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35
The riskadjusted cost of financial distress.
 Journal of Finance,
, 2007
"... Abstract In this paper we argue that systematic risk matters for the valuation of financial distress costs. Since financial distress is more likely to happen in bad times, the riskadjusted probability of financial distress is larger than the historical probability. We propose a methodology for the ..."
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Cited by 75 (3 self)
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Abstract In this paper we argue that systematic risk matters for the valuation of financial distress costs. Since financial distress is more likely to happen in bad times, the riskadjusted probability of financial distress is larger than the historical probability. We propose a methodology for the valuation of distress costs, which uses observed corporate bond spreads to estimate riskadjusted probabilities of financial distress. Because credit spreads are so large (the "credit spread puzzle"), the magnitude of the distress riskadjustment can be substantial, suggesting that a valuation of distress costs that ignores systematic risk significantly underestimates the true value. For a firm whose bonds are rated BBB, our benchmark calculations suggest that the NPV of distress increases from 1.4% of predistress firm value if we use historical default probabilities, to 4.5% using riskadjusted probabilities derived from bond spreads. Marginal distress costs also increase substantially. For example, a leverage increase that changes ratings from AA to BBB is associated with an increase in distress costs of 2.7% using riskadjusted probabilities, but only 1.1% using historical probabilities. We argue that the magnitude of these marginal, riskadjusted distress costs is similar to the magnitude of the marginal tax benefits of debt derived by
Stock Options and Credit Default Swaps: A Joint Framework for Valuation and Estimation
 JOURNAL OF FINANCIAL ECONOMETRICS, 2009, 1–41
, 2009
"... 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 ..."
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Cited by 58 (9 self)
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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 jumpdiffusion 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.
Explaining the level of credit spreads: optionimplied jump risk premia in a firm value model
, 2005
"... Prices of equity index put options contain information on the price of systematic downward jump risk. We use a structural jumpdiffusion firm value model to assess the level of credit spreads that is generated by optionimplied jump risk premia. In our compound option pricing model, an equity index ..."
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Cited by 45 (2 self)
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Prices of equity index put options contain information on the price of systematic downward jump risk. We use a structural jumpdiffusion firm value model to assess the level of credit spreads that is generated by optionimplied jump risk premia. In our compound option pricing model, an equity index option is an option on a portfolio of call options on the underlying firm values. We calibrate the model parameters to historical information on default risk, the equity premium and equity return distribution, and S&P 500 index option prices. Our results show that a model without jumps fails to fit the equity return distribution and option prices, and generates a low outofsample prediction for credit spreads. Adding jumps and jump risk premia improves the fitofthe model in terms of equity and option characteristics considerably and brings predicted credit spread levels much closer to observed levels.
A jump to default extended CEV model: An application of Bessel processes
, 2005
"... We consider the problem of developing a ßexible and analytically tractable framework which uniÞes the valuation of corporate liabilities, credit derivatives, and equity derivatives. Theory and empirical evidence suggest that default indicators such as credit default swap (CDS) spreads and corporate ..."
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Cited by 43 (3 self)
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We consider the problem of developing a ßexible and analytically tractable framework which uniÞes the valuation of corporate liabilities, credit derivatives, and equity derivatives. Theory and empirical evidence suggest that default indicators such as credit default swap (CDS) spreads and corporate bond yields are positively related to historical volatility and implied volatilities of equity options. Theory and empirical evidence also suggest that a stocks realized volatility is negatively related to its price (leverage effect) and that implied volatilities are decreasing in the options strike price (skew). We propose a parsimonious reducedform model of default which captures all of these fundamental relationships. We assume that the stock price follows a diffusion, punctuated by a possible jump to zero (default). To capture the positive link between default and volatility, we assume that the hazard rate of default is an increasing affine function of the instantaneous variance of returns on the underlying stock. To capture the negative link between volatility and stock price, we assume a Constant Elasticity of Variance (CEV) speciÞcation for the instantaneous stock volatility prior to default. We show that deterministic changes of time and scale reduce our
Credit spreads, optimal capital structure, and implied volatility with endogenous default and jump risk
, 2005
"... We propose a twosided jump model for credit risk by extending the LelandToft endogenous default model based on the geometric Brownian motion. The model shows that jump risk and endogenous default can have significant impacts on credit spreads, optimal capital structure, and implied volatility of e ..."
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Cited by 34 (6 self)
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We propose a twosided jump model for credit risk by extending the LelandToft endogenous default model based on the geometric Brownian motion. The model shows that jump risk and endogenous default can have significant impacts on credit spreads, optimal capital structure, and implied volatility of equity options: (1) The jump and endogenous default can produce a variety of nonzero credit spreads, including upward, humped, and downward shapes; interesting enough, the model can even produce, consistent with empirical findings, upward credit spreads for speculative grade bonds. (2) The jump risk leads to much lower optimal debt/equity ratio; in fact, with jump risk, highly risky firms tend to have very little debt. (3) The twosided jumps lead to a variety of shapes for the implied volatility of equity options, even for long maturity options; and although in generel credit spreads and implied volatility tend to move in the same direction under exogenous default models, but this may not be true in presence of endogenous default and jumps. In terms of mathematical contribution, we give a proof of a version of the “smooth fitting ” principle for the jump model, justifying a conjecture first suggested by Leland and Toft under the Brownian model. 1
Macroeconomic Conditions, Firm Characteristics, and Credit Spreads.Working Paper
, 2005
"... ABSTRACT We study a structural model that allows us to examine how credit spreads are affected by the interaction of macroeconomic conditions and firm characteristics. Unlike most other structural models, our model explicitly incorporates equilibrium macroeconomic dynamics and models a firm's ..."
