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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,
Do stock prices and volatility jump? Reconciling evidence from spot and option prices
, 2001
"... This paper studies the empirical performance of jumpdiffusion models that allow for stochastic volatility and correlated jumps affecting both prices and volatility. The results show that the models in question provide reasonable fit to both option prices and returns data in the insample estimation ..."
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Cited by 97 (2 self)
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This paper studies the empirical performance of jumpdiffusion models that allow for stochastic volatility and correlated jumps affecting both prices and volatility. The results show that the models in question provide reasonable fit to both option prices and returns data in the insample estimation period. This contrasts previous findings where stochastic volatility paths are found to be too smooth relative to the option implied dynamics. While the models perform well during the high volatility estimation period, they tend to overprice long dated contracts outofsample. This evidence points towards a too simplistic specification of the mean dynamics of volatility.
MCMC Analysis of Diffusion Models with Application to Finance
 Journal of Business and Economic Statistics
, 1998
"... This paper proposes a new method for estimation of parameters in diffusion processes from ..."
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Cited by 88 (3 self)
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This paper proposes a new method for estimation of parameters in diffusion processes from
Reprojecting Partially Observed Systems with Application to Interest Rate Diffusions from January 5, 1992, to March 31, 1995
, 1996
"... We introduce reprojection as a general purpose technique for characterizing the observable dynamics of a partially observed nonlinear system. System parameters are estimated by method of moments wherein moments implied by the system are matched to moments implied by the transition density for observ ..."
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Cited by 81 (13 self)
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We introduce reprojection as a general purpose technique for characterizing the observable dynamics of a partially observed nonlinear system. System parameters are estimated by method of moments wherein moments implied by the system are matched to moments implied by the transition density for observables that is determined by projecting the data onto its Hermite representation. Reprojection imposes the constraints implied by the system on the transition density and is accomplished by projecting a long simulation of the estimated system onto the Hermite representation. We utilize the technique to assess the dynamics of several diffusion models for the shortterm interest rate that have been proposed and compare them to a new model that has feedback from the interest rate into both the drift and diffusion coefficients of a volatility equation. This effort entails the development of new graphical diagnostics.
"Peso Problem" Explanations for Term Structure Anomalies
, 1997
"... We examine the empirical evidence on the expectations hypothesis of the term structure of interest rates in the United States, the United Kingdom, and Germany using the CampbellShiller (1991) regressions and a vectorautoregressive methodology. We argue that anomalies in the U.S. term structure, do ..."
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Cited by 76 (13 self)
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We examine the empirical evidence on the expectations hypothesis of the term structure of interest rates in the United States, the United Kingdom, and Germany using the CampbellShiller (1991) regressions and a vectorautoregressive methodology. We argue that anomalies in the U.S. term structure, documented by Campbell and Shiller (1991), may be due to a generalized peso problem in which a highinterest rate regime occuued less frequently in the sample of U.S. data than was rationally anticipated. We formalize this idea as a regimeswitching model of shortterm interest rates estimated with data from seven countries. Technically, this model extends recent research on regimeswitching models with statedependent transitions to a crosssectional setting. Use of the small sample distributions generated by the regimeswitching model for inference considerably weakens the evidence against the expectations hypothesis, but it remains somewhat implausible that our datagenerating process produced the U.S. data. However, a model that combines moderate timevariation in term premiums with pesoproblem effects is largely consistent with term structure
The Stochastic Behavior of Interest Rates: Implications from a Multifactor, Nonlinear ContinuousTime Model
, 1998
"... This paper presents a general, nonlinear version of existing multifactor models, such as Longstaff and Schwartz (1992). The novel aspect of our approach is that rather than choosing the model parameterization out of "thin air", our processes are generated from the data using approximation methods ..."
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Cited by 20 (3 self)
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This paper presents a general, nonlinear version of existing multifactor models, such as Longstaff and Schwartz (1992). The novel aspect of our approach is that rather than choosing the model parameterization out of "thin air", our processes are generated from the data using approximation methods for multifactor continuoustime Markov processes. In applying this technique to the short and longend of the term structure for a general twofactor diffusion process for interest rates, a major finding is that the volatility of interest rates is increasing in the level of interest rates only for sharply, upward sloping term structures. In fact, the slope of the term structure plays a larger role in determining the magnitude of the diffusion coefficient. As an application, we analyze the model's implications for term structure pricing, focusing on the conditional distribution of interest rates and the term structure of term premiums and volatilities.
