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

AbstractWe 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.

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Implied Stochastic Volatility Models

Review of Financial Studies ◽

10.1093/rfs/hhaa041 ◽

2020 ◽

Vol 34 (1) ◽

pp. 394-450 ◽

Cited By ~ 2

Author(s):

Yacine Aït-Sahalia ◽

Chenxu Li ◽

Chen Xu Li

Keyword(s):

Stochastic Volatility ◽

Implied Volatility ◽

Generalized Method Of Moments ◽

Estimation Method ◽

Stochastic Volatility Model ◽

Nonparametric Model ◽

Stochastic Volatility Models ◽

Volatility Models ◽

Volatility Model ◽

Out Of Sample

Abstract This paper proposes “implied stochastic volatility models” designed to fit option-implied volatility data and implements a new estimation method for such models. The method is based on explicitly linking observed shape characteristics of the implied volatility surface to the coefficient functions that define the stochastic volatility model. The method can be applied to estimate a fully flexible nonparametric model, or to estimate by the generalized method of moments any arbitrary parametric stochastic volatility model, affine or not. Empirical evidence based on S&P 500 index options data show that the method is stable and performs well out of sample.

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Sentiment-Driven Stochastic Volatility Model: A High-Frequency Textual Tool for Economists

SSRN Electronic Journal ◽

10.2139/ssrn.3397314 ◽

2019 ◽

Author(s):

Jozef Barunik ◽

Cathy Yi‐Hsuan Chen ◽

Jan Vecer

Keyword(s):

Stochastic Volatility ◽

High Frequency ◽

Stochastic Volatility Model ◽

Volatility Model

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Moment based estimation of supOU processes and a related stochastic volatility model

Statistics & Risk Modeling ◽

10.1515/strm-2012-1152 ◽

2015 ◽

Vol 32 (1) ◽

pp. 1-24 ◽

Cited By ~ 3

Author(s):

Robert Stelzer ◽

Thomas Tosstorff ◽

Marc Wittlinger

Keyword(s):

Stochastic Volatility ◽

Method Of Moments ◽

Long Memory ◽

Generalized Method Of Moments ◽

Memory Effects ◽

Stochastic Volatility Model ◽

Volatility Model ◽

Consistent Estimators

AbstractAfter a quick review of superpositions of OU (supOU) processes, integrated supOU processes and the supOU stochastic volatility model we estimate these processes by using the generalized method of moments (GMM). We show that the GMM approach yields consistent estimators and that it works very well in practice. Moreover, we discuss the influence of long memory effects.

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Fitting the Heston Stochastic Volatility Model to Chinese Stocks

International Finance and Banking ◽

10.5296/ifb.v1i1.5571 ◽

2014 ◽

Vol 1 (1) ◽

pp. 74 ◽

Cited By ~ 5

Author(s):

Ahmet Goncu ◽

Hao Yang

Keyword(s):

Stock Returns ◽

Stochastic Volatility ◽

Trading Volume ◽

Goodness Of Fit ◽

Empirical Distribution ◽

Composite Index ◽

Stochastic Volatility Model ◽

Heston Model ◽

Volatility Model ◽

Return Distributions

In this article we investigate the goodness-of-fit of the Heston stochastic volatility model for the Shanghai composite index and five Chinese stocks from different industries with the highest trading volume. We have jointly estimated the parameters of the Heston stochastic volatility for the daily, weekly and monthly timescales model by employing a kernel density of the empirical returns to minimize the mean-squared deviations between the theoretical and empirical return distributions. We find that the Heston model is able to characterize the empirical distribution of Chinese stock returns at the daily, weekly and monthly timescales.

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