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58
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
The Information Content of OptionImplied Volatility for Credit Default Swap Valuation. Working Paper
, 2005
"... Abstract Credit default swaps (CDS) are similar to outofthemoney put options in that both offer a low cost and effective protection against downside risk. This study investigates whether put optionimplied volatility is an important determinant of CDS spreads. Using a large sample of firms with b ..."
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Cited by 39 (0 self)
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Abstract Credit default swaps (CDS) are similar to outofthemoney put options in that both offer a low cost and effective protection against downside risk. This study investigates whether put optionimplied volatility is an important determinant of CDS spreads. Using a large sample of firms with both CDS and options data, we find that individual firms' put optionimplied volatility dominates historical volatility in explaining the timeseries variation in CDS spreads. To understand this result, we show that implied volatility is a more efficient forecast for future realized volatility than historical volatility. More importantly, the volatility risk premium embedded in option prices covaries with the CDS spread. These findings complement existing empirical evidence based on marketlevel data.
Understanding the Role of Recovery in Default Risk Models: Empirical Comparisons and Implied Recovery Rates
, 2006
"... This article presents a framework for studying the role of recovery on defaultable debt prices for a wide class of processes describing recovery rates and default probability. These debt models have the ability to differentiate the impact of recovery rates and default probability, and can be employe ..."
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Cited by 36 (0 self)
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This article presents a framework for studying the role of recovery on defaultable debt prices for a wide class of processes describing recovery rates and default probability. These debt models have the ability to differentiate the impact of recovery rates and default probability, and can be employed to infer the market expectation of recovery rates implicit in bond prices. Empirical implementation of these models suggests two central findings. First, the recovery concept that specifies recovery as a fraction of the discounted par value has broader empirical support. Second, parametric debt valuation models can provide a useful assessment of recovery rates embedded in bond prices.
Time Changed Markov Processes in Unified CreditEquity Modeling ∗
, 2008
"... This paper develops a novel class of hybrid creditequity models with statedependent jumps, localstochastic volatility and default intensity based on time changes of Markov processes with killing. We model the defaultable stock price process as a time changed Markov diffusion process with statede ..."
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Cited by 17 (4 self)
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This paper develops a novel class of hybrid creditequity models with statedependent jumps, localstochastic volatility and default intensity based on time changes of Markov processes with killing. We model the defaultable stock price process as a time changed Markov diffusion process with statedependent local volatility and killing rate (default intensity). When the time change is a Lévy subordinator, the stock price process exhibits jumps with statedependent Lévy measure. When the time change is a time integral of an activity rate process, the stock price process has localstochastic volatility and default intensity. When the time change process is a Lévy subordinator in turn time changed with a time integral of an activity rate process, the stock price process has statedependent jumps, localstochastic volatility and default intensity. We develop two analytical approaches to the pricing of credit and equity derivatives in this class of models. The two approaches are based on the Laplace transform inversion and the spectral expansion approach, respectively. If the resolvent (the Laplace transform of the transition semigroup) of the Markov process and the Laplace transform of the time change are both available in closed form, the expectation operator of the
Identifying realized jumps on financial markets
, 2006
"... This paper extends the jump detection method based on bipower variation and swap variance measures to identify realized jumps on financial markets and to estimate parametrically the jump intensity, mean, and variance. Such an approach does not require specifying and estimating the underlying drift ..."
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Cited by 17 (0 self)
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This paper extends the jump detection method based on bipower variation and swap variance measures to identify realized jumps on financial markets and to estimate parametrically the jump intensity, mean, and variance. Such an approach does not require specifying and estimating the underlying drift and diffusion functions. Finite sample evidence suggests that the jump parameters can be accurately estimated and that the statistical inferences can be reliable relative to the maximum likelihood estimation, under the appropriate choice of jump detection test level and assuming that jumps are rare and large. The bipower variation approach performs slightly better than the swap variance approach when the jump contribution to total variance is small. Applications to equity market, treasury bond, individual stock, and exchange rate reveal important differences in jump frequencies and volatilities across asset classes over time. For high investment grade credit spread indices, the estimated jump volatility has a better forecasting power than interest rate factors, volatility factors including optionimplied volatility, and FamaFrench risk factors.