Estimation of Continuous Time Models for Stock Returns and Interest Rates
 MACROECONOMIC DYNAMICS
, 1997
"... Efficient Method of Moments (EMM) is used to estimate and test continuous time diffusion models for stock returns and interest rates. For stock returns, a fourstate, twofactor diffusion with one state observed can account for the dynamics of the daily return on the S&P composite index, 19271987. ..."
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Cited by 16 (2 self)
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Efficient Method of Moments (EMM) is used to estimate and test continuous time diffusion models for stock returns and interest rates. For stock returns, a fourstate, twofactor diffusion with one state observed can account for the dynamics of the daily return on the S&P composite index, 19271987. This contrasts with results indicating that discretetime, stochastic volatility models cannot explain these dynamics. For interest rates, a trivariate yield factor model is estimated from weekly, 19621995, Treasury rates. The yield factor model is sharply rejected, although extensions permitting convexities in the local variance come closer to fitting the data.
Do Interest Rates Really Follow ContinuousTime Markov Diffusions?
, 1997
"... This paper examines whether the discontinuities observed in the discrete data are the result of the discreteness of sampling, or rather evidence of genuine nondiffusion dynamics of the continuoustime interest rate process. The issue is to isolate the observable implications for the data of being a ..."
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Cited by 14 (0 self)
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This paper examines whether the discontinuities observed in the discrete data are the result of the discreteness of sampling, or rather evidence of genuine nondiffusion dynamics of the continuoustime interest rate process. The issue is to isolate the observable implications for the data of being an incomplete discrete sample from a continuoustime diffusion. This paper's answer relies on testing a necessary and sufficient restriction on the conditional densities of diffusions, at the sampling interval of the observed data. This restriction characterizes the continuity of the unobservable complete sample path.
Specification Analysis of Continuous Time Models in Finance
, 1996
"... The paper describes the use of the GallantTauchen efficient method of moments (EMM) technique for diagnostic checking of stochastic differential equations (SDEs) estimated from financial market data. The EMM technique is a simulationbased method that uses the score function of an auxiliary model, ..."
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Cited by 3 (1 self)
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The paper describes the use of the GallantTauchen efficient method of moments (EMM) technique for diagnostic checking of stochastic differential equations (SDEs) estimated from financial market data. The EMM technique is a simulationbased method that uses the score function of an auxiliary model, called the score generator, to define a generalized method of moments (GMM) objective function. The technique can handle multivariate SDEs where the state vector is not completely observed. The optimized GMM objective function is distributed as chisquare and may be used to test model adequacy. Elements of the score function that have large values reflect features of data that a rejected SDE specification does not describe well and may be used for diagnostic checking. The diagnostics are illustrated by estimating a YieldFactor Model from weekly, 19621995, term structure data comprised of short (3 month), medium (12 month), and long (10 year) Treasury rates. The YieldFactor Model is sharp...
of Interest Rate Volatility
, 2007
"... This paper presents a general, nonlinear version of existing multifactor models, such as Longstaff and Schwartz (1992). The novel aspect of our approach is that rather than choosing the model parameterization out of “thin air”, our processes are generated from the data using approximation methods fo ..."
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This paper presents a general, nonlinear version of existing multifactor models, such as Longstaff and Schwartz (1992). The novel aspect of our approach is that rather than choosing the model parameterization out of “thin air”, our processes are generated from the data using approximation methods for multifactor continuoustime Markov processes. In applying this technique to the short and longend of the term structure for a general twofactor diffusion process for interest rates, a major finding is that the volatility of interest rates is increasing in the level of interest rates mostly for sharply upward sloping term structures. In fact, the slope of the term structure plays a larger role in determining the magnitude of the diffusion coefficient. As an application, When one sees so many coauthors on a single paper and they are not from the hard sciences, the natural question is why? Looking at both the number and quality of contributors to this volume and how much econometric talent Rob Engle has helped nurture through his career, however, it becomes quite clear that the only way we could participate in Rob’s Festschrift