scholarly journals FRACTIONAL COINTEGRATION IN STOCHASTIC VOLATILITY MODELS

2008 ◽  
Vol 24 (5) ◽  
pp. 1207-1253 ◽  
Author(s):  
Afonso Gonçalves da Silva ◽  
Peter M. Robinson
Keyword(s):  
Stochastic Volatility ◽  
Latent Variables ◽  
Factor Model ◽  
Strong Dependence ◽  
Common Factor ◽  
Monte Carlo Experiment ◽  
Finite Sample ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Finite Sample Properties

Asset returns are frequently assumed to be determined by one or more common factors. We consider a bivariate factor model where the unobservable common factor and idiosyncratic errors are stationary and serially uncorrelated but have strong dependence in higher moments. Stochastic volatility models for the latent variables are employed, in view of their direct application to asset pricing models. Assuming that the underlying persistence is higher in the factor than in the errors, a fractional cointegrating relationship can be recovered by suitable transformation of the data. We propose a narrow band semiparametric estimate of the factor loadings, which is shown to be consistent with a rate of convergence, and its finite-sample properties are investigated in a Monte Carlo experiment.

COMPUTATION OF VOLATILITY IN STOCHASTIC VOLATILITY MODELS WITH HIGH FREQUENCY DATA

2010 ◽  
Vol 13 (05) ◽  
pp. 767-787 ◽  
Author(s):  
EMILIO BARUCCI ◽  
MARIA ELVIRA MANCINO
Keyword(s):  
Stochastic Volatility ◽  
High Frequency ◽  
Asset Price ◽  
Heston Model ◽  
High Frequency Data ◽  
Monte Carlo Experiment ◽  
Price Model ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Correlation Parameters

We consider general stochastic volatility models driven by continuous Brownian semimartingales, we show that the volatility of the variance and the leverage component (covariance between the asset price and the variance) can be reconstructed pathwise by exploiting Fourier analysis from the observation of the asset price. Specifying parametrically the asset price model we show that the method allows us to compute the parameters of the model. We provide a Monte Carlo experiment to recover the volatility and correlation parameters of the Heston model.

scholarly journals ESTIMATION OF STOCHASTIC VOLATILITY MODELS BY NONPARAMETRIC FILTERING

2015 ◽  
Vol 32 (4) ◽  
pp. 861-916 ◽  
Author(s):  
Shin Kanaya ◽  
Dennis Kristensen
Keyword(s):  
Stochastic Volatility ◽  
Estimation Method ◽  
Estimation Methods ◽  
Regularity Conditions ◽  
Microstructure Noise ◽  
Finite Sample ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Volatility Model ◽  
Two Step Estimation

A two-step estimation method of stochastic volatility models is proposed: In the first step, we nonparametrically estimate the (unobserved) instantaneous volatility process. In the second step, standard estimation methods for fully observed diffusion processes are employed, but with the filtered/estimated volatility process replacing the latent process. Our estimation strategy is applicable to both parametric and nonparametric stochastic volatility models, and can handle both jumps and market microstructure noise. The resulting estimators of the stochastic volatility model will carry additional biases and variances due to the first-step estimation, but under regularity conditions we show that these vanish asymptotically and our estimators inherit the asymptotic properties of the infeasible estimators based on observations of the volatility process. A simulation study examines the finite-sample properties of the proposed estimators.

scholarly journals VOLATILITY INFERENCE AND RETURN DEPENDENCIES IN STOCHASTIC VOLATILITY MODELS

2019 ◽  
Vol 22 (03) ◽  
pp. 1950013
Author(s):  
OLIVER PFANTE ◽  
NILS BERTSCHINGER
Keyword(s):  
Mutual Information ◽  
Stock Returns ◽  
Stochastic Volatility ◽  
Wide Class ◽  
Factor Model ◽  
Stochastic Volatility Models ◽  
Information Theoretic ◽  
Random Dynamics ◽  
Fundamental Information ◽  
Volatility Models

Stochastic volatility models describe stock returns [Formula: see text] as driven by an unobserved process capturing the random dynamics of volatility [Formula: see text]. The present paper quantifies how much information about volatility [Formula: see text] and future stock returns can be inferred from past returns in stochastic volatility models in terms of Shannon’s mutual information. In particular, we show that across a wide class of stochastic volatility models, including a two-factor model, returns observed on the scale of seconds would be needed to obtain reliable volatility estimates. In addition, we prove that volatility forecasts beyond several weeks are essentially impossible for fundamental information theoretic reasons.

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