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

2015 ◽  
Vol 32 (1) ◽  
pp. 1-24 ◽  
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.

scholarly journals ON THE LOG PERIODOGRAM REGRESSION ESTIMATOR OF THE MEMORY PARAMETER IN LONG MEMORY STOCHASTIC VOLATILITY MODELS

2001 ◽  
Vol 17 (4) ◽  
pp. 686-710 ◽  
Author(s):  
Rohit S. Deo ◽  
Clifford M. Hurvich
Keyword(s):  
Stochastic Volatility ◽  
Long Memory ◽  
Recent Literature ◽  
Stochastic Volatility Model ◽  
Asymptotic Bias ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Volatility Model ◽  
Memory Parameter ◽  
Memory Series

We consider semiparametric estimation of the memory parameter in a long memory stochastic volatility model. We study the estimator based on a log periodogram regression as originally proposed by Geweke and Porter-Hudak (1983, Journal of Time Series Analysis 4, 221–238). Expressions for the asymptotic bias and variance of the estimator are obtained, and the asymptotic distribution is shown to be the same as that obtained in recent literature for a Gaussian long memory series. The theoretical result does not require omission of a block of frequencies near the origin. We show that this ability to use the lowest frequencies is particularly desirable in the context of the long memory stochastic volatility model.

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

2016 ◽  
Vol 20 (1) ◽  
Author(s):  
Kyungsub Lee
Keyword(s):  
Stochastic Volatility ◽  
High Frequency ◽  
Generalized Method Of Moments ◽  
Estimation Method ◽  
Stochastic Volatility Model ◽  
Variation Method ◽  
Moment Conditions ◽  
Volatility Model ◽  
Return Distributions ◽  
The Moment

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.

Implied Stochastic Volatility Models

2020 ◽  
Vol 34 (1) ◽  
pp. 394-450 ◽  
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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