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111
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...
Closedform likelihood expansions for multivariate diffusions (2002). NBER Working Paper No. W8956. Available at SSRN: http://ssrn.com/abstract=313657
"... This paper provides closedform expansions for the loglikelihood function of multivariate diffusions sampled at discrete time intervals. The coefficients of the expansion are calculated explicitly by exploiting the special structure afforded by the diffusion model. Examples of interest in financial ..."
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Cited by 67 (3 self)
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This paper provides closedform expansions for the loglikelihood function of multivariate diffusions sampled at discrete time intervals. The coefficients of the expansion are calculated explicitly by exploiting the special structure afforded by the diffusion model. Examples of interest in financial statistics and Monte Carlo evidence are included, along with the convergence of the expansion to the true likelihood function.
Is the Short Rate Drift Actually Nonlinear?
, 1999
"... AitSahalia (1996) and Stanton (1997) use nonparametric estimators applied to short term interest rate data to conclude that the drift function contains important nonlinearities. We study the finitesample properties of their estimators by applying them to simulated sample paths of a squareroot dif ..."
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Cited by 50 (1 self)
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AitSahalia (1996) and Stanton (1997) use nonparametric estimators applied to short term interest rate data to conclude that the drift function contains important nonlinearities. We study the finitesample properties of their estimators by applying them to simulated sample paths of a squareroot diffusion. Although the drift function is linear, both estimators suggest nonlinearities of the type and magnitude reported in AitSahalia (1996) and Stanton (1997). Combined with the results of a weighted least squares estimator, this evidence implies that nonlinearity of the short rate drift is not a robust stylized fact.
Term structure dynamics in theory and reality
 Review of Financial Studies
, 2003
"... This paper is a critical survey of models designed for pricing fixed income securities and their associated term structures of market yields. Our primary focus is on the interplay between the theoretical specification of dynamic term structure models and their empirical fit to historical changes in ..."
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Cited by 48 (8 self)
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This paper is a critical survey of models designed for pricing fixed income securities and their associated term structures of market yields. Our primary focus is on the interplay between the theoretical specification of dynamic term structure models and their empirical fit to historical changes in the shapes of yield curves. We begin by overviewing the dynamic term structure models that have been fit to treasury or swap yield curves and in which the risk factors follow diffusions, jumpdiffusion, or have “switching regimes. ” Then the goodnessoffits of these models are assessed relative to their abilities to: (i) match linear projections of changes in yields onto the slope of the yield curve; (ii) match the persistence of conditional volatilities, and the shapes of term structures of unconditional volatilities, of yields; and (iii) to reliably price caps, swaptions, and other fixedincome derivatives. For the case of defaultable securities we explore the relative fits to historical yield spreads. 1
A selective overview of nonparametric methods in financial econometrics
 Statist. Sci
, 2005
"... Abstract. This paper gives a brief overview of the nonparametric techniques that are useful for financial econometric problems. The problems include estimation and inference for instantaneous returns and volatility functions of timehomogeneous and timedependent diffusion processes, and estimation ..."
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Cited by 35 (8 self)
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Abstract. This paper gives a brief overview of the nonparametric techniques that are useful for financial econometric problems. The problems include estimation and inference for instantaneous returns and volatility functions of timehomogeneous and timedependent diffusion processes, and estimation of transition densities and state price densities. We first briefly describe the problems and then outline the main techniques and main results. Some useful probabilistic aspects of diffusion processes are also briefly summarized to facilitate our presentation and applications.
On the simultaneous calibration of multifactor lognormal interestrate models to Black volatilities and to the correlation matrix Riccardo Rebonato
, 1999
"... It is shown in this paper that it is not only possible, but indeed expedient and advisable, to perform a simultaneous calibration of a lognormal BGM interestrate model to the percentage volatilities of the individual rates and to the correlation surface. One of the contributions of the paper it to ..."
