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A Markov Model for the Term Structure of Credit Risk Spreads
 Review of Financial Studies
, 1997
"... This article provides a Markov model for the term structure of credit risk spreads. The model is based on Jarrow and Turnbull (1995), with the bankruptcy process following a discrete state space Markov chain in credit ratings. The parameters of this process are easily estimated using observable data ..."
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Cited by 237 (12 self)
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This article provides a Markov model for the term structure of credit risk spreads. The model is based on Jarrow and Turnbull (1995), with the bankruptcy process following a discrete state space Markov chain in credit ratings. The parameters of this process are easily estimated using observable data. This model is useful for pricing and hedging corporate debt with imbedded options, for pricing and hedging OTC derivatives with counterparty risk, for pricing and hedging (foreign) government bonds subject to default risk (e.g., municipal bonds), for pricing and hedging credit derivatives, and for risk management. This article presents a simple model for valuing risky debt that explicitly incorporates a firm's credit rating as an indicator of the likelihood of default. As such, this article presents an arbitragefree model for the term structure of credit risk spreads and their evolution through time. This model will prove useful for the pricing and hedging of corporate debt with We would like to thank John Tierney of Lehman Brothers for providing the bond index price data, and Tal Schwartz for computational assistance. We would also like to acknowledge helpful comments received from an anonymous referee. Send all correspondence to Robert A. Jarrow, Johnson Graduate School of Management, Cornell University, Ithaca, NY 14853. The Review of Financial Studies Summer 1997 Vol. 10, No. 2, pp. 481523 1997 The Review of Financial Studies 08939454/97/$1.50 imbedded options, for the pricing and hedging of OTC derivatives with counterparty risk, for the pricing and hedging of (foreign) government bonds subject to default risk (e.g., municipal bonds), and for the pricing and hedging of credit derivatives (e.g. credit sensitive notes and spread adjusted notes). This model can also...
Default risk and diversification: Theory and empirical implications
 Mathematical Finance
, 2005
"... Recent advances in the theory of credit risk allow the use of standard term structure machinery for default risk modeling and estimation. The empirical literature in this area often interprets the drift adjustments of the default intensity’s diffusion state variables as the only default risk premium ..."
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Cited by 15 (1 self)
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Recent advances in the theory of credit risk allow the use of standard term structure machinery for default risk modeling and estimation. The empirical literature in this area often interprets the drift adjustments of the default intensity’s diffusion state variables as the only default risk premium. We show that this interpretation implies a restriction on the form of possible default risk premia, which can be justified through exact and approximate notions of “diversifiable default risk. ” The equivalence between the empirical and martingale default intensities that follows from diversifiable default risk greatly facilitates the pricing and management of credit risk. We emphasize that this is not an equivalence in distribution, and illustrate its importance using credit spread dynamics estimated in Duffee (1999). We also argue that the assumption of diversifiability is implicitly used in certain existing models of mortgagebacked securities.
Sato Processes in Default Modelling
, 2008
"... Classically, in reduced form default models the instantaneous default intensity is the modelling object and survival probabilities are given by the Laplace transform of At = R t 0 sds. Instead, recent literature has shown a tendency towards specifying the process A directly. We will refer to A as th ..."
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Classically, in reduced form default models the instantaneous default intensity is the modelling object and survival probabilities are given by the Laplace transform of At = R t 0 sds. Instead, recent literature has shown a tendency towards specifying the process A directly. We will refer to A as the cumulative hazard process. We present a new cumulative hazard based framework where survival probabilities are still obtained in closed form but where A belongs to the class of selfsimilar additive processes also termed Sato processes. We analyze two speci…cations for the cumulative hazard process; SatoGamma and SatoIG processes where the unit time distribution A1 is described by a Gamma law and Inverse Gaussian law respectively. The models are calibrated to data on the single names included in the iTraxx Europe index and compared with two OrnsteinUhlenbeck type intensity models. It is shown how the Sato models achieve similar calibration errors with fever parameters, and with more stable parameter estimates in time.