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Probabilistic and statistical properties of moment variations and their use in inference and estimation based on high frequency return data

Probabilistic and statistical properties of moment variations and their use in inference and... Abstract We discuss the probabilistic properties of the variation based third and fourth moments of financial returns as estimators of the actual moments of the return distributions. The moment variations are defined under non-parametric assumptions with quadratic variation method but for the computational tractability, we use a square root stochastic volatility model for the derivations of moment conditions for estimations. Using the S&P 500 index high frequency data, the realized versions of the moment variations is used for the estimation of a stochastic volatility model. We propose a simple estimation method of a stochastic volatility model using the sample averages of the variations and ARMA estimation. In addition, we compare the results with a generalized method of moments estimation based on the successive relation between realized moments and their lagged values. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Studies in Nonlinear Dynamics & Econometrics de Gruyter

Probabilistic and statistical properties of moment variations and their use in inference and estimation based on high frequency return data

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Publisher
de Gruyter
Copyright
Copyright © 2016 by the
ISSN
1081-1826
eISSN
1558-3708
DOI
10.1515/snde-2014-0037
Publisher site
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Abstract

Abstract We discuss the probabilistic properties of the variation based third and fourth moments of financial returns as estimators of the actual moments of the return distributions. The moment variations are defined under non-parametric assumptions with quadratic variation method but for the computational tractability, we use a square root stochastic volatility model for the derivations of moment conditions for estimations. Using the S&P 500 index high frequency data, the realized versions of the moment variations is used for the estimation of a stochastic volatility model. We propose a simple estimation method of a stochastic volatility model using the sample averages of the variations and ARMA estimation. In addition, we compare the results with a generalized method of moments estimation based on the successive relation between realized moments and their lagged values.

Journal

Studies in Nonlinear Dynamics & Econometrics – de Gruyter

Published: Feb 1, 2016

References

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    Mykland
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    Harvey
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    Heston
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    Bakshi
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    Harvey
  • ARMA Representation of Integrated and Realized Variances
    Meddahi
  • Realized Variance and Market Microstructure Noise of
    Hansen
  • Variation with Stochastic Volatility and Jumps of
    Barndorff
  • The Skew Risk Premium in the Equity Index Market of
    Kozhan
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    Bollerslev
  • Dynamic Estimation of Volatility Risk Premia and Investor Risk Aversion from Option - Implied and Realized Volatilities of
    Bollerslev
  • Preference and the Valuation of Risk Assets The of
    Kraus
  • High Moment Variations and their Application of
    Choe
  • High Moment Variations and their Application of
    Choe
  • Realized of
    Neuberger
  • Estimating Stochastic Volatility Diffusion Using Conditional Moments of Integrated Volatility of
    Bollerslev
  • The Leverage Effect Puzzle : Disentangling Sources of Bias at High Frequency of
    Sahalia
  • Estimation of Objective and Risk - Neutral Distributions Based on Moments of Integrated Volatility of
    Garcia
  • Autoregressive Conditional of
    Brooks
  • On More Robust Estimation of Skewness
    Kim
  • Variation with Stochastic Volatility and Jumps of
    Barndorff
  • The Relation Between Physical and Risk - Neutral Cumulants of
    Zhao
  • Modeling Forecasting Realized Volatility
    Andersen
  • Analysis of Realized Volatility and its Use in Estimating Stochastic Volatility Models of the Methodology
    Barndorff
  • Autoregressive Conditional The of and
    Harvey
  • Autoregressive Conditional of
    Brooks
  • Da Process Fast Calibration Application to Trade Clustering Limit of
    Fonseca
  • Autoregressive Conditional Volatility The of and
    León
  • Realized of
    Neuberger
  • Estimation of Objective and Risk - Neutral Distributions Based on Moments of Integrated Volatility of
    Garcia
  • Conditional Skewness in Asset Pricing Tests of
    Harvey
  • Estimating Stochastic Volatility Diffusion Using Conditional Moments of Integrated Volatility of
    Bollerslev
  • Modeling Forecasting Realized Volatility
    Andersen
  • Pricing Forward Skew Dependent Derivatives Multifactor Versus Single - Factor Stochastic Volatility Models of
    Marabel Romo
  • Analysis of Realized Volatility and its Use in Estimating Stochastic Volatility Models of the Methodology
    Barndorff
  • Inference for Continuous Semimartingales Observed at High Frequency
    Mykland
  • Closed - Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options of
    Heston
  • The Relation Between Physical and Risk - Neutral Cumulants of
    Zhao
  • On More Robust Estimation of Skewness
    Kim
  • The Skew Risk Premium in the Equity Index Market of
    Kozhan
  • The Leverage Effect Puzzle : Disentangling Sources of Bias at High Frequency of
    Sahalia
  • Individual Comparisons by Ranking
    Wilcoxon
  • Moment Swaps
    Schoutens
  • Option Valuation with Conditional of
    Christoffersen
  • Pricing Forward Skew Dependent Derivatives Multifactor Versus Single - Factor Stochastic Volatility Models of
    Marabel Romo
  • Da Process Fast Calibration Application to Trade Clustering Limit of
    Fonseca
  • Autoregressive Conditional Volatility The of and
    León
  • Moment Swaps
    Schoutens
  • Stock Return Characteristics Skew Laws and the Differential Pricing of Individual Equity Options of
    Bakshi
  • Realized Variance and Market Microstructure Noise of
    Hansen
  • Preference and the Valuation of Risk Assets The of
    Kraus
  • ARMA Representation of Integrated and Realized Variances
    Meddahi
  • Option Valuation with Conditional of
    Christoffersen
  • Individual Comparisons by Ranking
    Wilcoxon