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65
Modeling Term Structures of Defaultable Bonds
, 1999
"... This article presents convenient reducedform models of the valuation of contingent claims subject to default risk, focusing on applications to the term structure of interest rates for corporate or sovereign bonds. Examples include the valuation of a creditspread option ..."
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Cited by 436 (23 self)
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This article presents convenient reducedform models of the valuation of contingent claims subject to default risk, focusing on applications to the term structure of interest rates for corporate or sovereign bonds. Examples include the valuation of a creditspread option
Term structures of credit spreads with incomplete accounting information
 Econometrica
, 2001
"... Abstract: We study the implications of imperfect information for term structures of credit spreads on corporate bonds. We suppose that bond investors cannot observe the issuer’s assets directly, and receive instead only periodic and imperfect accounting reports. For a setting in which the assets of ..."
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Cited by 194 (10 self)
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Abstract: We study the implications of imperfect information for term structures of credit spreads on corporate bonds. We suppose that bond investors cannot observe the issuer’s assets directly, and receive instead only periodic and imperfect accounting reports. For a setting in which the assets of the firm are a geometric Brownian motion until informed equityholders optimally liquidate, we derive the conditional distribution of the assets, given accounting data and survivorship. Contrary to the perfectinformation case, there exists a defaultarrival intensity process. That intensity is calculated in terms of the conditional distribution of assets. Credit yield spreads are characterized in terms of accounting information. Generalizations are provided. 1 We are exceptionally grateful to Michael Harrison for his significant contributions to this paper, which are noted within. We are also grateful for insightful research assistance
Structural Models of Corporate Bond Pricing: An Empirical Analysis
, 2003
"... This paper empirically tests five structural models of corporate bond pricing: those of Merton (1974), Geske (1977), Leland and Toft (1996), Longsta# and Schwartz (1995), and CollinDufresne and Goldstein (2001). We implement the models using a sample of 182 bond prices from firms with simple capita ..."
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Cited by 150 (5 self)
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This paper empirically tests five structural models of corporate bond pricing: those of Merton (1974), Geske (1977), Leland and Toft (1996), Longsta# and Schwartz (1995), and CollinDufresne and Goldstein (2001). We implement the models using a sample of 182 bond prices from firms with simple capital structures during the period 19861997. The conventional wisdom is that structural models do not generate spreads as high as those seen in the bond market, and true to expectations we find that the predicted spreads in our implementation of the Merton model are too low. However, most of the other structural models predict spreads that are too high on average. Nevertheless, accuracy is a problem, as the newer models tend to severely overstate the credit risk of firms with high leverage or volatility and yet su#er from a spread underprediction problem with safer bonds. The Leland and Toft model is an exception in that it overpredicts spreads on most bonds, particularly those with high coupons. More accurate structural models must avoid features that increase the credit risk on the riskier bonds while scarcely a#ecting the spreads of the safest bonds.
Closed Form Solutions for Term structure Derivatives with Log Normal Interest Rates
 Journal of Finance
, 1997
"... Abstract. We derive a unified term structure of interest rates model which gives closed form solutions for caps and floors written on interest rates as well as puts and calls written on zerocoupon bonds. The crucial assumption is that the simple interest rate over a fixed finite period that matches ..."
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Cited by 84 (1 self)
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Abstract. We derive a unified term structure of interest rates model which gives closed form solutions for caps and floors written on interest rates as well as puts and calls written on zerocoupon bonds. The crucial assumption is that the simple interest rate over a fixed finite period that matches the contract, which we want to price, is lognormally distributed. Moreover, this assumption is shown to be consistent with the HeathJarrowMorton model for a specific choice of volatility. 1.
Continuous Time Bayesian Networks
"... In this paper we present a language for finite state continuous time Bayesian networks (CTBNs), which describe structured stochastic processes that evolve over continuous time. The state of the system is decomposed into a set of local variables whose values change over time. The dynamics of the syst ..."
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Cited by 62 (9 self)
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In this paper we present a language for finite state continuous time Bayesian networks (CTBNs), which describe structured stochastic processes that evolve over continuous time. The state of the system is decomposed into a set of local variables whose values change over time. The dynamics of the system are described by specifying the behavior of each local variable as a function of its parents in a directed (possibly cyclic) graph. The model specifies, at any given point in time, the distribution over two aspects: when a local variable changes its value and the next value it takes. These distributions are determined by the variable’s current value and the current values of its parents in the graph. More formally, each variable is modelled as a finite state continuous time Markov process whose transition intensities are functions of its parents. We present a probabilistic semantics for the language in terms of the generative model a CTBN defines over sequences of events. We list types of queries one might ask of a CTBN, discuss the conceptual and computational difficulties associated with exact inference, and provide an algorithm for approximate inference which takes advantage of the structure within the process.