AccountingBased versus MarketBased CrossSectional Models of CDS Spreads
, 2008
"... The relevance of accounting data to providers of capital has been strongly debated. In this paper we provide compelling evidence that accounting metrics are important to providers of debt capital over and above that contained in financial markets. Models of firm distress are mostly either purely acc ..."
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Cited by 17 (0 self)
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The relevance of accounting data to providers of capital has been strongly debated. In this paper we provide compelling evidence that accounting metrics are important to providers of debt capital over and above that contained in financial markets. Models of firm distress are mostly either purely accountingbased (e.g. Altman, 1968; Ohlson, 1980) or purely marketbased (e.g. Merton, 1974). We examine the information content of accountingbased and marketbased metrics in pricing firm distress using a sample of Credit Default Swap (CDS) spreads. Credit Default Swaps are derivatives that offer protection from the event a given firm defaults on its obligations. CDS spreads provide a clean measure of default risk as they are the compensation that market participants require for bearing that risk. Using a sample of 2,860 quarterly CDS spreads available over the period 20012005 we find that a model of distress which is entirely composed of accountingbased metrics performs comparably, if not better, than marketbased structural models of default. Furthermore, we find that both sources of information (accounting and marketbased) are complementary in pricing distress. These results support the notion that accounting metrics have direct value or valuationrelevance to debtholders and holders of credit derivatives.
The economic role of jumps and recovery rates in the market for corporate default risk. Working paper
, 2007
"... as well as friendly support, and to Dow Jones for providing us with complete ICB sector information. We ..."
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Cited by 12 (2 self)
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as well as friendly support, and to Dow Jones for providing us with complete ICB sector information. We
Credit risk modelling using timechanged Brownian motion
, 2007
"... Motivated by the interplay between structural and reduced form credit models, and in particular the rating class model of Jarrow, Lando and Turnbull, we propose to model the firm value process as a timechanged Brownian motion. We are lead to consider modifying the classic first passage problem for ..."
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Cited by 10 (5 self)
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Motivated by the interplay between structural and reduced form credit models, and in particular the rating class model of Jarrow, Lando and Turnbull, we propose to model the firm value process as a timechanged Brownian motion. We are lead to consider modifying the classic first passage problem for stochastic processes to capitalize on this time change structure. We demonstrate that the distribution functions of such “first passage times of the second kind ” are efficiently computable in a wide range of useful examples, and thus this notion of first passage can be used to define the time of default in generalized structural credit models. General formulas for credit derivatives are then proven, and shown to be easily computable. Finally, we show that by treating many firm value processes as dependent time changes of independent Brownian motions, one can obtain multifirm credit models with rich and plausible dynamics and enjoying the possibility of efficient valuation of portfolio credit derivatives.
Economic uncertainty, disagreement, and credit markets, Working paper
, 2010
"... Using an economy populated with agents with heterogeneous beliefs this paper delivers important implications for the role of common and firm specific components of economic uncertainty on credit spreads. We first derive a positive relation between uncertainty and belief heterogeneity in an equilibri ..."
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Cited by 9 (1 self)
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Using an economy populated with agents with heterogeneous beliefs this paper delivers important implications for the role of common and firm specific components of economic uncertainty on credit spreads. We first derive a positive relation between uncertainty and belief heterogeneity in an equilibrium model of credit risk in which agents with different subjective economic uncertainty parameters disagree about the expected growth rate of future cash flows. Then using the model solutions, we obtain testable empirical predictions for the impact of economic uncertainty and differences in beliefs on credit spreads and asset prices. We merge a dataset of firmspecific differences in beliefs and credit spreads and test these predictions empirically. The empirical tests provide 5 new results that are original to the literature: (a) Countercyclical uncertainty is positively related to a common disagreement component about future earning opportunities by financial analysts; (b) The common component of the difference in beliefs in earnings forecasts is the most significant variable in timeseries regressions for credit spreads. At the same time, firmspecific difference in beliefs is the most significant component in the crosssection; (c) Uncertainty induces a significant comovement between credit spreads and stock volatility; (d) During the 2008 Credit Crisis the link between uncertainty and credit spreads was even stronger than in previous crisis periods; (e) Uncertainty and belief heterogeneity have significant explanatory power for noarbitrage violations implied by single factor models in