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Cited by 34 (1 self)
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It is shown in this paper that it is not only possible, but indeed expedient and advisable, to perform a simultaneous calibration of a lognormal BGM interestrate model to the percentage volatilities of the individual rates and to the correlation surface. One of the contributions of the paper it to show that the task can be accomplished in two separate and independent steps: the first part of the calibration (i.e. to cap volatilities) can always be accomplished exactly thanks to straightforward geometrical relationships; the fitting to the correlation surface, thanks to a simple theorem, can then be carried out in a numerically efficient way so that the calibration to the volatilities is not spoiled by the second part of the procedure. The ability to carry out the two tasks separately greatly simplifies the overall task. Actual calculations are shown for a 3 and 4factor implementation of the approach, and the quality of the overall agreement between the target and model correlation surfaces is commented upon. Finally, the dangers of overparametrization, i.e. of forcing (near) exact fitting to certain portions of the correlation matrix, are analysed by looking at the cases of a trigger swap, a Bermudan swaption and a oneway floater (resettable cap). 1
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.
On The Stability Of LogNormal Interest Rate Models And The Pricing Of Eurodollar Futures
, 1995
"... . The lognormal distribution assumption for the term structure of interest is the most natural way to exclude negative spot and forward rates. However, imposing this assumption on the continuously compounded interest rate has a serious drawback: expected rollover returns are infinite even if the rol ..."
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Cited by 29 (1 self)
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. The lognormal distribution assumption for the term structure of interest is the most natural way to exclude negative spot and forward rates. However, imposing this assumption on the continuously compounded interest rate has a serious drawback: expected rollover returns are infinite even if the rollover period is arbitrarily short. As a consequence such models cannot price one of the most widely used hedging instrument on the Euromoney market, namely the Eurofuture contract. The purpose of this paper is to show that the problem with lognormal models result from modelling the wrong rate, namely the continuously compounded rate. If instead one models the effective annual rate the problem disappears, i.e. the expected rollover returns are finite. The paper studies the resulting dynamics of the continuously compounded rate which is neither normal nor lognormal. 1. Introduction Most models of the term structure of interest rate which start with modelling the short rate r(t) are of the for...
Pricing Interest Rate Derivatives: A General Approach”, Working Paper
, 1999
"... comments of the editor and an anonymous referee, who have helped tremendously in improving the content and exposition of the paper. Thanks also to Marco Avellaneda, Steven Evans, Eric ..."
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Cited by 28 (2 self)
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comments of the editor and an anonymous referee, who have helped tremendously in improving the content and exposition of the paper. Thanks also to Marco Avellaneda, Steven Evans, Eric
Timedependent diffusion models for term structure dynamics
 STATISTICA NEERLANDICA
, 2003
"... In an effort to capture the time variation on the instantaneous return and volatility functions, a family of timedependent diffusion processes is introduced to model the term structure dynamics. This allows one to examine how the instantaneous return and price volatility change over time and price ..."
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Cited by 20 (9 self)
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In an effort to capture the time variation on the instantaneous return and volatility functions, a family of timedependent diffusion processes is introduced to model the term structure dynamics. This allows one to examine how the instantaneous return and price volatility change over time and price level. Nonparametric techniques, based on kernel regression, are used to estimate the timevarying coefficient functions in the drift and diffusion. The newly proposed semiparametric model includes most of the wellknown shortterm interest rate models, such as those proposed by Cox, Ingersoll and Ross (1985) and Chan, Karolyi, Longstaff and Sanders (1992). It can be used to test the goodnessoffit of these famous timehomogeneous short rate models. The newly proposed method complements the timehomogeneous nonparametric estimation techniques of Stanton (1997) and Fan and Yao (1998), and is shown through simulations to truly capture the heteroscedasticity and timeinhomogeneous structure in volatility. A family of new statistics is introduced to test whether the timehomogeneous models adequately fit interest rates for certain periods of the economy. We illustrate the new methods by using weekly threemonth treasury bill data.