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103
A yieldfactor model of interest rates
 Math. Finance
, 1996
"... This paper presents a consistent and arbitragefree multifactor model of the term structure of interest rates in which yields at selected fixed maturities follow a parametric multivariate Markov diffusion process with “stochastic volatility. ” The yield of any zerocoupon bond is taken to be a matur ..."
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Cited by 384 (14 self)
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This paper presents a consistent and arbitragefree multifactor model of the term structure of interest rates in which yields at selected fixed maturities follow a parametric multivariate Markov diffusion process with “stochastic volatility. ” The yield of any zerocoupon bond is taken to be a maturitydependent affine combination of the selected “basis ” set of yields. We provide necessary and sufficient conditions on the stochastic model for this affine representation. We include numerical techniques for solving the model, as wcll as numerical techniques for calculating the prices of termstructure derivative prices. The case of jump diffusions i \ also considered. I.
2000): “Specification Analysis of Affine Term Structure Models
 Journal of Finance
"... This paper explores the structural differences and relative goodnessoffits of affine term structure models ~ATSMs!. Within the family of ATSMs there is a tradeoff between flexibility in modeling the conditional correlations and volatilities of the risk factors. This tradeoff is formalized by our ..."
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Cited by 336 (30 self)
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This paper explores the structural differences and relative goodnessoffits of affine term structure models ~ATSMs!. Within the family of ATSMs there is a tradeoff between flexibility in modeling the conditional correlations and volatilities of the risk factors. This tradeoff is formalized by our classification of Nfactor affine family into N � 1 nonnested subfamilies of models. Specializing to threefactor ATSMs, our analysis suggests, based on theoretical considerations and empirical evidence, that some subfamilies of ATSMs are better suited than others to explaining historical interest rate behavior. IN SPECIFYING A DYNAMIC TERM STRUCTURE MODEL—one that describes the comovement over time of short and longterm bond yields—researchers are inevitably confronted with tradeoffs between the richness of econometric representations of the state variables and the computational burdens of pricing and estimation. It is perhaps not surprising then that virtually all of the empirical implementations of multifactor term structure models that use time series data on long and shortterm bond yields simultaneously have focused on special cases of “affine ” term structure models ~ATSMs!.AnATSM accommodates timevarying means and volatilities of the state variables through affine specifications of the riskneutral drift and volatility coefficients. At the same time, ATSMs yield essentially closedform expressions for zerocouponbond prices ~Duffie and Kan ~1996!!, which greatly facilitates pricing and econometric implementation. The focus on ATSMs extends back at least to the pathbreaking studies by Vasicek ~1977! and Cox, Ingersoll, and Ross ~1985!, who presumed that the instantaneous short rate r~t! was an affine function of an Ndimensional state vector Y~t!, r~t! � d 0 � d y Y~t!, and that Y~t! followed Gaussian and squareroot diffusions, respectively. More recently, researchers have explored formulations of ATSMs that extend the onefactor Markov represen
A NoArbitrage Vector Autoregression of Term Structure Dynamics with Macroeconomic and Latent Variables
, 2002
"... ..."
Testing ContinuousTime Models of the Spot Interest Rate
 Review of Financial Studies
, 1996
"... Different continuoustime models for interest rates coexist in the literature. We test parametric models by comparing their implied parametric density to the same density estimated nonparametrically. We do not replace the continuoustime model by discrete approximations, even though the data are rec ..."
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Cited by 194 (7 self)
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Different continuoustime models for interest rates coexist in the literature. We test parametric models by comparing their implied parametric density to the same density estimated nonparametrically. We do not replace the continuoustime model by discrete approximations, even though the data are recorded at discrete intervals. The principal source of rejection of existing models is the strong nonlinearity of the drift. Around its mean, where the drift is essentially zero, the spot rate behaves like a random walk. The drift then meanreverts strongly when far away from the mean. The volatility is higher when away from the mean. The continuoustime financial theory has developed extensive tools to price derivative securities when the underlying traded asset(s) or nontraded factor(s) follow stochastic differential equations [see Merton (1990) for examples]. However, as a practical matter, how to specify an appropriate stochastic differential equation is for the most part an unanswered question. For example, many different continuoustime The comments and suggestions of Kerry Back (the editor) and an anonymous referee were very helpful. I am also grateful to George Constantinides,
A Nonparametric Model of Term Structure Dynamics and the Market Price of Interest Rate Risk
, 1997
"... This article presents a technique for nonparametrically estimating continuoustime di#usion processes which are observed at discrete intervals. We illustrate the methodology by using daily three and six month Treasury Bill data, from January 1965 to July 1995, to estimate the drift and di#usion of t ..."
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Cited by 126 (5 self)
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This article presents a technique for nonparametrically estimating continuoustime di#usion processes which are observed at discrete intervals. We illustrate the methodology by using daily three and six month Treasury Bill data, from January 1965 to July 1995, to estimate the drift and di#usion of the short rate, and the market price of interest rate risk. While the estimated di#usion is similar to that estimated by Chan, Karolyi, Longsta# and Sanders (1992), there is evidence of substantial nonlinearity in the drift. This is close to zero for low and medium interest rates, but mean reversion increases sharply at higher interest rates.
