The Statistical and Economic Role of Jumps in Continuous-Time Interest Rate Models

This paper analyzes the role of jumps in continuous-time short rate models. I first develop a test to detect jump-induced misspecification and, using Treasury bill rates, find evidence for the presence of jumps. Second, I specify and estimate a nonparametric jump-diffusion model. Results indicate that jumps play an important statistical role. Estimates of jump times and sizes indicate that unexpected news about the macroeconomy generates the jumps. Finally, I investigate the pricing implications of jumps. Jumps generally have a minor impact on yields, but they are important for pricing interest rate options. Copyright 2004 by The American Finance Association.

[1]  Monika Piazzesi.  Bond Yields and the Federal Reserve , 2005, Journal of Political Economy.

[2]  T. Alderweireld,et al.  A Theory for the Term Structure of Interest Rates , 2004, cond-mat/0405293.

[3]  F. Bandi,et al.  On the functional estimation of jump-diffusion models , 2003 .

[4]  C. S. Jones.  Nonlinear Mean Reversion in the Short-Term Interest Rate , 2003 .

[5]  R. Goldstein,et al.  Identification and Estimation of 'Maximal' Affine Term Structure Models: An Application to Stochastic Volatility , 2003 .

[6]  F. Bandi.  Short-term interest rate dynamics: a spatial approach , 2002 .

[7]  Jun Pan.  The jump-risk premia implicit in options: evidence from an integrated time-series study $ , 2002 .

[8]  Sanjiv Ranjan Das,et al.  Pricing Interest Rate Derivatives: A General Approach , 2002 .

[9]  Sanjiv Ranjan Das.  The Surprise Element: Jumps in Interest Rates , 2002 .

[10]  E. Elton,et al.  Economic News and Bond Prices: Evidence from the U.S. Treasury Market , 2001, Journal of Financial and Quantitative Analysis.

[11]  Peter C. B. Phillips,et al.  Fully Nonparametric Estimation of Scalar Diffusion Models , 2001 .

[12]  Jump-Diffusion Term Structure and Ito Conditional Moment Generator , 2001 .

[13]  Jun Pan.  The Jump-Risk Premia Implicit in Options : Evidence from an Integrated Time-Series Study , 2001 .

[14]  Nicholas G. Polson,et al.  The Impact of Jumps in Volatility and Returns , 2000 .

[15]  P. Glasserman,et al.  The Term Structure of Simple Forward Rates with Jump Risk , 2000 .

[16]  Robert F. Dittmar,et al.  Quadratic Term Structure Models: Theory and Evidence , 2000 .

[17]  Andrew Ang,et al.  A no-arbitrage vector autoregression of term structure dynamics with macroeconomic and latent variables , 2003 .

[18]  C. Christiansen,et al.  Implied Volatility of Interest Rate Options: An Empirical Investigation of the Market Model , 1999 .

[19]  D. Ahn,et al.  A Parametric Nonlinear Model of Term Structure Dynamics , 1999 .

[20]  M. Fleming,et al.  The Term Structure of Announcement Effects , 1999 .

[21]  Chris Downing.  Nonparametric estimation of multifactor continuous time interest rate models , 1999 .

[22]  R. Sundaram,et al.  Of Smiles and Smirks: A Term Structure Perspective , 1998, Journal of Financial and Quantitative Analysis.

[23]  M. Fleming,et al.  Liquidity in U.S. Treasury Spot and Futures Markets , 1999 .

[24]  Christopher T. Downing.  Nonparametric Estimation of Multifactor Continuous Time Interest-Rate Models , 1999 .

[25]  Neil D. Pearson,et al.  Is the Short Rate Drift Actually Nonlinear , 2000 .

[26]  Neil D. Pearson,et al.  Using Proxies for the Short Rate: When Are Three Months Like an Instant? , 1999 .

[27]  G. J. Jiang,et al.  Nonparametric Modeling of U.S. Interest Rate Term Structure Dynamics and Implications on the Prices of Derivative Securities , 1998, Journal of Financial and Quantitative Analysis.

[28]  Maturity Induced Bias in Estimating Spot-Rate Diffusion Models , 1998 .

[29]  Jaeho Cho.  A Theory of the Term Structure of Interest Rates Under Non-expected Intertemporal Preferences , 1998 .

[30]  M. Pritsker.  Nonparametric Density Estimation and Tests of Continuous Time Interest Rate Models , 1998 .