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Cited by 11 (2 self)
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ABSTRACT We study a structural model that allows us to examine how credit spreads are affected by the interaction of macroeconomic conditions and firm characteristics. Unlike most other structural models, our model explicitly incorporates equilibrium macroeconomic dynamics and models a firm's cash flow as primitive processes. Corporate securities are priced as contingent claims written on cash flows. Default occurs when the firm's cash flow cannot cover the interest payments and the recovery rate is dependent on the economic condition at default. Our model produces the following predictions: (i) credit spread is negatively correlated with interest rate and, ceteris paribus, this correlation is stronger for bonds with higher default probabilities; (ii) credit spread yield curves are upward sloping for lowgrade bonds; (iii) firm characteristics other than leverage ratios have significant effects on credit spreads and these effects also vary with economic conditions. These predictions are consistent with the available empirical evidence and generate implications for further empirical investigation. JEL Classification ABSTRACT We study a structural model that allows us to examine how credit spreads are affected by the interaction of macroeconomic conditions and firm characteristics. Unlike most other structural models, our model explicitly incorporates equilibrium macroeconomic dynamics and models a firm's cash flow as primitive processes. Corporate securities are priced as contingent claims written on cash flows. Default occurs when the firm's cash flow cannot cover the interest payments and the recovery rate is dependent on the economic condition at default. Our model produces the following predictions: (i) credit spread is negatively correlated with interest rate and, ceteris paribus, this correlation is stronger for bonds with higher default probabilities; (ii) credit spread yield curves are upward sloping for lowgrade bonds; (iii) firm characteristics other than leverage ratios have significant effects on credit spreads and these effects also vary with economic conditions. These predictions are consistent with the available empirical evidence and generate implications for further empirical investigation. JEL Classification Number: G12; G13; E43; E44
Limited arbitrage between equity and credit markets
 Journal of Financial Economics
, 2012
"... Abstract We document that shorthorizon pricing discrepancies across firms' equity and credit markets are common and that an economically significant proportion of these are anomalous, indicating a lack of integration between the two markets. Proposing a statistical measure of market integrati ..."
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Cited by 8 (1 self)
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Abstract We document that shorthorizon pricing discrepancies across firms' equity and credit markets are common and that an economically significant proportion of these are anomalous, indicating a lack of integration between the two markets. Proposing a statistical measure of market integration, we investigate whether equitycredit market integration is related to impediments to arbitrage. We find that time variation in integration across a firm's equity and credit markets is related to firmspecific impediments to arbitrage such as liquidity in equity and credit markets and idiosyncratic risk. Our evidence provides a potential resolution to the puzzle of why Merton model hedge ratios match empirically observed stockbond elasticities
The Complete Picture of Credit Default Swap Spreads  A Quantile Regression Approach, Working Paper
, 2008
"... 1 The complete picture of Credit Default Swap spreadsa Quantile Regression approach We study the determinants of Credit Default Swap (CDS) spreads through quantile regressions. In addition to traditional variables, the results indicate that CDS spreads are also determined by illiquidity costs. Howe ..."
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Cited by 5 (0 self)
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1 The complete picture of Credit Default Swap spreadsa Quantile Regression approach We study the determinants of Credit Default Swap (CDS) spreads through quantile regressions. In addition to traditional variables, the results indicate that CDS spreads are also determined by illiquidity costs. However, contrary to stocks or bonds, we show that CDS transaction costs should be measured by absolute, rather than relative, bidask spreads. Quantile regressions indicate that both the slopes and the goodnessoffit of the model increase with CDS premiums, which is consistent with the credit spread puzzle. Furthermore, our results imply that the empirical models of CDS spreads based on classical mean regressions presented in most previous studies are only successful for the subset of highrisk firms.
Jump Risk, Stock Returns, and Slope of Implied Volatility Smile ∗
, 2008
"... Under the jumpdiffusion framework, expected stock return is dependent on the average jump size of stock price, which can be inferred from the slope of option implied volatility smile. This implies a negative relation between expected stock return and slope of implied volatility smile, which is stro ..."
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Cited by 4 (0 self)
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Under the jumpdiffusion framework, expected stock return is dependent on the average jump size of stock price, which can be inferred from the slope of option implied volatility smile. This implies a negative relation between expected stock return and slope of implied volatility smile, which is strongly supported by the empirical evidence. For over 4,000 stocks ranked by slope of implied volatility smile during 1996 – 2005, the difference between average returns of the lowest and highest quintile portfolios is 22.2 % per year. The findings cannot be explained by risk factors like RM − Rf, SMB, HML, and MOM; or by stock characteristics like size, booktomarket, leverage, volatility, skewness, and volume.