Is default event risk priced in corporate bonds. Working
, 2002
"... We identify and estimate the sources of risk that cause corporate bonds to earn an excess return over defaultfree bonds. In particular, we estimate the risk premium associated with a default event. Default is modelled using a jump process with stochastic intensity. For a large set of firms, we mode ..."
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Cited by 86 (1 self)
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We identify and estimate the sources of risk that cause corporate bonds to earn an excess return over defaultfree bonds. In particular, we estimate the risk premium associated with a default event. Default is modelled using a jump process with stochastic intensity. For a large set of firms, we model the default intensity of each firm as a function of common and firmspecific factors. In the model, corporate bond excess returns can be due to risk premia on factors driving the intensities and due to a risk premium on the default jump risk. The model is estimated using data on corporate bond prices for 104 US firms and historical default rate data. We find significant risk premia on the factors that drive intensities. However, these risk premia cannot fully explain the size of corporate bond excess returns. Next, we estimate the size of the default jump risk premium, correcting for possible tax and liquidity effects. The estimates show that this event risk premium is a significant and economically important determinant of excess corporate bond returns.
Modeling Sovereign Yield Spreads: A Case Study of Russian Debt
 Journal of Finance
, 2003
"... We construct a model for pricing sovereign debt that accounts for the risks of both default and restructuring, and allows for compensation for illiquidity. Using a new and relatively efficient method, we estimate the model using Russian dollardenominated bonds. We consider the determinants of the R ..."
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Cited by 85 (7 self)
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We construct a model for pricing sovereign debt that accounts for the risks of both default and restructuring, and allows for compensation for illiquidity. Using a new and relatively efficient method, we estimate the model using Russian dollardenominated bonds. We consider the determinants of the Russian yield spread, the yield differential across different Russian bonds, and the implications for market integration, relative liquidity, relative expected recovery rates, and implied expectations of different default scenarios. THIS PAPER DEVELOPS A MODEL of the termstructure of credit spreads on sovereign bonds that accommodates: (i) Default or repudiation: The sovereign announces that it will stop making payments on its debt; (ii) Restructuring or renegotiation: The sovereign and the lenders ‘‘agree’ ’ to reduce (or postpone) the remaining payments; and (iii) A‘‘regime switch,’’such as a change of government or the default of another sovereign bond that changes the perceived risk of future defaults.We build on the framework of Duffie and Singleton (1999), showing that
Term Structure of Interest Rates with Regime Shifts
 Journal of Finance
, 2002
"... We develop a term structure model where the short interest rate and the market price of risks are subject to discrete regime shifts. Empirical evidence from efficient method of moments estimation provides considerable support for the regime shifts model. Standard models, which include affine specifi ..."
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Cited by 79 (1 self)
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We develop a term structure model where the short interest rate and the market price of risks are subject to discrete regime shifts. Empirical evidence from efficient method of moments estimation provides considerable support for the regime shifts model. Standard models, which include affine specifications with up to three factors, are sharply rejected in the data. Our diagnostics show that only the regime shifts model can account for the welldocumented violations of the expectations hypothesis, the observed conditional volatility, and the conditional correlation across yields. We find that regimes are intimately related to business cycles. MANY PAPERS DOCUMENT THAT THE UNIVARIATE short interest rate process can be reasonably well modeled in the time series as a regime switching process ~see Hamilton ~1988!, Garcia and Perron ~1996!!. In addition to this statistical evidence, there are economic reasons as well to believe that regime shifts are important to understanding the behavior of the entire yield curve. For example, business cycle expansion and contraction “regimes ” potentially
Quadratic Term Structure Models: Theory and Evidence
, 1999
"... This paper theoretically explores the characteristics underpinning quadratic term structure models (QTSMs), which designate the yield on a bond as a quadratic function of underlying state variables. We develop a comprehensive QTSM, which is maximally exible and thus encompasses the features of sever ..."
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Cited by 73 (1 self)
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This paper theoretically explores the characteristics underpinning quadratic term structure models (QTSMs), which designate the yield on a bond as a quadratic function of underlying state variables. We develop a comprehensive QTSM, which is maximally exible and thus encompasses the features of several diverse models including the double squareroot model of Longsta (1989), the univariate quadratic model of Beaglehole and Tenney (1992), and the SquaredAutoregressiveIndependentVariable Nominal Term Structure (SAINTS) model of Constantinides (1992). We document a complete classication of admissibility and empirical identication for the QTSM, and demonstrate that the QTSM can overcome limitations inherent in ane term structure models (ATSMs). Using the Ecient Method of Moments of Gallant and Tauchen (1996), we test the empirical performance of the model in determining bond prices and compare the performance to the ATSMs. The results of the goodnessoft tests suggest that the QTSMs...