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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.
Valuation of default sensitive claims under imperfect information. Working paper
, 2006
"... We propose an evaluation method for financial assets subject to default risk, when investors face imperfect information about the state variable triggering the default. The model we propose generalizes the one by Duffie and Lando (2001) in the following way: (i) it incorporates informational noise i ..."
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Cited by 38 (1 self)
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We propose an evaluation method for financial assets subject to default risk, when investors face imperfect information about the state variable triggering the default. The model we propose generalizes the one by Duffie and Lando (2001) in the following way: (i) it incorporates informational noise in continuous time, (ii) it respects the (H) hypothesis, (iii) it precludes arbitrage from insiders. The model is sufficiently general to encompass a large class of structural models. In this setting we show that the default time is totally inaccessible in the market’s filtration and derive the martingale hazard process. Finally, we provide pricing formulas for defaultsensitive claims and illustrate with particular examples the shapes of the credit spreads and the conditional default probabilities. An important feature of the conditional default probabilities is they are non Markovian. This might shed some light on observed phenomena such as the ”rating momentum”. 1
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
Beyond Hazard Rates: a New Framework for Creditrisk Modelling
"... A new approach to credit risk modelling is introduced that avoids the use of inaccessible stopping times. Default events are associated directly with the failure of obligors to make contractually agreed payments. Noisy information about impending cash flows is available to market participants. In th ..."
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Cited by 18 (11 self)
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A new approach to credit risk modelling is introduced that avoids the use of inaccessible stopping times. Default events are associated directly with the failure of obligors to make contractually agreed payments. Noisy information about impending cash flows is available to market participants. In this framework the market filtration is modelled explicitly, and is assumed to be generated by one or more independent market information processes. Each such information process carries partial information about the values of the market factors that determine future cash flows. For each market factor, the rate at which true information is provided to market participants concerning the eventual value of the factor is a parameter of the model. Analytical expressions that can be readily used for simulation are presented for the price processes of defaultable bonds with stochastic recovery. Similar expressions can be formulated for other debt instruments, including multiname products. An explicit formula is derived for the value of an option on a defaultable discount bond. It is shown that the value of such an option is an increasing function of the rate at which true information is provided about the terminal payoff of the bond. One notable feature of the framework is that it satisfies an overall dynamic consistency condition that makes it suitable as a basis for practical modelling situations where frequent recalibration may be necessary.
Sequential defaults and incomplete information
 Journal of Risk
"... We propose a multifirm firstpassage credit model in which investors have incomplete information. In this model, investors observe neither a firm’s value nor its default barrier. The model takes into account the shortterm risk inherent in default events, the marketwide impact of defaults on secur ..."
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Cited by 18 (2 self)
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We propose a multifirm firstpassage credit model in which investors have incomplete information. In this model, investors observe neither a firm’s value nor its default barrier. The model takes into account the shortterm risk inherent in default events, the marketwide impact of defaults on security prices due to counterparty relations among firms, and the cyclical default dependence effects observed in credit markets. We explicitly calculate the pricing trend and the arrival intensity of the kthtodefault. These results furnish (1) tractable reducedform formulae for arrival probabilities of sequential dependent defaults and prices of multiname credit derivatives, and (2) an algorithm for the simulation of sequential unpredictable default times. 1
Large Portfolio Losses: A Dynamic Contagion Model
 Annals of Applied Probability
"... Using particle system methodologies we study the propagation of financial distress in a network of firms facing credit risk. We investigate the phenomenon of a credit crisis and quantify the losses that a bank may suffer in a large credit portfolio. Applying a large deviation principle we compute th ..."
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Cited by 17 (3 self)
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Using particle system methodologies we study the propagation of financial distress in a network of firms facing credit risk. We investigate the phenomenon of a credit crisis and quantify the losses that a bank may suffer in a large credit portfolio. Applying a large deviation principle we compute the limiting distributions of the system and determine the time evolution of the credit quality indicators of the firms, deriving moreover the dynamics of a global financial health indicator. We finally describe a suitable version of the “Central Limit Theorem ” useful to study large portfolio losses. Simulation results are provided as well as applications to portfolio loss distribution analysis. 1. Introduction. 1.1. General aspects. The main purpose of this paper is to describe propagation of financial distress in a network of firms linked by business relationships. Once the model for financial contagion has been described, we quantify the impact of contagion on the losses suffered by a financial institution
Intensity process and compensator: A new filtration expansion approach and the Jeulin–Yor theorem. The Annals of Applied Probability
, 2007
"... Let (Xt)t≥0 be a continuoustime, timehomogeneous strong Markov process with possible jumps and let τ be its first hitting time of a Borel subset of the state space. Suppose X is sampled at random times and suppose also that X has not hit the Borel set by time t. What is the intensity process of τ ..."
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Cited by 16 (2 self)
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Let (Xt)t≥0 be a continuoustime, timehomogeneous strong Markov process with possible jumps and let τ be its first hitting time of a Borel subset of the state space. Suppose X is sampled at random times and suppose also that X has not hit the Borel set by time t. What is the intensity process of τ based on this information? This question from credit risk encompasses basic mathematical problems concerning the existence of an intensity process and filtration expansions, as well as some conceptual issues for credit risk. By revisiting and extending the famous Jeulin–Yor [Lecture Notes in Math. 649 (1978) 78–97] result regarding compensators under a general filtration expansion framework, a novel computation methodology for the intensity process of a stopping time is proposed. En route, an analogous characterization result for martingales of Jacod and Skorohod [Lecture Notes in Math. 1583 (1994) 21–35] under local jumping filtration is derived.
Credit Risk Models with Incomplete Information
, 2007
"... Incomplete information is at the heart of informationbased credit risk models. In this paper, we rigorously define incomplete information with the notion of “delayed filtrations”. We characterize two distinct types of delayed information, continuous and discrete: the first generated by a time chang ..."
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Cited by 15 (0 self)
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Incomplete information is at the heart of informationbased credit risk models. In this paper, we rigorously define incomplete information with the notion of “delayed filtrations”. We characterize two distinct types of delayed information, continuous and discrete: the first generated by a time change of filtrations and the second by finitely many marked point processes. This notion unifies the noisy information in Duffie and Lando (2001) and the partial information in CollinDufresne et al. (2004), under which structural models are translated into reducedform intensitybased models. We illustrate through a simple example the importance of this notion of delayed information, as well as the potential pitfall for abusing the Laplacian approximation techniques for calculating the intensity process in an informationbased model. The authors are grateful to the Associate Editor and the two anonymous referees for their constructive suggestions and enlightening remarks.