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310
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 122 (18 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.
The Term Structure of Real Rates and Expected Inflation
, 2004
"... Changes in nominal interest rates must be due to either movements in real interest rates, expected inflation, or the inflation risk premium. We develop a term structure model with regime switches, timevarying prices of risk, and inflation to identify these components of the nominal yield curve. We ..."
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Cited by 114 (17 self)
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Changes in nominal interest rates must be due to either movements in real interest rates, expected inflation, or the inflation risk premium. We develop a term structure model with regime switches, timevarying prices of risk, and inflation to identify these components of the nominal yield curve. We find that the unconditional real rate curve is fairly flat at 1.44%, but slightly humped. In one regime, the real term structure is steeply downward sloping. Real rates (nominal rates) are procyclical (countercyclical) and inflation is negatively correlated with real rates. An inflation risk premium that increases with the horizon fully accounts for the generally upward sloping nominal term structure. We find that expected inflation drives about 80 % of the variation of nominal yields at both short and long maturities, but during normal times, all of the
Exact and computationally efficient likelihoodbased estimation for discretely observed diffusion processes
 Journal of the Royal Statistical Society, Series B: Statistical Methodology
, 2006
"... The objective of this paper is to present a novel methodology for likelihoodbased inference for discretely observed diffusions. We propose Monte Carlo methods, which build on recent advances on the exact simulation of diffusions, for performing maximum likelihood and Bayesian estimation. ..."
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Cited by 112 (21 self)
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The objective of this paper is to present a novel methodology for likelihoodbased inference for discretely observed diffusions. We propose Monte Carlo methods, which build on recent advances on the exact simulation of diffusions, for performing maximum likelihood and Bayesian estimation.
Closedform likelihood expansions for multivariate diffusions
, 2008
"... 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 109 (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.
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 105 (11 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
Using Daily Range Data to Calibrate Volatility Diffusions and Extract the Forward Integrated Variance
, 1999
"... A common model for security price dynamics is the continuous time stochastic volatility model. For this model, Hull and White (1987) show that the price of a derivative claim is the conditional expectation of the BlackScholes price with the forward integrated variance replacing the BlackScholes va ..."
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Cited by 103 (5 self)
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A common model for security price dynamics is the continuous time stochastic volatility model. For this model, Hull and White (1987) show that the price of a derivative claim is the conditional expectation of the BlackScholes price with the forward integrated variance replacing the BlackScholes variance. Implementing the Hull and White characterization requires both estimates of the price dynamics and the conditional distribution of the forward integrated variance given observed variables. Using daily data on closetoclose price movement and the daily range, we find that standard models do not fit the data very well and a more general three factor model does better, as it mimics the longmemory feature of financial volatility. We develop techniques for estimating the conditional distribution of the forward integrated variance given observed variables. 1 Introduction This paper has two objectives: The first is to extend and implement methods for estimating diffusion models of secu...
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 82 (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.
Nonparametric Specification Testing for ContinuousTime Models with Application to Spot Interest Rates
, 2002
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Asset Pricing Under The Quadratic Class
 Journal of Financial and Quantitative Analysis
, 2002
"... We identify and characterize a class of term structure models where bond yields are quadratic functions of the state vector. We label this class the quadratic class and aim to lay a solid theoretical foundation for its future empirical application. We consider asset pricing in general and derivative ..."
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Cited by 77 (14 self)
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We identify and characterize a class of term structure models where bond yields are quadratic functions of the state vector. We label this class the quadratic class and aim to lay a solid theoretical foundation for its future empirical application. We consider asset pricing in general and derivative pricing in particular under the quadratic class. We provide two general transform methods in pricing a wide variety of fixed income derivatives in closed or semiclosed form. We further illustrate how the quadratic model and the transform methods can be applied to more general settings. # Swiss Banking Institute, University of Zurich, Plattenstr. 14, 8032 Zurich, Switzerland and Graduate School of Business, Fordham University, 113 West 60th Street, New York, NY 10023, USA, respectively. We thank Marco Avellaneda, David Backus, Peter Carr, Pierre Collin, Silverio Foresi, Michael Gallmeyer, Richard Green, Massoud Heidari, Burton Hollifield, Regis Van Steenkiste, Chris Telmer, Stanley Zin, and, in particular, Jonathan M. Karpo# (the editor) as well as two anonymous referees for helpful comments. I.
Jumps in financial markets: A new nonparametric test and jump clustering
, 2007
"... This article introduces a new nonparametric test to detect jump arrival times and realized jump sizes in asset prices up to the intraday level. We demonstrate that the likelihood of misclassification of jumps becomes negligible when we use highfrequency returns. Using our test, we examine jump dyn ..."
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Cited by 71 (4 self)
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This article introduces a new nonparametric test to detect jump arrival times and realized jump sizes in asset prices up to the intraday level. We demonstrate that the likelihood of misclassification of jumps becomes negligible when we use highfrequency returns. Using our test, we examine jump dynamics and their distributions in the U.S. equity markets. The results show that individual stock jumps are associated with prescheduled earnings announcements and other companyspecific news events. Additionally, S&P 500 Index jumps are associated with general market news announcements. This suggests different pricing models for individual equity options versus index options. (JEL G12, G22, G14) Financial markets sometimes generate significant discontinuities, socalled jumps, in financial variables. A number of recent empirical and theoretical studies proved the existence of jumps and their substantial impact on financial management, from portfolio and risk management to option and bond pricing