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12
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 344 (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
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 89 (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
Estimating Stochastic Volatility Diffusion Using Conditional Moments of Integrated Volatility
, 2000
"... We exploit the distributional information contained in highfrequency intraday data in constructing a simple conditional moment estimator for stochastic volatility diffusions. The estimator is based on the analytical solutions of the first two conditional moments for the integrated volatility, which ..."
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Cited by 59 (6 self)
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We exploit the distributional information contained in highfrequency intraday data in constructing a simple conditional moment estimator for stochastic volatility diffusions. The estimator is based on the analytical solutions of the first two conditional moments for the integrated volatility, which is effectively approximated by the quadratic variation of the process. We successfully implement the resulting GMM estimator with highfrequency fiveminute foreign exchange and equity index returns. Our simulation evidence and actual empirical results indicate that the method is very reliable and accurate. The computational speed of the procedure compares very favorably to other existing estimation methods in the literature.
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 50 (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
Affine processes and applications in finance
 Annals of Applied Probability
, 2003
"... Abstract. We provide the definition and a complete characterization of regular affine processes. This type of process unifies the concepts of continuousstate branching processes with immigration and OrnsteinUhlenbeck type processes. We show, and provide foundations for, a wide range of financial ap ..."
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Cited by 39 (5 self)
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Abstract. We provide the definition and a complete characterization of regular affine processes. This type of process unifies the concepts of continuousstate branching processes with immigration and OrnsteinUhlenbeck type processes. We show, and provide foundations for, a wide range of financial applications for regular affine processes.
JumpDiffusion Term Structure and Itô Conditional Moment Generator
, 2001
"... This paper implements a Multivariate Weighted Nonlinear Least Square estimator for a class of jumpdiffusion interest rate processes (hereafter MWNLSJD), which also admit closed form solutions to bond prices under a noarbitrage argument. The instantaneous interest rate is modeled as a mixture of ..."
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Cited by 2 (0 self)
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This paper implements a Multivariate Weighted Nonlinear Least Square estimator for a class of jumpdiffusion interest rate processes (hereafter MWNLSJD), which also admit closed form solutions to bond prices under a noarbitrage argument. The instantaneous interest rate is modeled as a mixture of a squareroot diffusion process and a Poisson jump process. One can derive analytically the first four conditional moments, which form the basis of the MWNLSJD estimator. A diagnostic conditional moment test can also be constructed from the fitted moment conditions. The market prices of diffusion and jump risks are calibrated by minimizing the pricing errors between a modelimplied yield curve and a target yield curve. The time series estimation of the shortterm interest rate suggests that the jump aug mentation is highly significant and that the pure diffusion process is strongly rejected. The crosssectional evidence indicates that the jumpdiffusion yield curves are both more flexible in reducing pricing errors and are more consistent with the Martingale pricing principle.
Identification and Estimation of 'Maximal' Affine Term . . .
, 2003
"... We propose a canonical representation for affine term structure models where the state vector is comprised of the first few Taylorseries components of the yield curve and their quadratic (co)variations. With this representation: (i) the state variables have simple physical interpretations such as ..."
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We propose a canonical representation for affine term structure models where the state vector is comprised of the first few Taylorseries components of the yield curve and their quadratic (co)variations. With this representation: (i) the state variables have simple physical interpretations such as level, slope and curvature, (ii) their dynamics remain affine and tractable, (iii) the model is by construction ‘maximal’ (i.e., it is the most general model that is econometrically identifiable), and (iv) modelinsensitive estimates of the state vector process implied from the term structure are readily available. (Furthermore, this representation may be useful for identifying the state variables in a squaredGaussian framework where typically there is no onetoone mapping between observable yields and latent state variables). We find that the ‘unrestricted’ A 1 (3) model of Dai and Singleton (2000) estimated by ‘inverting’ the yield curve for the state variables generates volatility estimates that are negatively correlated with the time series of volatility estimated using a standard GARCH approach. This occurs because
Identification and Estimation of . . .
, 2003
"... We propose a canonical representation for affine term structure models where the state vector is comprised of the first few Taylorseries components of the yield curve and their quadratic (co)variations. With this representation: (i) the state variables have simple physical interpretations such as ..."
Abstract
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We propose a canonical representation for affine term structure models where the state vector is comprised of the first few Taylorseries components of the yield curve and their quadratic (co)variations. With this representation: (i) the state variables have simple physical interpretations such as level, slope and curvature, (ii) their dynamics remain affine and tractable, (iii) the model is by construction ‘maximal ’ (i.e., it is the most general model that is econometrically identifiable), and (iv) modelinsensitive estimates of the state vector process implied from the term structure are readily available. We find that the ‘unrestricted ’ A 1(3) model of Dai and Singleton (2000) estimated by ‘inverting ’ the yield curve for the state variables generates volatility estimates that are negatively correlated with the time series of volatility estimated using a standard GARCH approach. This occurs because the ‘unrestricted’ A 1 (3) model imposes the restriction that the volatility state variable is simultaneously a linear combination of yields (i.e., it impacts the crosssection of yields), and the quadratic variation of
Density is Unknown
, 2009
"... In this paper we consider the estimation of Markov models where the transition density is unknown. The approach we propose is based on the empirical characteristic function (ECF) estimation procedure with an approximate optimal weight function. The approximate optimal weight function is obtained thr ..."
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In this paper we consider the estimation of Markov models where the transition density is unknown. The approach we propose is based on the empirical characteristic function (ECF) estimation procedure with an approximate optimal weight function. The approximate optimal weight function is obtained through an Edgeworth/GramCharlier expansion of the logarithmic transition density of the Markov process. We derive the estimating equations and demonstrate that they are similar to the approximate maximum likelihood estimation (AMLE). However, in contrast to the conventional AMLE our approach ensures the consistency of the estimator even with the approximate likelihood function. We illustrate our approach with examples of various Markov processes. Monte Carlo simulations are performed to investigate the finite sample properties of the proposed estimator in comparison with other methods.