Adaptive Realized Kernels

We design adaptive realized kernels to estimate the integrated volatility in a framework that combines a stochastic volatility model with leverage effect for the efficient price and a semiparametric microstructure noise model speci ed at the highest frequency. Some time dependence parameters of the noise model must be estimated before adaptive realized kernels can be implemented. We study their performance by simulation and illustrate their use with twelve stocks listed in the Dow Jones Industrial. As expected, we nd that adaptive realized kernels achieves the optimal trade-off between the discretization error and the microstructure noise. (This abstract was borrowed from another version of this item.)

[1]  E. Ghysels,et al.  Rolling-Sample Volatility Estimators: Some New Theoretical, Simulation and Empirical Results , 2002 .

[2]  Neil Shephard,et al.  Designing Realised Kernels to Measure the Ex-Post Variation of Equity Prices in the Presence of Noise , 2008 .

[3]  Jean Jacod,et al.  Microstructure Noise in the Continuous Case: The Pre-Averaging Approach - JLMPV-9 , 2007 .

[4]  P. Hansen,et al.  Realized Variance and Market Microstructure Noise , 2005 .

[5]  Michael Wolf,et al.  Subsampling for heteroskedastic time series , 1997 .

[6]  N. Shephard,et al.  Realized Kernels in Practice: Trades and Quotes , 2009 .

[7]  Kosuke Oya,et al.  Estimation and Testing for Dependence in Market Microstructure Noise , 2008 .

[8]  N. Shephard,et al.  Realised Kernels in Practice: Trades and Quotes , 2008 .

[9]  W. Newey,et al.  A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelationconsistent Covariance Matrix , 1986 .

[10]  N. Shephard,et al.  Estimating quadratic variation using realized variance , 2002 .

[11]  Mark Podolskij,et al.  Estimation of Volatility Functionals in the Simultaneous Presence of Microstructure Noise and Jumps , 2006 .

[12]  Donald W. K. Andrews,et al.  An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator , 1992 .

[13]  Jim Gatheral,et al.  Zero-intelligence realized variance estimation , 2009, Finance Stochastics.

[14]  P. Protter,et al.  Asymptotic error distributions for the Euler method for stochastic differential equations , 1998 .

[15]  Federico M. Bandi,et al.  Microstructure Noise, Realized Variance, and Optimal Sampling , 2008 .

[16]  B. Hansen Least Squares Model Averaging , 2007 .

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

[18]  Eric Ghysels,et al.  IN-SAMPLE ASYMPTOTICS AND ACROSS-SAMPLE EFFICIENCY GAINS FOR HIGH FREQUENCY DATA STATISTICS , 2021, Econometric Theory.

[19]  Francis X. Diebold,et al.  Modeling and Forecasting Realized Volatility , 2001 .

[20]  R. C. Merton,et al.  On Estimating the Expected Return on the Market: An Exploratory Investigation , 1980 .

[21]  K. French,et al.  Expected stock returns and volatility , 1987 .

[22]  N. Shephard,et al.  Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise , 2006 .

[23]  Mark Podolskij,et al.  Estimation of Volatility Functionals in the Simultaneous Presence of Microstructure Noise and Jumps , 2007, 0909.0827.

[24]  B. Bollen,et al.  Estimating Daily Volatility in Financial Markets Utilizing Intraday Data , 2002 .

[25]  B. M. Hill,et al.  A Simple General Approach to Inference About the Tail of a Distribution , 1975 .

[26]  Ioannis Karatzas,et al.  Brownian Motion and Stochastic Calculus , 1987 .

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

[28]  Bin Zhou,et al.  High Frequency Data and Volatility in Foreign Exchange Rates , 2013 .

[29]  W. Newey,et al.  A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelationconsistent Covariance Matrix , 1986 .

[30]  Lan Zhang,et al.  A Tale of Two Time Scales , 2003 .

[31]  S. Heston A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options , 1993 .

[32]  Yacine Ait-Sahalia,et al.  How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise , 2003 .

[33]  Joel Hasbrouck,et al.  Assessing the Quality of a Security Market: A New Approach to Transaction-Cost Measurement , 1993 .

[34]  Jean Jacod,et al.  Diffusions with measurement errors. I. Local Asymptotic Normality , 2001 .

[35]  L. Devroye Non-Uniform Random Variate Generation , 1986 .