Econometric analysis of realized volatility and its use in estimating stochastic volatility models

Summary. The availability of intraday data on the prices of speculative assets means that we can use quadratic variation‐like measures of activity in financial markets, called realized volatility, to study the stochastic properties of returns. Here, under the assumption of a rather general stochastic volatility model, we derive the moments and the asymptotic distribution of the realized volatility error—the difference between realized volatility and the discretized integrated volatility (which we call actual volatility). These properties can be used to allow us to estimate the parameters of stochastic volatility models without recourse to the use of simulation‐intensive methods.

[1]  H. Lebesgue,et al.  Intégrale, Longueur, Aire , 1902 .

[2]  G. H. H.,et al.  The Theory of Functions of a Real Variable and the Theory of Fourier's Series , 1907, Nature.

[3]  Ernest William Hobson.  The Theory of Functions of a Real Variable and the Theory of Fourier's Series , 1907 .

[4]  P. Whittle,et al.  Prediction and Regulation. , 1965 .

[5]  P. Clark.  A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices , 1973 .

[6]  C. Granger.  Long memory relationships and the aggregation of dynamic models , 1980 .

[7]  J. Poterba,et al.  The Persistence of Volatility and Stock Market Fluctuations , 1984 .

[8]  Jonathan D. Cryer,et al.  Time Series Analysis , 1986 .

[9]  Stephen L Taylor,et al.  Modelling Financial Time Series , 1987 .

[10]  G. Schwert.  Why Does Stock Market Volatility Change Over Time? , 1988 .

[11]  D. Cox,et al.  Asymptotic techniques for use in statistics , 1989 .

[12]  Andrew Harvey,et al.  Forecasting, Structural Time Series Models and the Kalman Filter , 1990 .

[13]  O. E. Barndorff-Nielsen,et al.  Parametric modelling of turbulence , 1990, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[14]  D. Cox.  LONG‐RANGE DEPENDENCE, NON‐LINEARITY AND TIME IRREVERSIBILITY , 1991 .

[15]  R. Engle,et al.  A Permanent and Transitory Component Model of Stock Return Volatility , 1993 .

[16]  Stephen L Taylor,et al.  MODELING STOCHASTIC VOLATILITY: A REVIEW AND COMPARATIVE STUDY , 1994 .

[17]  Dean P. Foster,et al.  Continuous Record Asymptotics for Rolling Sample Variance Estimators , 1994 .

[18]  Daniel B. Nelson,et al.  ARCH MODELS a , 1994 .

[19]  Tim Bollerslev,et al.  Chapter 49 Arch models , 1994 .

[20]  N. Shephard,et al.  Stochastic Volatility: Likelihood Inference And Comparison With Arch Models , 1996 .

[21]  N. Shephard.  Statistical aspects of ARCH and stochastic volatility , 1996 .

[22]  C. Granger,et al.  Modeling volatility persistence of speculative returns: A new approach , 1996 .

[23]  A. Harvey,et al.  5 Stochastic volatility , 1996 .

[24]  T. Bollerslev,et al.  Intraday periodicity and volatility persistence in financial markets , 1997 .

[25]  Stephen L Taylor,et al.  The incremental volatility information in one million foreign exchange quotations , 1997 .

[26]  Covariance Matrix Estimation for Estimators of Mixing Wold's Arma , 1997 .

[27]  Inder Rana,et al.  An introduction to measure and integration , 1997 .

[28]  A. Gallant,et al.  Estimating stochastic differential equations efficiently by minimum chi-squared , 1997 .

[29]  Ole E. Barndorff-Nielsen,et al.  Processes of normal inverse Gaussian type , 1997, Finance Stochastics.

[30]  T. Bollerslev,et al.  Deutsche Mark–Dollar Volatility: Intraday Activity Patterns, Macroeconomic Announcements, and Longer Run Dependencies , 1998 .

[31]  N. Shephard,et al.  Likelihood INference for Discretely Observed Non-linear Diffusions , 2001 .

[32]  N. Prabhala,et al.  The relation between implied and realized volatility , 1998 .

[33]  T. Bollerslev,et al.  ANSWERING THE SKEPTICS: YES, STANDARD VOLATILITY MODELS DO PROVIDE ACCURATE FORECASTS* , 1998 .

[34]  F. Comte,et al.  Long memory in continuous‐time stochastic volatility models , 1998 .

[35]  Jurgen A. Doornik,et al.  Statistical algorithms for models in state space using SsfPack 2.2 , 1999 .

[36]  F. Diebold,et al.  The Distribution of Exchange Rate Volatility , 1999 .

[37]  G. Mason,et al.  Beyond Merton’s Utopia: Effects of Non-normality and Dependence on the Precision of Variance Estimates Using High-frequency Financial Data , 2000 .

[38]  N. Meddahi,et al.  Série Scientifique Scientific Series Temporal Aggregation of Volatility Models , 2022 .

[39]  Thierry Jeantheau,et al.  Stochastic volatility models as hidden Markov models and statistical applications , 2000 .

[40]  Nelson Areal,et al.  The Realized Volatility of Ftse-100 Futures Prices , 2000 .

[41]  M. Sørensen,et al.  Prediction-based estimating functions , 2000 .

[42]  Christian Francq,et al.  Covariance matrix estimation for estimators of mixing weak ARMA models , 2000 .

[43]  R. Gencay,et al.  An Introduc-tion to High-Frequency Finance , 2001 .

[44]  O. Barndorff-Nielsen.  Superposition of Ornstein--Uhlenbeck Type Processes , 2001 .

[45]  N. Shephard,et al.  Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics , 2001 .

[46]  F. Diebold,et al.  The distribution of realized stock return volatility , 2001 .

[47]  N. Shephard,et al.  Realised power variation and stochastic volatility models , 2003 .

[48]  N. Shephard,et al.  How accurate is the asymptotic approximation to the distribution of realised variance , 2001 .

[49]  T. Bollerslev,et al.  Estimating Stochastic Volatility Diffusion Using Conditional Moments of Integrated Volatility , 2001 .

[50]  Thomas H. McCurdy,et al.  Nonlinear Features of Realized FX Volatility , 2001 .

[51]  Eric Ghysels,et al.  Rolling-Sample Volatility Estimators , 2002 .

[52]  T. Bollerslev,et al.  Estimating Stochastic Volatility Diffusion Using Conditional Moments of Integrated Volatility , 2001 .