[31]  M. Fleming,et al.  What Moves the Bond Market? , 1997 .

[32]  Richard Stanton.  A Nonparametric Model of Term Structure Dynamics and the Market Price of Interest Rate Risk , 1997 .

[33]  D. Duffie,et al.  An Econometric Model of the Term Structure of Interest-Rate Swap Yields , 1997 .

[34]  P. Honoré.  Modelling Interest Rate Dynamics in a Corridor with Jump Processes , 1997 .

[35]  K. Singleton,et al.  Specification Analysis of Affine Term Structure Models , 1997 .

[36]  Timothy G. Conley,et al.  Short-term interest rates as subordinated diffusions , 1997 .

[37]  Timothy G. Conley,et al.  BOOTSTRAPPING THE LONG RUN , 1997, Macroeconomic Dynamics.

[38]  Gurdip Bakshi,et al.  Empirical Performance of Alternative Option Pricing Models , 1997 .

[39]  P. Honoré.  Maximum Likelihood Estimation of Non-Linear Continuous-Time Term-Structure Models , 1997 .

[40]  T. Andersen,et al.  Estimating continuous-time stochastic volatility models of the short-term interest rate , 1997 .

[41]  Tomas Björk,et al.  Bond Market Structure in the Presence of Marked Point Processes , 1997 .

[42]  H. Pham.  Optimal stopping, free boundary, and American option in a jump-diffusion model , 1997 .

[43]  D. Duffie,et al.  An Overview of Value at Risk , 1997 .

[44]  G. J. Jiang,et al.  A Nonparametric Approach to the Estimation of Diffusion Processes, With an Application to a Short-Term Interest Rate Model , 1997, Econometric Theory.

[45]  J.,et al.  Speci cation Analysis ofA ne Term Structure Models 1 , 1997 .

[46]  E. Elton,et al.  Economic News and the Yield Curve: Evidence from the U.S. Treasury Market , 1996 .

[47]  Xiuli Chao,et al.  On martingale measures when asset returns have unpredictable jumps , 1996 .

[48]  Sanjiv Ranjan Das,et al.  Analytical Approximations of the Term Structure for Jump-Diffusion Processes , 1996 .

[49]  Yacine Aït-Sahalia.  Testing Continuous-Time Models of the Spot Interest Rate , 1996 .

[50]  James D. Hamilton.  The Daily Market for Federal Funds , 1996, Journal of Political Economy.

[51]  D. Duffie,et al.  A Yield-factor Model of Interest Rates , 1996 .

[52]  Yacine Aït-Sahalia.  Nonparametric Pricing of Interest Rate Derivative Securities , 1995 .

[53]  Yacine Ait-Sahalia.  Testing Continuous-Time Models of the Spot Interest Rate , 1995 .

[54]  Andreas Brandt,et al.  Marked Point Processes on the Real Line: The Dynamical Approach , 1995 .

[55]  G. Duffee.  Idiosyncratic variation of Treasury bill yields , 1996 .

[56]  E. Mammen,et al.  Comparing Nonparametric Versus Parametric Regression Fits , 1993 .

[57]  Campbell R. Harvey,et al.  An Empirical Comparison of Alternative Models of the Short-Term Interest Rate , 1992 .

[58]  Testing Continuous Time Models of the Term Structure of Interest Rates in the Finnish Money Market , 1992 .

[59]  H. Thompson,et al.  Jump‐Diffusion Processes and the Term Structure of Interest Rates , 1988 .

[60]  A. Shiryaev,et al.  Limit Theorems for Stochastic Processes , 1987 .

[61]  S. Ross,et al.  AN INTERTEMPORAL GENERAL EQUILIBRIUM MODEL OF ASSET PRICES , 1985 .

[62]  G. Mil’shtein.  A Method of Second-Order Accuracy Integration of Stochastic Differential Equations , 1979 .

[63]  Oldrich A. Vasicek.  An equilibrium characterization of the term structure , 1977 .

[64]  G. N. Mil’shtejn.  Approximate Integration of Stochastic Differential Equations , 1975 .

[65]  E. Renshaw,et al.  STOCHASTIC DIFFERENTIAL EQUATIONS , 1974 .

[66]  R. M. Loynes,et al.  Studies In The Theory Of Random Processes , 1966 .

[67]  G. A. Barnard,et al.  Discussion of Professor Bartlett''s paper , 1963 .

[68]  Frederick Mosteller,et al.  Identification and estimation. , 1955 .