks such as illiquidity. Putable corporate bonds allow investors to sell their holdings back to the issuer and may thus provide insurance against all of these risks. We first document empirically that embedded put option values are related to proxies for all three. In a second step, we develop a valuation model that simultaneously captures default and interest rate risk. We use this model to disentangle the reduction in yield spread enjoyed by putable bonds that can be attributed to each risk. Perhaps surprisingly, the most important reduction is due to mitigated default or spread risk, followed by term structure risk. The reduction in the non-default component is present but rather small.

Putable Bonds, Credit Risk, Liquidity Premium, Bivariate Lattice

Abstract:
We study the link between corporate bond risk premia and equity returns in a large panel of corporate bond transaction data. In contrast to previous work, we find that a significant part of the time variation in bond risk premia can be explained by equity implied bond risk premium estimates. We also document a large time variation in the expected loss component of bond spreads. This component is related to total asset volatility, whereas the risk premium is related to systematic volatility. In addition, we show by means of linear regressions that augmenting the set of variables predicted by typical structural models with equity-implied bond default risk premia significantly increases explanatory power.

corporate bonds, credit risk, structural model, volatility, default risk premia, idiosyncratic risk.

Abstract:
Characterizing the dependence between companies’ defaults is a central problem in the credit risk literature, and the dependence structure is a first order determinant of the value of credit portfolios and structured credit products such as collateralized debt obligations (CDO), as well as the relative values of CDO tranches. We compare correlation measures implied by CDO prices with time-varying correlations implied by equity returns and CDS spreads. We use flexible dynamic equicorrelation techniques introduced by Engle and Kelly (2008) to capture time variation in CDS-implied and equity return-implied correlations. We perform this analysis using North American firms from the CDX index, as well as European firms from the iTraxx index. All correlation time series are highly time-varying and persistent, and correlations extracted from CDSs and CDOs increased significantly in European and North American markets during the turbulent second half of 2007. Interestingly, we find that the correlation time-series implied by CDO prices co-moves very strongly with the correlation time-series extracted from CDS spreads, but somewhat less strongly with the correlations between equity returns. These findings suggest that the cross-sectional dependence in these complex structured products is fairly well measured. However, changes in CDO prices may be due to changes in correlation, and more sophisticated models with time-varying correlations are thus needed to value CDOs.

credit risk, structured products, dynamic equicorrelation, CDS, CDO, default

Abstract:
Reduced form credit risk models are often thought to be better suited for pricing corporate bonds than structural models. In this paper we challenge this view; by conditioning not only on equity but also on bond and dividend information, our structural model performs well in comparison to previously tested reduced form models. Moreover, we consider pricing of bond portfolios and show that model errors are to a large extent diversifiable.

Credit risk, yield spreads, structural models

Abstract:
We develop a methodology to study the linkages between equity and corporate bond risk premia and apply it to a large panel of corporate bond transaction data. We and that a significant part of the time variation in bond default risk premia can be explained by equity implied bond risk premium estimates. We compute these estimates using a recent structural credit risk model. In addition, we show by means of linear regressions that augmenting the set of variables predicted by typical structural models with equity-implied bond default risk premia significantly increases explanatory power. This in turn suggests that time varying risk premia are a desirable feature for future structural models.

corporate bonds, credit risk, structural model, volatility, default risk premia, idiosyncratic risk

Abstract:
This paper studies the characteristics of firm level equity volatility. There is a lack of consensus in the finance literature as to the relative statistical and economic significance of the leverage and feedback effects on equity volatility. We provide a dynamic framework to investigate simultaneously the leverage and the feedback effects at the firm level. Using the intersection of all firms in CRSP and COMPUSTAT from 1971 to 2005, we build a fixed-effects Panel Vector Autoregression (PVAR) model to investigate the dynamic relationship among leverage, volatility and (realized) risk premium. We find a much larger leverage effect than reported in Christie (1982) and further confirm the leverage effect hypothesis. More importantly, our dynamic model reveals that the leverage effect accumulates over time. The accumulation of the leverage effect over time renders it at least up to five times larger than previously thought. We also study impulse response functions and contemporaneous correlations among the variables and explain their implications.

Financial leverage, stock volatility, panel data, VAR