Optimal Consumption and Portfolio Selection with Stochastic Differential Utility
, 1999
"... We develop the utility gradient (or martingale) approach for computing portfolio and consumption plans that maximize stochastic differential utility (SDU), a continuoustime version of recursive utility due to D. Duffie and L. Epstein (1992, Econometrica 60, 353 394). We characterize the firstorder ..."
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Cited by 61 (3 self)
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We develop the utility gradient (or martingale) approach for computing portfolio and consumption plans that maximize stochastic differential utility (SDU), a continuoustime version of recursive utility due to D. Duffie and L. Epstein (1992, Econometrica 60, 353 394). We characterize the firstorder conditions of optimality as a system of forward backward SDEs, which, in the Markovian case, reduces to a system of PDEs and forward only SDEs that is amenable to numerical computation. Another contribution is a proof of existence, uniqueness, and basic properties for a parametric class of homothetic SDUs that can be thought of as a continuoustime version of the CES Kreps Porteus utilities studied by L. Epstein and A. Zin (1989, Econometrica 57, 937 969). For this class, we derive closedform solutions in terms of a single backward SDE (without imposing a Markovian structure). We conclude with several tractable concrete examples involving the type of ``affine'' state price dynamics that are familiar from the term structure literature.
Is credit event risk priced? Modeling contagion via the updating of beliefs
, 2003
"... We propose a reducedform model where jumpstodefault are priced because they generate a marketwide jump in credit spreads. While this framework is consistent with a counterparty risk interpretation (e.g., Jarrow and Yu (2001)), it is most naturally interpreted as an updating of beliefs due to an ..."
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Cited by 48 (3 self)
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We propose a reducedform model where jumpstodefault are priced because they generate a marketwide jump in credit spreads. While this framework is consistent with a counterparty risk interpretation (e.g., Jarrow and Yu (2001)), it is most naturally interpreted as an updating of beliefs due to an unexpected event. Simple analytic solutions are obtained for the prices of risky debt regardless of the number of firms that share in the contagious response. As a special case, we show that the contagious response can be induced via a liquidityshock, with no impact on actual default intensities. Empirically, we find that credit events of large firms generate a market wide increase in credit spreads and a significant ‘flighttoquality ’ response in the Treasury market. A calibration argument suggests that the premium associated with jumptodefault risk for a typical investment grade firm has an upper bound of a few basis points per year, but that the risk premium for contagionrisk may be considerably larger.
Modeling Credit Risk with Partial Information
 Annals of Applied Probability
, 2002
"... This paper provides an alternative approach to Duffe and Lando [7] for obtaining a reduced form credit risk model from a structural model. ..."
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Cited by 35 (8 self)
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This paper provides an alternative approach to Duffe and Lando [7] for obtaining a reduced form credit risk model from a structural model.
Continuoustime methods in finance: A review and an assessment
 Journal of Finance
, 2000
"... I survey and assess the development of continuoustime methods in finance during the last 30 years. The subperiod 1969 to 1980 saw a dizzying pace of development with seminal ideas in derivatives securities pricing, term structure theory, asset pricing, and optimal consumption and portfolio choices. ..."
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Cited by 32 (0 self)
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I survey and assess the development of continuoustime methods in finance during the last 30 years. The subperiod 1969 to 1980 saw a dizzying pace of development with seminal ideas in derivatives securities pricing, term structure theory, asset pricing, and optimal consumption and portfolio choices. During the period 1981 to 1999 the theory has been extended and modified to better explain empirical regularities in various subfields of finance. This latter subperiod has seen significant progress in econometric theory, computational and estimation methods to test and implement continuoustime models. Capital market frictions and bargaining issues are being increasingly incorporated in continuoustime theory. THE ROOTS OF MODERN CONTINUOUSTIME METHODS in finance can be traced back to the seminal contributions of Merton ~1969, 1971, 1973b! in the late 1960s and early 1970s. Merton ~1969! pioneered the use of continuoustime modeling in financial economics by formulating the intertemporal consumption and portfolio choice problem of an investor in a stochastic dynamic programming setting.